:: CALCUL_1 semantic presentation

REAL is set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite cardinal limit_cardinal set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
K294() is set
{} is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural ext-real non positive non negative V28() V29() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V45() set
the Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural ext-real non positive non negative V28() V29() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V45() set is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural ext-real non positive non negative V28() V29() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V45() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
0 is Relation-like non-empty empty-yielding NAT -defined Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural ext-real non positive non negative V28() V29() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V45() Element of NAT
4 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
{4} is non empty trivial finite V37() 1 -element set
9 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
6 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
7 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
8 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg 1 is non empty trivial finite 1 -element Element of bool NAT
{1} is non empty trivial finite V37() 1 -element set
Seg 2 is non empty finite 2 -element Element of bool NAT
{1,2} is non empty finite V37() set
Proof_Step_Kinds is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT : b₁ <= 9 } is set
f is non empty set
p is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg f is finite f -element Element of bool NAT
[:NAT,f:] is Relation-like non empty non trivial non finite set
bool [:NAT,f:] is non empty non trivial non finite set
p | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
y0 is Relation-like NAT -defined Seg f -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
proj2 f1 is finite set
rng p is finite Element of bool f
bool f is non empty set
F is set
F is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg b is finite b -element Element of bool NAT
p | (Seg b) is Relation-like NAT -defined Seg b -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg b is finite b -element Element of bool NAT
p | (Seg b) is Relation-like NAT -defined Seg b -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
<*> f is Relation-like non-empty empty-yielding NAT -defined f -valued Function-like one-to-one constant functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural ext-real non positive non negative V28() V29() finite finite-yielding V37() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V45() FinSequence of f
[:NAT,f:] is Relation-like non empty non trivial non finite set
x is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
x is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
f is Relation-like NAT -defined f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
y0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg f1 is finite f1 -element Element of bool NAT
p | (Seg f1) is Relation-like NAT -defined Seg f1 -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
[:NAT,f:] is Relation-like non empty non trivial non finite set
bool [:NAT,f:] is non empty non trivial non finite set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg y0 is finite y0 -element Element of bool NAT
p | (Seg y0) is Relation-like NAT -defined Seg y0 -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
[:NAT,f:] is Relation-like non empty non trivial non finite set
bool [:NAT,f:] is non empty non trivial non finite set
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg f1 is finite f1 -element Element of bool NAT
p | (Seg f1) is Relation-like NAT -defined Seg f1 -defined NAT -defined f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,f:]
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p . (len p) is set
VERUM f is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom p is finite Element of bool NAT
rng p is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p is set
proj2 f is finite set
dom f is finite Element of bool NAT
x is set
f . x is set
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . y0 is set
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom f is finite Element of bool NAT
p is set
proj2 f is finite set
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . x is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
rng p is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
rng x is finite Element of bool (CQC-WFF f)
f is Element of bool NAT
x | f is Relation-like NAT -defined f -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
Seq (x | f) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
rng (x | f) is finite Element of bool (CQC-WFF f)
proj2 (Seq (x | f)) is finite set
dom (x | f) is finite Element of bool f
bool f is non empty set
Sgm (dom (x | f)) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(x | f) * (Sgm (dom (x | f))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite Element of bool [:NAT,(CQC-WFF f):]
rng ((x | f) * (Sgm (dom (x | f)))) is finite Element of bool (CQC-WFF f)
y0 is set
dom p is finite Element of bool NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
p . f1 is set
[f1,(p . f1)] is V22() set
{f1,(p . f1)} is non empty finite set
{f1} is non empty trivial finite V37() 1 -element set
{{f1,(p . f1)},{f1}} is non empty finite V37() set
(Seq (x | f)) . f1 is set
dom (Seq (x | f)) is finite Element of bool NAT
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len ((CQC-WFF f),p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
x + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg f is finite f -element Element of bool NAT
p | (Seg f) is Relation-like NAT -defined Seg f -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
dom ((CQC-WFF f),p) is finite Element of bool NAT
dom p is finite Element of bool NAT
(dom p) /\ (Seg f) is finite Element of bool NAT
Seg (len ((CQC-WFF f),p)) is finite len ((CQC-WFF f),p) -element Element of bool NAT
Seg (len p) is finite len p -element Element of bool NAT
(Seg (len p)) /\ (Seg f) is finite Element of bool NAT
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
<*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
rng p is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
rng ((CQC-WFF f),p) is finite Element of bool (CQC-WFF f)
{(f,p)} is non empty trivial finite 1 -element Element of bool (CQC-WFF f)
(rng ((CQC-WFF f),p)) \/ {(f,p)} is non empty finite Element of bool (CQC-WFF f)
len ((CQC-WFF f),p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom p is finite Element of bool NAT
Seg (len p) is finite len p -element Element of bool NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
dom ((CQC-WFF f),p) is finite Element of bool NAT
Seg (len ((CQC-WFF f),p)) is finite len ((CQC-WFF f),p) -element Element of bool NAT
p | (Seg (len ((CQC-WFF f),p))) is Relation-like NAT -defined Seg (len ((CQC-WFF f),p)) -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
p | (dom ((CQC-WFF f),p)) is Relation-like NAT -defined dom ((CQC-WFF f),p) -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
p . x is set
((CQC-WFF f),p) . x is set
(((CQC-WFF f),p) ^ <*(f,p)*>) . x is set
dom <*(f,p)*> is non empty trivial finite 1 -element Element of bool NAT
<*(f,p)*> . 1 is set
len <*(f,p)*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + (len <*(f,p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (((CQC-WFF f),p) ^ <*(f,p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
rng <*(f,p)*> is non empty trivial finite 1 -element Element of bool (CQC-WFF f)
(rng ((CQC-WFF f),p)) \/ (rng <*(f,p)*>) is non empty finite Element of bool (CQC-WFF f)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len ((CQC-WFF f),p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(x ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),(x ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (x ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(x ^ <*p*>) . (len (x ^ <*p*>)) is set
f1 is set
dom x is finite Element of bool NAT
F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
x . F is set
[F,(x . F)] is V22() set
{F,(x . F)} is non empty finite set
{F} is non empty trivial finite V37() 1 -element set
{{F,(x . F)},{F}} is non empty finite V37() set
dom (x ^ <*p*>) is non empty finite Element of bool NAT
(x ^ <*p*>) . F is set
(x ^ <*p*>) | (dom x) is Relation-like NAT -defined dom x -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
Seg (len x) is finite len x -element Element of bool NAT
(x ^ <*p*>) | (Seg (len x)) is Relation-like NAT -defined Seg (len x) -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f ^ p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (f ^ p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p ^ f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
len (p ^ f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + (len p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len p) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
dom p is finite Element of bool NAT
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p ^ x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) | (dom p) is Relation-like NAT -defined dom p -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
Seq ((p ^ x) | (dom p)) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p ^ x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg (len p) is finite len p -element Element of bool NAT
y0 is finite len p -element Element of bool NAT
(p ^ x) | y0 is Relation-like NAT -defined y0 -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
Seq ((p ^ x) | y0) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
dom p is finite Element of bool NAT
f1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
p is set
<*p*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
x is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
x ^ <*f*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(x ^ <*f*>) ^ <*p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len ((x ^ <*f*>) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (x ^ <*f*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*p*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len (x ^ <*f*>)) + (len <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len (x ^ <*f*>)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len <*f*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*f*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((len x) + (len <*f*>)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((len x) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (1 + 1) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is set
<*f*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like set
p is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p ^ <*f*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len (p ^ <*f*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom (p ^ <*f*>) is non empty finite Element of bool NAT
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len p) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg p is finite p -element Element of bool NAT
p + f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
{(p + f)} is non empty trivial finite V37() 1 -element Element of bool NAT
(Seg p) \/ {(p + f)} is non empty finite Element of bool NAT
Sgm ((Seg p) \/ {(p + f)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
len (Sgm ((Seg p) \/ {(p + f)})) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
card ((Seg p) \/ {(p + f)}) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
card (Seg p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(card (Seg p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
f + p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg (p + f) is finite p + f -element Element of bool NAT
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg p is finite p -element Element of bool NAT
p + f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
{(p + f)} is non empty trivial finite V37() 1 -element Element of bool NAT
(Seg p) \/ {(p + f)} is non empty finite Element of bool NAT
Sgm ((Seg p) \/ {(p + f)}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm ((Seg p) \/ {(p + f)})) is finite Element of bool NAT
p + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg (p + 1) is non empty finite p + 1 -element Element of bool NAT
len (Sgm ((Seg p) \/ {(p + f)})) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
<*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) ^ x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),p) ^ x) ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len ((CQC-WFF f),p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
Seg (len ((CQC-WFF f),p)) is finite len ((CQC-WFF f),p) -element Element of bool NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + ((len x) + 1) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
{((len ((CQC-WFF f),p)) + ((len x) + 1))} is non empty trivial finite V37() 1 -element Element of bool NAT
(Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))} is non empty finite Element of bool NAT
((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))}) is Relation-like NAT -defined (Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))} -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
Seq (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})) is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
a is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),p)) + (len x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((len ((CQC-WFF f),p)) + (len x)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (((CQC-WFF f),p) ^ x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len <*(f,p)*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len (((CQC-WFF f),p) ^ x)) + (len <*(f,p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((len ((CQC-WFF f),p)) + (len x)) + (len <*(f,p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom ((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) is non empty finite Element of bool NAT
x ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) ^ (x ^ <*(f,p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined Function-like FinSubsequence-like set
dom b is Element of bool NAT
(dom ((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>)) /\ ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))}) is finite Element of bool NAT
Sgm (dom b) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
dom (Sgm (dom b)) is finite Element of bool NAT
(len ((CQC-WFF f),p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg ((len ((CQC-WFF f),p)) + 1) is non empty finite (len ((CQC-WFF f),p)) + 1 -element Element of bool NAT
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom p is finite Element of bool NAT
a is set
a is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((len ((CQC-WFF f),p)) + 1) + (len x) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
a is set
a is set
k is set
[a,k] is V22() set
{a,k} is non empty finite set
{a} is non empty trivial finite 1 -element set
{{a,k},{a}} is non empty finite V37() set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
Seg ((len ((CQC-WFF f),p)) + ((len x) + 1)) is non empty finite (len ((CQC-WFF f),p)) + ((len x) + 1) -element Element of bool NAT
Sgm (Seg (len ((CQC-WFF f),p))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
Sgm {((len ((CQC-WFF f),p)) + ((len x) + 1))} is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (Seg (len ((CQC-WFF f),p)))) ^ (Sgm {((len ((CQC-WFF f),p)) + ((len x) + 1))}) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
<*((len ((CQC-WFF f),p)) + ((len x) + 1))*> is Relation-like NAT -defined NAT -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of NAT
(Sgm (Seg (len ((CQC-WFF f),p)))) ^ <*((len ((CQC-WFF f),p)) + ((len x) + 1))*> is Relation-like NAT -defined NAT -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of NAT
idseq (len ((CQC-WFF f),p)) is Relation-like NAT -defined Function-like finite len ((CQC-WFF f),p) -element FinSequence-like FinSubsequence-like set
id (Seg (len ((CQC-WFF f),p))) is Relation-like Seg (len ((CQC-WFF f),p)) -defined Seg (len ((CQC-WFF f),p)) -valued Function-like one-to-one V14( Seg (len ((CQC-WFF f),p))) finite Element of bool [:(Seg (len ((CQC-WFF f),p))),(Seg (len ((CQC-WFF f),p))):]
[:(Seg (len ((CQC-WFF f),p))),(Seg (len ((CQC-WFF f),p))):] is Relation-like finite set
bool [:(Seg (len ((CQC-WFF f),p))),(Seg (len ((CQC-WFF f),p))):] is non empty finite V37() set
(idseq (len ((CQC-WFF f),p))) ^ <*((len ((CQC-WFF f),p)) + ((len x) + 1))*> is Relation-like NAT -defined Function-like non empty finite (len ((CQC-WFF f),p)) + 1 -element FinSequence-like FinSubsequence-like set
(len ((CQC-WFF f),p)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),p) is finite Element of bool NAT
dom (idseq (len ((CQC-WFF f),p))) is finite len ((CQC-WFF f),p) -element Element of bool NAT
(Sgm (dom b)) . p is set
(idseq (len ((CQC-WFF f),p))) . p is set
Seq b is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
(Sgm (dom b)) * b is Relation-like NAT -defined Function-like finite set
(Seq b) . p is set
b . p is set
b | (Seg (len ((CQC-WFF f),p))) is Relation-like NAT -defined Seg (len ((CQC-WFF f),p)) -defined NAT -defined Function-like finite FinSubsequence-like set
(b | (Seg (len ((CQC-WFF f),p)))) . p is set
((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | (Seg (len ((CQC-WFF f),p))) is Relation-like NAT -defined Seg (len ((CQC-WFF f),p)) -defined NAT -defined CQC-WFF f -valued Function-like finite FinSubsequence-like Element of bool [:NAT,(CQC-WFF f):]
(((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | (Seg (len ((CQC-WFF f),p)))) . p is set
((CQC-WFF f),p) . p is set
((CQC-WFF f),p) ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . p is set
dom (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})) is finite Element of bool ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})
bool ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))}) is non empty finite V37() set
Sgm (dom (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))}))) is Relation-like NAT -defined NAT -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of NAT
rng (Sgm (dom (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})))) is finite Element of bool NAT
(((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})) * (Sgm (dom (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite Element of bool [:NAT,(CQC-WFF f):]
dom ((((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))})) * (Sgm (dom (((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) | ((Seg (len ((CQC-WFF f),p))) \/ {((len ((CQC-WFF f),p)) + ((len x) + 1))}))))) is finite Element of bool NAT
dom (Seq b) is finite Element of bool NAT
dom <*(f,p)*> is non empty trivial finite 1 -element Element of bool NAT
len (idseq (len ((CQC-WFF f),p))) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . ((len ((CQC-WFF f),p)) + ((len x) + 1)) is set
((((CQC-WFF f),p) ^ x) ^ <*(f,p)*>) . (((len ((CQC-WFF f),p)) + (len x)) + 1) is set
<*(f,p)*> . 1 is set
p . (len p) is set
p . a is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is set
x is set
<*p,x*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
dom <*p,x*> is non empty finite 2 -element Element of bool NAT
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p,x*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f ^ <*p,x*>) . ((len f) + 1) is set
(len f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f ^ <*p,x*>) . ((len f) + 2) is set
len <*p,x*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*p,x*> . 2 is set
<*p,x*> . 1 is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
bool (bound_QC-variables f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
dom p is finite Element of bool NAT
x is set
f is set
f is set
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
p . f1 is set
y0 is set
still_not-bound_in F is Element of bool (bound_QC-variables f)
x is Element of bool (bound_QC-variables f)
f is Element of bool (bound_QC-variables f)
y0 is set
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
p . f1 is set
still_not-bound_in F is Element of bool (bound_QC-variables f)
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
p . f1 is set
still_not-bound_in F is Element of bool (bound_QC-variables f)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
[:NAT,(CQC-WFF f):] is Relation-like REAL -defined QC-WFF f -valued non empty non trivial non finite Element of bool [:REAL,(QC-WFF f):]
[:REAL,(QC-WFF f):] is Relation-like set
bool [:REAL,(QC-WFF f):] is non empty set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
p is set
x is set
f is set
p is set
x is set
f is set
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
p is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
p . x is set
(p . x) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . x) `1 is set
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,b) is Element of CQC-WFF f
(f,a) is Element of CQC-WFF f
p . F is set
(p . F) `1 is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len y is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),y)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,((CQC-WFF f),y)) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f,y) is Element of CQC-WFF f
p . p is set
(p . p) `1 is set
p . k is set
(p . k) `1 is set
<*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) ^ <*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>15</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>15</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>15</sub>) is Element of CQC-WFF f
c<sub>16</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>17</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>18</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>18</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>18</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>19</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>19</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>18</sub>)) is Element of CQC-WFF f
c<sub>20</sub> is Element of CQC-WFF f
'not' c<sub>20</sub> is Element of CQC-WFF f
(f,c<sub>18</sub>) is Element of CQC-WFF f
'not' (f,c<sub>18</sub>) is Element of CQC-WFF f
(f,c<sub>19</sub>) is Element of CQC-WFF f
p . c<sub>17</sub> is set
(p . c<sub>17</sub>) `1 is set
p . c₁₆ is set
(p . c₁₆) `1 is set
((CQC-WFF f),((CQC-WFF f),c<sub>18</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>20</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>18</sub>)) ^ <*c<sub>20</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>21</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>21</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>21</sub>) is Element of CQC-WFF f
c<sub>22</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>23</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>24</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>24</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>25</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>25</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>23</sub> is set
(p . c<sub>23</sub>) `1 is set
p . c₂₂ is set
(p . c₂₂) `1 is set
(f,c<sub>24</sub>) is Element of CQC-WFF f
(f,c<sub>25</sub>) is Element of CQC-WFF f
(f,c<sub>24</sub>) '&' (f,c<sub>25</sub>) is Element of CQC-WFF f
<*((f,c<sub>24</sub>) '&' (f,c<sub>25</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>24</sub>) ^ <*((f,c<sub>24</sub>) '&' (f,c<sub>25</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>26</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>26</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>26</sub>) is Element of CQC-WFF f
c<sub>27</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>29</sub> is Element of CQC-WFF f
c<sub>30</sub> is Element of CQC-WFF f
c<sub>29</sub> '&' c<sub>30</sub> is Element of CQC-WFF f
c<sub>28</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>28</sub>) is Element of CQC-WFF f
p . c<sub>27</sub> is set
(p . c<sub>27</sub>) `1 is set
((CQC-WFF f),c₂₈) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₉*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₈) ^ <*c₂₉*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₃₁ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₃₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₃₁) is Element of CQC-WFF f
c₃₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₃₄ is Element of CQC-WFF f
c₃₅ is Element of CQC-WFF f
c₃₄ '&' c₃₅ is Element of CQC-WFF f
c₃₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₃₃) is Element of CQC-WFF f
p . c₃₂ is set
(p . c₃₂) `1 is set
((CQC-WFF f),c<sub>33</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>35</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>33</sub>) ^ <*c<sub>35</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>36</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>36</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>36</sub>) is Element of CQC-WFF f
c<sub>37</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>38</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>38</sub>) is Element of CQC-WFF f
c<sub>40</sub> is Element of bound_QC-variables f
c<sub>39</sub> is Element of CQC-WFF f
All (c<sub>40</sub>,c<sub>39</sub>) is Element of CQC-WFF f
p . c<sub>37</sub> is set
(p . c<sub>37</sub>) `1 is set
((CQC-WFF f),c₃₈) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₄₁ is Element of bound_QC-variables f
c₃₉ . (c₄₀,c₄₁) is Element of CQC-WFF f
<*(c₃₉ . (c₄₀,c₄₁))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₃₈) ^ <*(c₃₉ . (c₄₀,c₄₁))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₄₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₄₂) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₄₂) is Element of CQC-WFF f
c₄₃ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₄₄ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₄₄) is Element of CQC-WFF f
c₄₅ is Element of CQC-WFF f
c₄₆ is Element of bound_QC-variables f
c₄₇ is Element of bound_QC-variables f
c₄₅ . (c₄₆,c₄₇) is Element of CQC-WFF f
((CQC-WFF f),c₄₄) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₄₄)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
All (c₄₆,c₄₅) is Element of CQC-WFF f
still_not-bound_in (All (c₄₆,c₄₅)) is Element of bool (bound_QC-variables f)
p . c₄₃ is set
(p . c₄₃) `1 is set
<*(All (c<sub>46</sub>,c<sub>45</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>44</sub>) ^ <*(All (c<sub>46</sub>,c<sub>45</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>48</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>48</sub> ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>49</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>50</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>50</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>51</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>51</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>50</sub>) is Element of CQC-WFF f
(f,c<sub>51</sub>) is Element of CQC-WFF f
p . c<sub>49</sub> is set
(p . c<sub>49</sub>) `1 is set
c₅₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₅₂ ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₅₃ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₅₄ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₅₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₅₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₅₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₅₆ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₅₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₅₅)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₅₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₅₆)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₅₅)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c₅₅)) is Element of CQC-WFF f
(f,((CQC-WFF f),c₅₆)) is Element of CQC-WFF f
(f,c₅₅) is Element of CQC-WFF f
(f,c₅₆) is Element of CQC-WFF f
p . c₅₄ is set
(p . c₅₄) `1 is set
p . c<sub>53</sub> is set
(p . c<sub>53</sub>) `1 is set
<*(f,c₅₅)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₅₅)) ^ <*(f,c₅₅)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₅₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₅₇ ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₅₈ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₅₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₆₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₆₀ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₆₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₁ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₆₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₆₀)) is Element of CQC-WFF f
c₆₂ is Element of CQC-WFF f
'not' c₆₂ is Element of CQC-WFF f
(f,c₆₀) is Element of CQC-WFF f
'not' (f,c₆₀) is Element of CQC-WFF f
(f,c₆₁) is Element of CQC-WFF f
p . c₅₉ is set
(p . c₅₉) `1 is set
p . c<sub>58</sub> is set
(p . c<sub>58</sub>) `1 is set
((CQC-WFF f),((CQC-WFF f),c₆₀)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₆₂*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₆₀)) ^ <*c₆₂*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₃ ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₄ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₆₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₆₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₆₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₆₇) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c₆₅ is set
(p . c₆₅) `1 is set
p . c<sub>64</sub> is set
(p . c<sub>64</sub>) `1 is set
(f,c₆₆) is Element of CQC-WFF f
(f,c₆₇) is Element of CQC-WFF f
(f,c₆₆) '&' (f,c₆₇) is Element of CQC-WFF f
<*((f,c₆₆) '&' (f,c₆₇))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₆₆) ^ <*((f,c₆₆) '&' (f,c₆₇))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₈ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₈ ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₆₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₇₁ is Element of CQC-WFF f
c₇₂ is Element of CQC-WFF f
c₇₁ '&' c₇₂ is Element of CQC-WFF f
c₇₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₇₀) is Element of CQC-WFF f
p . c₆₉ is set
(p . c₆₉) `1 is set
((CQC-WFF f),c<sub>70</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>71</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>70</sub>) ^ <*c<sub>71</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>73</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>73</sub> ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>74</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>76</sub> is Element of CQC-WFF f
c<sub>77</sub> is Element of CQC-WFF f
c<sub>76</sub> '&' c<sub>77</sub> is Element of CQC-WFF f
c<sub>75</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>75</sub>) is Element of CQC-WFF f
p . c<sub>74</sub> is set
(p . c<sub>74</sub>) `1 is set
((CQC-WFF f),c₇₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₇₇*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₇₅) ^ <*c₇₇*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₇₈ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₇₈ ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₇₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₈₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₈₀) is Element of CQC-WFF f
c₈₂ is Element of bound_QC-variables f
c₈₁ is Element of CQC-WFF f
All (c₈₂,c₈₁) is Element of CQC-WFF f
p . c₇₉ is set
(p . c₇₉) `1 is set
((CQC-WFF f),c<sub>80</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>83</sub> is Element of bound_QC-variables f
c<sub>81</sub> . (c<sub>82</sub>,c<sub>83</sub>) is Element of CQC-WFF f
<*(c<sub>81</sub> . (c<sub>82</sub>,c<sub>83</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>80</sub>) ^ <*(c<sub>81</sub> . (c<sub>82</sub>,c<sub>83</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>84</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>84</sub> ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>85</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>86</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>86</sub>) is Element of CQC-WFF f
c<sub>87</sub> is Element of CQC-WFF f
c<sub>88</sub> is Element of bound_QC-variables f
c<sub>89</sub> is Element of bound_QC-variables f
c<sub>87</sub> . (c<sub>88</sub>,c<sub>89</sub>) is Element of CQC-WFF f
((CQC-WFF f),c<sub>86</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>86</sub>)) is Element of bool (bound_QC-variables f)
All (c<sub>88</sub>,c<sub>87</sub>) is Element of CQC-WFF f
still_not-bound_in (All (c<sub>88</sub>,c<sub>87</sub>)) is Element of bool (bound_QC-variables f)
p . c<sub>85</sub> is set
(p . c<sub>85</sub>) `1 is set
<*(All (c₈₈,c₈₇))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₈₆) ^ <*(All (c₈₈,c₈₇))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₉₀ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₉₁ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₉₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₉₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₉₂) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₉₁) is Element of CQC-WFF f
(f,c₉₂) is Element of CQC-WFF f
p . c₉₀ is set
(p . c₉₀) `1 is set
c<sub>93</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>94</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>95</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>95</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>96</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>96</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>95</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>95</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>96</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>96</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>95</sub>)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c<sub>95</sub>)) is Element of CQC-WFF f
(f,((CQC-WFF f),c<sub>96</sub>)) is Element of CQC-WFF f
(f,c<sub>95</sub>) is Element of CQC-WFF f
(f,c<sub>96</sub>) is Element of CQC-WFF f
p . c<sub>94</sub> is set
(p . c<sub>94</sub>) `1 is set
p . c₉₃ is set
(p . c₉₃) `1 is set
<*(f,c<sub>95</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>95</sub>)) ^ <*(f,c<sub>95</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>97</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>98</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>98</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>99</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>99</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>98</sub>) is Element of CQC-WFF f
(f,c<sub>99</sub>) is Element of CQC-WFF f
p . c<sub>97</sub> is set
(p . c<sub>97</sub>) `1 is set
c₁₀₀ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₀₁ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₀₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₁₀₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₁₀₂) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₀₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₀₃) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₁₀₂)) is Element of CQC-WFF f
c₁₀₄ is Element of CQC-WFF f
'not' c₁₀₄ is Element of CQC-WFF f
(f,c₁₀₂) is Element of CQC-WFF f
'not' (f,c₁₀₂) is Element of CQC-WFF f
(f,c₁₀₃) is Element of CQC-WFF f
p . c₁₀₁ is set
(p . c₁₀₁) `1 is set
p . c<sub>100</sub> is set
(p . c<sub>100</sub>) `1 is set
((CQC-WFF f),((CQC-WFF f),c₁₀₂)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₁₀₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₀₂)) ^ <*c₁₀₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₀₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₀₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₀₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₀₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₀₇) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₀₆) is Element of CQC-WFF f
(f,c₁₀₇) is Element of CQC-WFF f
p . c₁₀₅ is set
(p . c₁₀₅) `1 is set
c<sub>108</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>109</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>110</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>110</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>111</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>111</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>109</sub> is set
(p . c<sub>109</sub>) `1 is set
p . c₁₀₈ is set
(p . c₁₀₈) `1 is set
(f,c<sub>110</sub>) is Element of CQC-WFF f
(f,c<sub>111</sub>) is Element of CQC-WFF f
(f,c<sub>110</sub>) '&' (f,c<sub>111</sub>) is Element of CQC-WFF f
<*((f,c<sub>110</sub>) '&' (f,c<sub>111</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>110</sub>) ^ <*((f,c<sub>110</sub>) '&' (f,c<sub>111</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>112</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>113</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>113</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>114</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>114</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>113</sub>) is Element of CQC-WFF f
(f,c<sub>114</sub>) is Element of CQC-WFF f
p . c<sub>112</sub> is set
(p . c<sub>112</sub>) `1 is set
c₁₁₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₁₇ is Element of CQC-WFF f
c₁₁₈ is Element of CQC-WFF f
c₁₁₇ '&' c₁₁₈ is Element of CQC-WFF f
c₁₁₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₁₆) is Element of CQC-WFF f
p . c₁₁₅ is set
(p . c₁₁₅) `1 is set
((CQC-WFF f),c<sub>116</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>117</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>116</sub>) ^ <*c<sub>117</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>119</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>120</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>120</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>121</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>121</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>120</sub>) is Element of CQC-WFF f
(f,c<sub>121</sub>) is Element of CQC-WFF f
p . c<sub>119</sub> is set
(p . c<sub>119</sub>) `1 is set
c₁₂₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₂₄ is Element of CQC-WFF f
c₁₂₅ is Element of CQC-WFF f
c₁₂₄ '&' c₁₂₅ is Element of CQC-WFF f
c₁₂₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₂₃) is Element of CQC-WFF f
p . c₁₂₂ is set
(p . c₁₂₂) `1 is set
((CQC-WFF f),c<sub>123</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>125</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>123</sub>) ^ <*c<sub>125</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>126</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>127</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>127</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>128</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>128</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>127</sub>) is Element of CQC-WFF f
(f,c<sub>128</sub>) is Element of CQC-WFF f
p . c<sub>126</sub> is set
(p . c<sub>126</sub>) `1 is set
c₁₂₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₃₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₃₀) is Element of CQC-WFF f
c₁₃₂ is Element of bound_QC-variables f
c₁₃₁ is Element of CQC-WFF f
All (c₁₃₂,c₁₃₁) is Element of CQC-WFF f
p . c₁₂₉ is set
(p . c₁₂₉) `1 is set
((CQC-WFF f),c<sub>130</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>133</sub> is Element of bound_QC-variables f
c<sub>131</sub> . (c<sub>132</sub>,c<sub>133</sub>) is Element of CQC-WFF f
<*(c<sub>131</sub> . (c<sub>132</sub>,c<sub>133</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>130</sub>) ^ <*(c<sub>131</sub> . (c<sub>132</sub>,c<sub>133</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>134</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>135</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>135</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>136</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>136</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>135</sub>) is Element of CQC-WFF f
(f,c<sub>136</sub>) is Element of CQC-WFF f
p . c<sub>134</sub> is set
(p . c<sub>134</sub>) `1 is set
c₁₃₇ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₃₈ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₃₈) is Element of CQC-WFF f
c₁₃₉ is Element of CQC-WFF f
c₁₄₀ is Element of bound_QC-variables f
c₁₄₁ is Element of bound_QC-variables f
c₁₃₉ . (c₁₄₀,c₁₄₁) is Element of CQC-WFF f
((CQC-WFF f),c₁₃₈) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₁₃₈)) is Element of bool (bound_QC-variables f)
All (c₁₄₀,c₁₃₉) is Element of CQC-WFF f
still_not-bound_in (All (c₁₄₀,c₁₃₉)) is Element of bool (bound_QC-variables f)
p . c₁₃₇ is set
(p . c₁₃₇) `1 is set
<*(All (c<sub>140</sub>,c<sub>139</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>138</sub>) ^ <*(All (c<sub>140</sub>,c<sub>139</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>142</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>143</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>144</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>144</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>145</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>145</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>144</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>144</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>145</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>145</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>144</sub>)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c<sub>144</sub>)) is Element of CQC-WFF f
(f,((CQC-WFF f),c<sub>145</sub>)) is Element of CQC-WFF f
(f,c<sub>144</sub>) is Element of CQC-WFF f
(f,c<sub>145</sub>) is Element of CQC-WFF f
p . c<sub>143</sub> is set
(p . c<sub>143</sub>) `1 is set
p . c₁₄₂ is set
(p . c₁₄₂) `1 is set
<*(f,c<sub>144</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>144</sub>)) ^ <*(f,c<sub>144</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>146</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>147</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>148</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>148</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>148</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>149</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>149</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>148</sub>)) is Element of CQC-WFF f
c<sub>150</sub> is Element of CQC-WFF f
'not' c<sub>150</sub> is Element of CQC-WFF f
(f,c<sub>148</sub>) is Element of CQC-WFF f
'not' (f,c<sub>148</sub>) is Element of CQC-WFF f
(f,c<sub>149</sub>) is Element of CQC-WFF f
p . c<sub>147</sub> is set
(p . c<sub>147</sub>) `1 is set
p . c₁₄₆ is set
(p . c₁₄₆) `1 is set
((CQC-WFF f),((CQC-WFF f),c<sub>148</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>150</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>148</sub>)) ^ <*c<sub>150</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>151</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>152</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>153</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>153</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>154</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>154</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>153</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>153</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>154</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>154</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>153</sub>)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c<sub>153</sub>)) is Element of CQC-WFF f
(f,((CQC-WFF f),c<sub>154</sub>)) is Element of CQC-WFF f
(f,c<sub>153</sub>) is Element of CQC-WFF f
(f,c<sub>154</sub>) is Element of CQC-WFF f
p . c<sub>152</sub> is set
(p . c<sub>152</sub>) `1 is set
p . c₁₅₁ is set
(p . c₁₅₁) `1 is set
<*(f,c<sub>153</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>153</sub>)) ^ <*(f,c<sub>153</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>155</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>156</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>157</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>157</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>158</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>158</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>156</sub> is set
(p . c<sub>156</sub>) `1 is set
p . c₁₅₅ is set
(p . c₁₅₅) `1 is set
(f,c<sub>157</sub>) is Element of CQC-WFF f
(f,c<sub>158</sub>) is Element of CQC-WFF f
(f,c<sub>157</sub>) '&' (f,c<sub>158</sub>) is Element of CQC-WFF f
<*((f,c<sub>157</sub>) '&' (f,c<sub>158</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>157</sub>) ^ <*((f,c<sub>157</sub>) '&' (f,c<sub>158</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>159</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>160</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>161</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>161</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>162</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>162</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>161</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>161</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>162</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>162</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>161</sub>)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c<sub>161</sub>)) is Element of CQC-WFF f
(f,((CQC-WFF f),c<sub>162</sub>)) is Element of CQC-WFF f
(f,c<sub>161</sub>) is Element of CQC-WFF f
(f,c<sub>162</sub>) is Element of CQC-WFF f
p . c<sub>160</sub> is set
(p . c<sub>160</sub>) `1 is set
p . c₁₅₉ is set
(p . c₁₅₉) `1 is set
<*(f,c<sub>161</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>161</sub>)) ^ <*(f,c<sub>161</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>163</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>165</sub> is Element of CQC-WFF f
c<sub>166</sub> is Element of CQC-WFF f
c<sub>165</sub> '&' c<sub>166</sub> is Element of CQC-WFF f
c<sub>164</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>164</sub>) is Element of CQC-WFF f
p . c<sub>163</sub> is set
(p . c<sub>163</sub>) `1 is set
((CQC-WFF f),c₁₆₄) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₁₆₅*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₆₄) ^ <*c₁₆₅*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₆₇ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₆₈ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₆₉ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₁₆₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₇₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₁₇₀ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₁₆₉) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₆₉)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₇₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₇₀)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₁₆₉)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c₁₆₉)) is Element of CQC-WFF f
(f,((CQC-WFF f),c₁₇₀)) is Element of CQC-WFF f
(f,c₁₆₉) is Element of CQC-WFF f
(f,c₁₇₀) is Element of CQC-WFF f
p . c₁₆₈ is set
(p . c₁₆₈) `1 is set
p . c<sub>167</sub> is set
(p . c<sub>167</sub>) `1 is set
<*(f,c₁₆₉)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₆₉)) ^ <*(f,c₁₆₉)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₇₁ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₇₃ is Element of CQC-WFF f
c₁₇₄ is Element of CQC-WFF f
c₁₇₃ '&' c₁₇₄ is Element of CQC-WFF f
c₁₇₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₇₂) is Element of CQC-WFF f
p . c₁₇₁ is set
(p . c₁₇₁) `1 is set
((CQC-WFF f),c<sub>172</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>174</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>172</sub>) ^ <*c<sub>174</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>175</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>176</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>177</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>177</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>178</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>178</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>177</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>177</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>178</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>178</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>177</sub>)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c<sub>177</sub>)) is Element of CQC-WFF f
(f,((CQC-WFF f),c<sub>178</sub>)) is Element of CQC-WFF f
(f,c<sub>177</sub>) is Element of CQC-WFF f
(f,c<sub>178</sub>) is Element of CQC-WFF f
p . c<sub>176</sub> is set
(p . c<sub>176</sub>) `1 is set
p . c₁₇₅ is set
(p . c₁₇₅) `1 is set
<*(f,c<sub>177</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>177</sub>)) ^ <*(f,c<sub>177</sub>)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>179</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>180</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>180</sub>) is Element of CQC-WFF f
c<sub>182</sub> is Element of bound_QC-variables f
c<sub>181</sub> is Element of CQC-WFF f
All (c<sub>182</sub>,c<sub>181</sub>) is Element of CQC-WFF f
p . c<sub>179</sub> is set
(p . c<sub>179</sub>) `1 is set
((CQC-WFF f),c₁₈₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₈₃ is Element of bound_QC-variables f
c₁₈₁ . (c₁₈₂,c₁₈₃) is Element of CQC-WFF f
<*(c₁₈₁ . (c₁₈₂,c₁₈₃))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₈₀) ^ <*(c₁₈₁ . (c₁₈₂,c₁₈₃))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₈₄ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₈₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₈₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₁₈₆ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₈₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₁₈₇ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₁₈₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₈₆)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₈₇) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₈₇)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₁₈₆)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),c₁₈₆)) is Element of CQC-WFF f
(f,((CQC-WFF f),c₁₈₇)) is Element of CQC-WFF f
(f,c₁₈₆) is Element of CQC-WFF f
(f,c₁₈₇) is Element of CQC-WFF f
p . c₁₈₅ is set
(p . c₁₈₅) `1 is set
p . c<sub>184</sub> is set
(p . c<sub>184</sub>) `1 is set
<*(f,c₁₈₆)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₁₈₆)) ^ <*(f,c₁₈₆)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₁₈₈ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₁₈₉ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₈₉) is Element of CQC-WFF f
c₁₉₀ is Element of CQC-WFF f
c₁₉₁ is Element of bound_QC-variables f
c₁₉₂ is Element of bound_QC-variables f
c₁₉₀ . (c₁₉₁,c₁₉₂) is Element of CQC-WFF f
((CQC-WFF f),c₁₈₉) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₁₈₉)) is Element of bool (bound_QC-variables f)
All (c₁₉₁,c₁₉₀) is Element of CQC-WFF f
still_not-bound_in (All (c₁₉₁,c₁₉₀)) is Element of bool (bound_QC-variables f)
p . c₁₈₈ is set
(p . c₁₈₈) `1 is set
<*(All (c<sub>191</sub>,c<sub>190</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>189</sub>) ^ <*(All (c<sub>191</sub>,c<sub>190</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>193</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>194</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>195</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>195</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>195</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>196</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>196</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>195</sub>)) is Element of CQC-WFF f
c<sub>197</sub> is Element of CQC-WFF f
'not' c<sub>197</sub> is Element of CQC-WFF f
(f,c<sub>195</sub>) is Element of CQC-WFF f
'not' (f,c<sub>195</sub>) is Element of CQC-WFF f
(f,c<sub>196</sub>) is Element of CQC-WFF f
p . c<sub>194</sub> is set
(p . c<sub>194</sub>) `1 is set
p . c₁₉₃ is set
(p . c₁₉₃) `1 is set
((CQC-WFF f),((CQC-WFF f),c<sub>195</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>197</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>195</sub>)) ^ <*c<sub>197</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>198</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>199</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>200</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>200</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>201</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>201</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>199</sub> is set
(p . c<sub>199</sub>) `1 is set
p . c₁₉₈ is set
(p . c₁₉₈) `1 is set
(f,c<sub>200</sub>) is Element of CQC-WFF f
(f,c<sub>201</sub>) is Element of CQC-WFF f
(f,c<sub>200</sub>) '&' (f,c<sub>201</sub>) is Element of CQC-WFF f
<*((f,c<sub>200</sub>) '&' (f,c<sub>201</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>200</sub>) ^ <*((f,c<sub>200</sub>) '&' (f,c<sub>201</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>202</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>203</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>204</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>204</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>204</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>205</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>205</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>204</sub>)) is Element of CQC-WFF f
c<sub>206</sub> is Element of CQC-WFF f
'not' c<sub>206</sub> is Element of CQC-WFF f
(f,c<sub>204</sub>) is Element of CQC-WFF f
'not' (f,c<sub>204</sub>) is Element of CQC-WFF f
(f,c<sub>205</sub>) is Element of CQC-WFF f
p . c<sub>203</sub> is set
(p . c<sub>203</sub>) `1 is set
p . c₂₀₂ is set
(p . c₂₀₂) `1 is set
((CQC-WFF f),((CQC-WFF f),c<sub>204</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>206</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>204</sub>)) ^ <*c<sub>206</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>207</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>209</sub> is Element of CQC-WFF f
c<sub>210</sub> is Element of CQC-WFF f
c<sub>209</sub> '&' c<sub>210</sub> is Element of CQC-WFF f
c<sub>208</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>208</sub>) is Element of CQC-WFF f
p . c<sub>207</sub> is set
(p . c<sub>207</sub>) `1 is set
((CQC-WFF f),c₂₀₈) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₀₉*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₀₈) ^ <*c₂₀₉*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₁₁ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₁₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₁₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₂₁₃ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₂₁₃) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₁₄ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₁₄) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₂₁₃)) is Element of CQC-WFF f
c₂₁₅ is Element of CQC-WFF f
'not' c₂₁₅ is Element of CQC-WFF f
(f,c₂₁₃) is Element of CQC-WFF f
'not' (f,c₂₁₃) is Element of CQC-WFF f
(f,c₂₁₄) is Element of CQC-WFF f
p . c₂₁₂ is set
(p . c₂₁₂) `1 is set
p . c<sub>211</sub> is set
(p . c<sub>211</sub>) `1 is set
((CQC-WFF f),((CQC-WFF f),c₂₁₃)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₁₅*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₂₁₃)) ^ <*c₂₁₅*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₁₆ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₁₈ is Element of CQC-WFF f
c₂₁₉ is Element of CQC-WFF f
c₂₁₈ '&' c₂₁₉ is Element of CQC-WFF f
c₂₁₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₁₇) is Element of CQC-WFF f
p . c₂₁₆ is set
(p . c₂₁₆) `1 is set
((CQC-WFF f),c<sub>217</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>219</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>217</sub>) ^ <*c<sub>219</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>220</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>221</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>222</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c<sub>222</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c<sub>222</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>223</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>223</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c<sub>222</sub>)) is Element of CQC-WFF f
c<sub>224</sub> is Element of CQC-WFF f
'not' c<sub>224</sub> is Element of CQC-WFF f
(f,c<sub>222</sub>) is Element of CQC-WFF f
'not' (f,c<sub>222</sub>) is Element of CQC-WFF f
(f,c<sub>223</sub>) is Element of CQC-WFF f
p . c<sub>221</sub> is set
(p . c<sub>221</sub>) `1 is set
p . c₂₂₀ is set
(p . c₂₂₀) `1 is set
((CQC-WFF f),((CQC-WFF f),c<sub>222</sub>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>224</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c<sub>222</sub>)) ^ <*c<sub>224</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>225</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>226</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>226</sub>) is Element of CQC-WFF f
c<sub>228</sub> is Element of bound_QC-variables f
c<sub>227</sub> is Element of CQC-WFF f
All (c<sub>228</sub>,c<sub>227</sub>) is Element of CQC-WFF f
p . c<sub>225</sub> is set
(p . c<sub>225</sub>) `1 is set
((CQC-WFF f),c₂₂₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₂₉ is Element of bound_QC-variables f
c₂₂₇ . (c₂₂₈,c₂₂₉) is Element of CQC-WFF f
<*(c₂₂₇ . (c₂₂₈,c₂₂₉))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₂₆) ^ <*(c₂₂₇ . (c₂₂₈,c₂₂₉))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₃₀ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₃₁ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₃₂ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len c₂₃₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),c₂₃₂) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₃₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₃₃) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₂₃₂)) is Element of CQC-WFF f
c₂₃₄ is Element of CQC-WFF f
'not' c₂₃₄ is Element of CQC-WFF f
(f,c₂₃₂) is Element of CQC-WFF f
'not' (f,c₂₃₂) is Element of CQC-WFF f
(f,c₂₃₃) is Element of CQC-WFF f
p . c₂₃₁ is set
(p . c₂₃₁) `1 is set
p . c<sub>230</sub> is set
(p . c<sub>230</sub>) `1 is set
((CQC-WFF f),((CQC-WFF f),c₂₃₂)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₃₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),c₂₃₂)) ^ <*c₂₃₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₃₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₃₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₃₆) is Element of CQC-WFF f
c₂₃₇ is Element of CQC-WFF f
c₂₃₈ is Element of bound_QC-variables f
c₂₃₉ is Element of bound_QC-variables f
c₂₃₇ . (c₂₃₈,c₂₃₉) is Element of CQC-WFF f
((CQC-WFF f),c₂₃₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₂₃₆)) is Element of bool (bound_QC-variables f)
All (c₂₃₈,c₂₃₇) is Element of CQC-WFF f
still_not-bound_in (All (c₂₃₈,c₂₃₇)) is Element of bool (bound_QC-variables f)
p . c₂₃₅ is set
(p . c₂₃₅) `1 is set
<*(All (c<sub>238</sub>,c<sub>237</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>236</sub>) ^ <*(All (c<sub>238</sub>,c<sub>237</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>240</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>241</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>242</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>242</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>243</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>243</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>241</sub> is set
(p . c<sub>241</sub>) `1 is set
p . c₂₄₀ is set
(p . c₂₄₀) `1 is set
(f,c<sub>242</sub>) is Element of CQC-WFF f
(f,c<sub>243</sub>) is Element of CQC-WFF f
(f,c<sub>242</sub>) '&' (f,c<sub>243</sub>) is Element of CQC-WFF f
<*((f,c<sub>242</sub>) '&' (f,c<sub>243</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>242</sub>) ^ <*((f,c<sub>242</sub>) '&' (f,c<sub>243</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>244</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>246</sub> is Element of CQC-WFF f
c<sub>247</sub> is Element of CQC-WFF f
c<sub>246</sub> '&' c<sub>247</sub> is Element of CQC-WFF f
c<sub>245</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>245</sub>) is Element of CQC-WFF f
p . c<sub>244</sub> is set
(p . c<sub>244</sub>) `1 is set
((CQC-WFF f),c₂₄₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₄₆*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₄₅) ^ <*c₂₄₆*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₄₈ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₄₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₅₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₅₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₅₁ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₅₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c₂₄₉ is set
(p . c₂₄₉) `1 is set
p . c<sub>248</sub> is set
(p . c<sub>248</sub>) `1 is set
(f,c₂₅₀) is Element of CQC-WFF f
(f,c₂₅₁) is Element of CQC-WFF f
(f,c₂₅₀) '&' (f,c₂₅₁) is Element of CQC-WFF f
<*((f,c₂₅₀) '&' (f,c₂₅₁))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₅₀) ^ <*((f,c₂₅₀) '&' (f,c₂₅₁))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₅₂ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₅₄ is Element of CQC-WFF f
c₂₅₅ is Element of CQC-WFF f
c₂₅₄ '&' c₂₅₅ is Element of CQC-WFF f
c₂₅₃ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₅₃) is Element of CQC-WFF f
p . c₂₅₂ is set
(p . c₂₅₂) `1 is set
((CQC-WFF f),c<sub>253</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>255</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>253</sub>) ^ <*c<sub>255</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>256</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>257</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>258</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>258</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>259</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>259</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c<sub>257</sub> is set
(p . c<sub>257</sub>) `1 is set
p . c₂₅₆ is set
(p . c₂₅₆) `1 is set
(f,c<sub>258</sub>) is Element of CQC-WFF f
(f,c<sub>259</sub>) is Element of CQC-WFF f
(f,c<sub>258</sub>) '&' (f,c<sub>259</sub>) is Element of CQC-WFF f
<*((f,c<sub>258</sub>) '&' (f,c<sub>259</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>258</sub>) ^ <*((f,c<sub>258</sub>) '&' (f,c<sub>259</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>260</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>261</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>261</sub>) is Element of CQC-WFF f
c<sub>263</sub> is Element of bound_QC-variables f
c<sub>262</sub> is Element of CQC-WFF f
All (c<sub>263</sub>,c<sub>262</sub>) is Element of CQC-WFF f
p . c<sub>260</sub> is set
(p . c<sub>260</sub>) `1 is set
((CQC-WFF f),c₂₆₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₆₄ is Element of bound_QC-variables f
c₂₆₂ . (c₂₆₃,c₂₆₄) is Element of CQC-WFF f
<*(c₂₆₂ . (c₂₆₃,c₂₆₄))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₆₁) ^ <*(c₂₆₂ . (c₂₆₃,c₂₆₄))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₆₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₆₆ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₆₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₆₇) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₆₈ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₆₈) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . c₂₆₆ is set
(p . c₂₆₆) `1 is set
p . c<sub>265</sub> is set
(p . c<sub>265</sub>) `1 is set
(f,c₂₆₇) is Element of CQC-WFF f
(f,c₂₆₈) is Element of CQC-WFF f
(f,c₂₆₇) '&' (f,c₂₆₈) is Element of CQC-WFF f
<*((f,c₂₆₇) '&' (f,c₂₆₈))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₆₇) ^ <*((f,c₂₆₇) '&' (f,c₂₆₈))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₆₉ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₇₀ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₇₀) is Element of CQC-WFF f
c₂₇₁ is Element of CQC-WFF f
c₂₇₂ is Element of bound_QC-variables f
c₂₇₃ is Element of bound_QC-variables f
c₂₇₁ . (c₂₇₂,c₂₇₃) is Element of CQC-WFF f
((CQC-WFF f),c₂₇₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₂₇₀)) is Element of bool (bound_QC-variables f)
All (c₂₇₂,c₂₇₁) is Element of CQC-WFF f
still_not-bound_in (All (c₂₇₂,c₂₇₁)) is Element of bool (bound_QC-variables f)
p . c₂₆₉ is set
(p . c₂₆₉) `1 is set
<*(All (c<sub>272</sub>,c<sub>271</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>270</sub>) ^ <*(All (c<sub>272</sub>,c<sub>271</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>274</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>276</sub> is Element of CQC-WFF f
c<sub>277</sub> is Element of CQC-WFF f
c<sub>276</sub> '&' c<sub>277</sub> is Element of CQC-WFF f
c<sub>275</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>275</sub>) is Element of CQC-WFF f
p . c<sub>274</sub> is set
(p . c<sub>274</sub>) `1 is set
((CQC-WFF f),c₂₇₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₇₆*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₇₅) ^ <*c₂₇₆*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₇₈ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₈₀ is Element of CQC-WFF f
c₂₈₁ is Element of CQC-WFF f
c₂₈₀ '&' c₂₈₁ is Element of CQC-WFF f
c₂₇₉ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₇₉) is Element of CQC-WFF f
p . c₂₇₈ is set
(p . c₂₇₈) `1 is set
((CQC-WFF f),c<sub>279</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c<sub>281</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>279</sub>) ^ <*c<sub>281</sub>*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>282</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>284</sub> is Element of CQC-WFF f
c<sub>285</sub> is Element of CQC-WFF f
c<sub>284</sub> '&' c<sub>285</sub> is Element of CQC-WFF f
c<sub>283</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>283</sub>) is Element of CQC-WFF f
p . c<sub>282</sub> is set
(p . c<sub>282</sub>) `1 is set
((CQC-WFF f),c₂₈₃) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₈₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₈₃) ^ <*c₂₈₄*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₈₆ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₈₇ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₈₇) is Element of CQC-WFF f
c₂₈₉ is Element of bound_QC-variables f
c₂₈₈ is Element of CQC-WFF f
All (c₂₈₉,c₂₈₈) is Element of CQC-WFF f
p . c₂₈₆ is set
(p . c₂₈₆) `1 is set
((CQC-WFF f),c<sub>287</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>290</sub> is Element of bound_QC-variables f
c<sub>288</sub> . (c<sub>289</sub>,c<sub>290</sub>) is Element of CQC-WFF f
<*(c<sub>288</sub> . (c<sub>289</sub>,c<sub>290</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>287</sub>) ^ <*(c<sub>288</sub> . (c<sub>289</sub>,c<sub>290</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>291</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>293</sub> is Element of CQC-WFF f
c<sub>294</sub> is Element of CQC-WFF f
c<sub>293</sub> '&' c<sub>294</sub> is Element of CQC-WFF f
c<sub>292</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>292</sub>) is Element of CQC-WFF f
p . c<sub>291</sub> is set
(p . c<sub>291</sub>) `1 is set
((CQC-WFF f),c₂₉₂) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₂₉₃*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₂₉₂) ^ <*c₂₉₃*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₂₉₅ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₂₉₆ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₂₉₆) is Element of CQC-WFF f
c₂₉₇ is Element of CQC-WFF f
c₂₉₈ is Element of bound_QC-variables f
c₂₉₉ is Element of bound_QC-variables f
c₂₉₇ . (c₂₉₈,c₂₉₉) is Element of CQC-WFF f
((CQC-WFF f),c₂₉₆) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₂₉₆)) is Element of bool (bound_QC-variables f)
All (c₂₉₈,c₂₉₇) is Element of CQC-WFF f
still_not-bound_in (All (c₂₉₈,c₂₉₇)) is Element of bool (bound_QC-variables f)
p . c₂₉₅ is set
(p . c₂₉₅) `1 is set
<*(All (c<sub>298</sub>,c<sub>297</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>296</sub>) ^ <*(All (c<sub>298</sub>,c<sub>297</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>300</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>302</sub> is Element of CQC-WFF f
c<sub>303</sub> is Element of CQC-WFF f
c<sub>302</sub> '&' c<sub>303</sub> is Element of CQC-WFF f
c<sub>301</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>301</sub>) is Element of CQC-WFF f
p . c<sub>300</sub> is set
(p . c<sub>300</sub>) `1 is set
((CQC-WFF f),c₃₀₁) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₃₀₃*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₃₀₁) ^ <*c₃₀₃*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₃₀₄ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₃₀₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₃₀₅) is Element of CQC-WFF f
c₃₀₇ is Element of bound_QC-variables f
c₃₀₆ is Element of CQC-WFF f
All (c₃₀₇,c₃₀₆) is Element of CQC-WFF f
p . c₃₀₄ is set
(p . c₃₀₄) `1 is set
((CQC-WFF f),c<sub>305</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>308</sub> is Element of bound_QC-variables f
c<sub>306</sub> . (c<sub>307</sub>,c<sub>308</sub>) is Element of CQC-WFF f
<*(c<sub>306</sub> . (c<sub>307</sub>,c<sub>308</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>305</sub>) ^ <*(c<sub>306</sub> . (c<sub>307</sub>,c<sub>308</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>309</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>311</sub> is Element of CQC-WFF f
c<sub>312</sub> is Element of CQC-WFF f
c<sub>311</sub> '&' c<sub>312</sub> is Element of CQC-WFF f
c<sub>310</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>310</sub>) is Element of CQC-WFF f
p . c<sub>309</sub> is set
(p . c<sub>309</sub>) `1 is set
((CQC-WFF f),c₃₁₀) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*c₃₁₂*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₃₁₀) ^ <*c₃₁₂*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₃₁₃ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₃₁₄ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₃₁₄) is Element of CQC-WFF f
c₃₁₅ is Element of CQC-WFF f
c₃₁₆ is Element of bound_QC-variables f
c₃₁₇ is Element of bound_QC-variables f
c₃₁₅ . (c₃₁₆,c₃₁₇) is Element of CQC-WFF f
((CQC-WFF f),c₃₁₄) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₃₁₄)) is Element of bool (bound_QC-variables f)
All (c₃₁₆,c₃₁₅) is Element of CQC-WFF f
still_not-bound_in (All (c₃₁₆,c₃₁₅)) is Element of bool (bound_QC-variables f)
p . c₃₁₃ is set
(p . c₃₁₃) `1 is set
<*(All (c<sub>316</sub>,c<sub>315</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>314</sub>) ^ <*(All (c<sub>316</sub>,c<sub>315</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c<sub>318</sub> is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c<sub>319</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>319</sub>) is Element of CQC-WFF f
c<sub>321</sub> is Element of bound_QC-variables f
c<sub>320</sub> is Element of CQC-WFF f
All (c<sub>321</sub>,c<sub>320</sub>) is Element of CQC-WFF f
p . c<sub>318</sub> is set
(p . c<sub>318</sub>) `1 is set
((CQC-WFF f),c₃₁₉) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₃₂₂ is Element of bound_QC-variables f
c₃₂₀ . (c₃₂₁,c₃₂₂) is Element of CQC-WFF f
<*(c₃₂₀ . (c₃₂₁,c₃₂₂))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₃₁₉) ^ <*(c₃₂₀ . (c₃₂₁,c₃₂₂))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
c₃₂₃ is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
c₃₂₄ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₃₂₄) is Element of CQC-WFF f
c₃₂₅ is Element of CQC-WFF f
c₃₂₆ is Element of bound_QC-variables f
c₃₂₇ is Element of bound_QC-variables f
c₃₂₅ . (c₃₂₆,c₃₂₇) is Element of CQC-WFF f
((CQC-WFF f),c₃₂₄) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),c₃₂₄)) is Element of bool (bound_QC-variables f)
All (c₃₂₆,c₃₂₅) is Element of CQC-WFF f
still_not-bound_in (All (c₃₂₆,c₃₂₅)) is Element of bool (bound_QC-variables f)
p . c₃₂₃ is set
(p . c₃₂₃) `1 is set
<*(All (c<sub>326</sub>,c<sub>325</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>324</sub>) ^ <*(All (c<sub>326</sub>,c<sub>325</sub>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
bool (CQC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
bool (CQC-WFF f) is non empty set
QC-pred_symbols f is non empty set
x is non empty set
K291(x) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
bool (CQC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-pred_symbols f is non empty set
x is non empty set
K291(x) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
dom ((CQC-WFF f),p) is finite Element of bool NAT
rng ((CQC-WFF f),p) is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) . x is set
QC-pred_symbols f is non empty set
x is non empty set
K291(x) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like QC-pred_symbols f -defined K291(x) -valued Function-like V30( QC-pred_symbols f,K291(x)) interpretation of f,x
y0 is Relation-like bound_QC-variables f -defined x -valued Function-like V30( bound_QC-variables f,x) Element of Valuations_in (f,x)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
f is non empty set
K291(f) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,f) is non empty M4( bound_QC-variables f,f)
y0 is Relation-like QC-pred_symbols f -defined K291(f) -valued Function-like V30( QC-pred_symbols f,K291(f)) interpretation of f,f
f1 is Relation-like bound_QC-variables f -defined f -valued Function-like V30( bound_QC-variables f,f) Element of Valuations_in (f,f)
rng ((CQC-WFF f),x) is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
F is Element of CQC-WFF f
rng ((CQC-WFF f),p) is finite Element of bool (CQC-WFF f)
f is Relation-like non empty QC-alphabet
QC-pred_symbols f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is non empty set
K291(p) is set
Valuations_in (f,p) is non empty M4( bound_QC-variables f,p)
x is Relation-like QC-pred_symbols f -defined K291(p) -valued Function-like V30( QC-pred_symbols f,K291(p)) interpretation of f,p
f is Relation-like bound_QC-variables f -defined p -valued Function-like V30( bound_QC-variables f,p) Element of Valuations_in (f,p)
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),y0) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y0) is Element of CQC-WFF f
f1 is Element of CQC-WFF f
rng y0 is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
rng ((CQC-WFF f),y0) is finite Element of bool (CQC-WFF f)
{(f,y0)} is non empty trivial finite 1 -element Element of bool (CQC-WFF f)
(rng ((CQC-WFF f),y0)) \/ {(f,y0)} is non empty finite Element of bool (CQC-WFF f)
rng y0 is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
rng ((CQC-WFF f),y0) is finite Element of bool (CQC-WFF f)
{(f,y0)} is non empty trivial finite 1 -element Element of bool (CQC-WFF f)
(rng ((CQC-WFF f),y0)) \/ {(f,y0)} is non empty finite Element of bool (CQC-WFF f)
f1 is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom y0 is finite Element of bool NAT
y0 . (len y0) is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),p)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),p)) is Element of CQC-WFF f
(f,p) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
f is non empty set
K291(f) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,f) is non empty M4( bound_QC-variables f,f)
y0 is Relation-like QC-pred_symbols f -defined K291(f) -valued Function-like V30( QC-pred_symbols f,K291(f)) interpretation of f,f
f1 is Relation-like bound_QC-variables f -defined f -valued Function-like V30( bound_QC-variables f,f) Element of Valuations_in (f,f)
len ((CQC-WFF f),x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),p) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
'not' (f,x) is Element of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
len ((CQC-WFF f),x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
QC-pred_symbols f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
y0 is non empty set
K291(y0) is set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like QC-pred_symbols f -defined K291(y0) -valued Function-like V30( QC-pred_symbols f,K291(y0)) interpretation of f,y0
F is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
y0 is non empty set
K291(y0) is set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like QC-pred_symbols f -defined K291(y0) -valued Function-like V30( QC-pred_symbols f,K291(y0)) interpretation of f,y0
F is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f,p) '&' (f,x) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
f is non empty set
K291(f) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,f) is non empty M4( bound_QC-variables f,f)
y0 is Relation-like QC-pred_symbols f -defined K291(f) -valued Function-like V30( QC-pred_symbols f,K291(f)) interpretation of f,f
f1 is Relation-like bound_QC-variables f -defined f -valued Function-like V30( bound_QC-variables f,f) Element of Valuations_in (f,f)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
QC-pred_symbols f is non empty set
y0 is non empty set
K291(y0) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like QC-pred_symbols f -defined K291(y0) -valued Function-like V30( QC-pred_symbols f,K291(y0)) interpretation of f,y0
F is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
QC-pred_symbols f is non empty set
y0 is non empty set
K291(y0) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like QC-pred_symbols f -defined K291(y0) -valued Function-like V30( QC-pred_symbols f,K291(y0)) interpretation of f,y0
F is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-pred_symbols f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
vSUB f is set
p is Element of CQC-WFF f
x is non empty set
K291(x) is set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like QC-pred_symbols f -defined K291(x) -valued Function-like V30( QC-pred_symbols f,K291(x)) interpretation of f,x
y0 is Relation-like bound_QC-variables f -defined x -valued Function-like V30( bound_QC-variables f,x) Element of Valuations_in (f,x)
f1 is Element of vSUB f
[p,f1] is V22() Element of CQC-Sub-WFF f
QC-Sub-WFF f is non empty set
CQC-Sub-WFF f is Element of bool (QC-Sub-WFF f)
bool (QC-Sub-WFF f) is non empty set
{p,f1} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,f1},{p}} is non empty finite V37() set
[p,f1] `1 is Element of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
QC-pred_symbols f is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
f is Element of bound_QC-variables f
p . (x,f) is Element of CQC-WFF f
y0 is non empty set
K291(y0) is set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like QC-pred_symbols f -defined K291(y0) -valued Function-like V30( QC-pred_symbols f,K291(y0)) interpretation of f,y0
F is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
F . f is Element of y0
Sbst (x,f) is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -valued Function-like one-to-one finite Element of vSUB f
{x} is non empty trivial finite 1 -element set
vSUB f is set
{x} --> f is Relation-like {x} -defined bound_QC-variables f -valued {f} -valued Function-like constant non empty V14({x}) V30({x},{f}) finite Element of bool [:{x},{f}:]
{f} is non empty trivial finite 1 -element set
[:{x},{f}:] is Relation-like non empty finite set
bool [:{x},{f}:] is non empty finite V37() set
[p,(Sbst (x,f))] is V22() Element of CQC-Sub-WFF f
QC-Sub-WFF f is non empty set
CQC-Sub-WFF f is Element of bool (QC-Sub-WFF f)
bool (QC-Sub-WFF f) is non empty set
{p,(Sbst (x,f))} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,(Sbst (x,f))},{p}} is non empty finite V37() set
CQC_Sub [p,(Sbst (x,f))] is Element of CQC-WFF f
Val_S (F,[p,(Sbst (x,f))]) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
[:(bound_QC-variables f),y0:] is Relation-like non empty set
bool [:(bound_QC-variables f),y0:] is non empty set
F . (Val_S (F,[p,(Sbst (x,f))])) is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
[p,(Sbst (x,f))] `2 is Element of vSUB f
@ ([p,(Sbst (x,f))] `2) is Relation-like bound_QC-variables f -defined bound_QC-variables f -valued Function-like Element of bool [:(bound_QC-variables f),(bound_QC-variables f):]
[:(bound_QC-variables f),(bound_QC-variables f):] is Relation-like non empty set
bool [:(bound_QC-variables f),(bound_QC-variables f):] is non empty set
F * (@ ([p,(Sbst (x,f))] `2)) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
@ (Sbst (x,f)) is Relation-like bound_QC-variables f -defined bound_QC-variables f -valued Function-like Element of bool [:(bound_QC-variables f),(bound_QC-variables f):]
F * (@ (Sbst (x,f))) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
x .--> f is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -valued Function-like one-to-one finite set
(x .--> f) * F is Relation-like bound_QC-variables f -defined y0 -valued Function-like finite set
dom F is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
x .--> (F . f) is Relation-like bound_QC-variables f -defined {x} -defined y0 -valued Function-like one-to-one finite set
{x} --> (F . f) is Relation-like {x} -defined y0 -valued {(F . f)} -valued Function-like constant non empty V14({x}) V30({x},{(F . f)}) finite Element of bool [:{x},{(F . f)}:]
{(F . f)} is non empty trivial finite 1 -element set
[:{x},{(F . f)}:] is Relation-like non empty finite set
bool [:{x},{(F . f)}:] is non empty finite V37() set
b is Element of y0
x | b is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined y0 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),y0:]
{x} --> b is Relation-like {x} -defined y0 -valued {b} -valued Function-like constant non empty V14({x}) V30({x},{b}) finite Element of bool [:{x},{b}:]
{b} is non empty trivial finite 1 -element set
[:{x},{b}:] is Relation-like non empty finite set
bool [:{x},{b}:] is non empty finite V37() set
F . (x | b) is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Element of bound_QC-variables f
p . (x,y0) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
f1 is non empty set
K291(f1) is set
Valuations_in (f,f1) is non empty M4( bound_QC-variables f,f1)
F is Relation-like QC-pred_symbols f -defined K291(f1) -valued Function-like V30( QC-pred_symbols f,K291(f1)) interpretation of f,f1
b is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
b . y0 is Element of f1
x | (b . y0) is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined f1 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),f1:]
{x} is non empty trivial finite 1 -element set
[:(bound_QC-variables f),f1:] is Relation-like non empty set
bool [:(bound_QC-variables f),f1:] is non empty set
{x} --> (b . y0) is Relation-like {x} -defined f1 -valued {(b . y0)} -valued Function-like constant non empty V14({x}) V30({x},{(b . y0)}) finite Element of bool [:{x},{(b . y0)}:]
{(b . y0)} is non empty trivial finite 1 -element set
[:{x},{(b . y0)}:] is Relation-like non empty finite set
bool [:{x},{(b . y0)}:] is non empty finite V37() set
b . (x | (b . y0)) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
a is Element of f1
x | a is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined f1 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),f1:]
{x} is non empty trivial finite 1 -element set
[:(bound_QC-variables f),f1:] is Relation-like non empty set
bool [:(bound_QC-variables f),f1:] is non empty set
{x} --> a is Relation-like {x} -defined f1 -valued {a} -valued Function-like constant non empty V14({x}) V30({x},{a}) finite Element of bool [:{x},{a}:]
{a} is non empty trivial finite 1 -element set
[:{x},{a}:] is Relation-like non empty finite set
bool [:{x},{a}:] is non empty finite V37() set
b . (x | a) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
f is Relation-like non empty QC-alphabet
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of bound_QC-variables f
x is non empty set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like bound_QC-variables f -defined x -valued Function-like V30( bound_QC-variables f,x) Element of Valuations_in (f,x)
y0 is Element of x
p | y0 is Relation-like bound_QC-variables f -defined {p} -defined bound_QC-variables f -defined x -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),x:]
{p} is non empty trivial finite 1 -element set
[:(bound_QC-variables f),x:] is Relation-like non empty set
bool [:(bound_QC-variables f),x:] is non empty set
{p} --> y0 is Relation-like {p} -defined x -valued {y0} -valued Function-like constant non empty V14({p}) V30({p},{y0}) finite Element of bool [:{p},{y0}:]
{y0} is non empty trivial finite 1 -element set
[:{p},{y0}:] is Relation-like non empty finite set
bool [:{p},{y0}:] is non empty finite V37() set
f . (p | y0) is Relation-like bound_QC-variables f -defined x -valued Function-like V30( bound_QC-variables f,x) Element of Valuations_in (f,x)
f1 is set
(f . (p | y0)) | f1 is Relation-like bound_QC-variables f -defined f1 -defined bound_QC-variables f -defined x -valued Function-like Element of bool [:(bound_QC-variables f),x:]
f | f1 is Relation-like bound_QC-variables f -defined f1 -defined bound_QC-variables f -defined x -valued Function-like Element of bool [:(bound_QC-variables f),x:]
dom ((f . (p | y0)) | f1) is Element of bool f1
bool f1 is non empty set
dom (f | f1) is Element of bool f1
a is set
(f . (p | y0)) . a is set
f . a is set
((f . (p | y0)) | f1) . a is set
(f | f1) . a is set
f is Relation-like non empty QC-alphabet
QC-pred_symbols f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
p is non empty set
K291(p) is set
Valuations_in (f,p) is non empty M4( bound_QC-variables f,p)
x is Relation-like QC-pred_symbols f -defined K291(p) -valued Function-like V30( QC-pred_symbols f,K291(p)) interpretation of f,p
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
y0 is Relation-like bound_QC-variables f -defined p -valued Function-like V30( bound_QC-variables f,p) Element of Valuations_in (f,p)
y0 | (f,f) is Relation-like bound_QC-variables f -defined (f,f) -defined bound_QC-variables f -defined p -valued Function-like Element of bool [:(bound_QC-variables f),p:]
[:(bound_QC-variables f),p:] is Relation-like non empty set
bool [:(bound_QC-variables f),p:] is non empty set
f1 is Relation-like bound_QC-variables f -defined p -valued Function-like V30( bound_QC-variables f,p) Element of Valuations_in (f,p)
f1 | (f,f) is Relation-like bound_QC-variables f -defined (f,f) -defined bound_QC-variables f -defined p -valued Function-like Element of bool [:(bound_QC-variables f),p:]
rng f is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
F is Element of CQC-WFF f
dom f is finite Element of bool NAT
still_not-bound_in F is Element of bool (bound_QC-variables f)
b is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
f . a is set
y0 | (still_not-bound_in F) is Relation-like bound_QC-variables f -defined still_not-bound_in F -defined bound_QC-variables f -defined p -valued Function-like Element of bool [:(bound_QC-variables f),p:]
f1 | (still_not-bound_in F) is Relation-like bound_QC-variables f -defined still_not-bound_in F -defined bound_QC-variables f -defined p -valued Function-like Element of bool [:(bound_QC-variables f),p:]
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
still_not-bound_in p is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
x is Element of bound_QC-variables f
f is Element of bound_QC-variables f
All (f,p) is Element of CQC-WFF f
still_not-bound_in (All (f,p)) is Element of bool (bound_QC-variables f)
y0 is non empty set
Valuations_in (f,y0) is non empty M4( bound_QC-variables f,y0)
f1 is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
F is Element of y0
x | F is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined y0 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),y0:]
{x} is non empty trivial finite 1 -element set
[:(bound_QC-variables f),y0:] is Relation-like non empty set
bool [:(bound_QC-variables f),y0:] is non empty set
{x} --> F is Relation-like {x} -defined y0 -valued {F} -valued Function-like constant non empty V14({x}) V30({x},{F}) finite Element of bool [:{x},{F}:]
{F} is non empty trivial finite 1 -element set
[:{x},{F}:] is Relation-like non empty finite set
bool [:{x},{F}:] is non empty finite V37() set
f1 . (x | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
f | F is Relation-like bound_QC-variables f -defined {f} -defined bound_QC-variables f -defined y0 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),y0:]
{f} is non empty trivial finite 1 -element set
{f} --> F is Relation-like {f} -defined y0 -valued {F} -valued Function-like constant non empty V14({f}) V30({f},{F}) finite Element of bool [:{f},{F}:]
[:{f},{F}:] is Relation-like non empty finite set
bool [:{f},{F}:] is non empty finite V37() set
(f1 . (x | F)) . (f | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
((f1 . (x | F)) . (f | F)) | (still_not-bound_in p) is Relation-like bound_QC-variables f -defined still_not-bound_in p -defined bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
f1 . (f | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like V30( bound_QC-variables f,y0) Element of Valuations_in (f,y0)
(f1 . (f | F)) | (still_not-bound_in p) is Relation-like bound_QC-variables f -defined still_not-bound_in p -defined bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
(x | F) +* (f | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like finite Element of bool [:(bound_QC-variables f),y0:]
f1 +* ((x | F) +* (f | F)) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
dom (f | F) is trivial finite Element of bool {f}
bool {f} is non empty finite V37() set
{f} is non empty trivial finite 1 -element Element of bool (bound_QC-variables f)
dom (x | F) is trivial finite Element of bool {x}
bool {x} is non empty finite V37() set
{x} is non empty trivial finite 1 -element Element of bool (bound_QC-variables f)
(f | F) +* (x | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like finite Element of bool [:(bound_QC-variables f),y0:]
f1 +* ((f | F) +* (x | F)) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
f1 +* (f | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
(f1 +* (f | F)) +* (x | F) is Relation-like bound_QC-variables f -defined y0 -valued Function-like Element of bool [:(bound_QC-variables f),y0:]
(still_not-bound_in p) \ {f} is Element of bool (bound_QC-variables f)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
still_not-bound_in (All (x,p)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
f is Element of bound_QC-variables f
p . (x,f) is Element of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y0) is Element of CQC-WFF f
((CQC-WFF f),y0) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),y0)) is Element of bool (bound_QC-variables f)
QC-pred_symbols f is non empty set
f1 is non empty set
K291(f1) is set
Valuations_in (f,f1) is non empty M4( bound_QC-variables f,f1)
F is Relation-like QC-pred_symbols f -defined K291(f1) -valued Function-like V30( QC-pred_symbols f,K291(f1)) interpretation of f,f1
b is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
a is Element of f1
x | a is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined f1 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),f1:]
{x} is non empty trivial finite 1 -element set
[:(bound_QC-variables f),f1:] is Relation-like non empty set
bool [:(bound_QC-variables f),f1:] is non empty set
{x} --> a is Relation-like {x} -defined f1 -valued {a} -valued Function-like constant non empty V14({x}) V30({x},{a}) finite Element of bool [:{x},{a}:]
{a} is non empty trivial finite 1 -element set
[:{x},{a}:] is Relation-like non empty finite set
bool [:{x},{a}:] is non empty finite V37() set
b . (x | a) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
f | a is Relation-like bound_QC-variables f -defined {f} -defined bound_QC-variables f -defined f1 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),f1:]
{f} is non empty trivial finite 1 -element set
{f} --> a is Relation-like {f} -defined f1 -valued {a} -valued Function-like constant non empty V14({f}) V30({f},{a}) finite Element of bool [:{f},{a}:]
[:{f},{a}:] is Relation-like non empty finite set
bool [:{f},{a}:] is non empty finite V37() set
b . (f | a) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
(b . (f | a)) | (f,((CQC-WFF f),y0)) is Relation-like bound_QC-variables f -defined (f,((CQC-WFF f),y0)) -defined bound_QC-variables f -defined f1 -valued Function-like Element of bool [:(bound_QC-variables f),f1:]
b | (f,((CQC-WFF f),y0)) is Relation-like bound_QC-variables f -defined (f,((CQC-WFF f),y0)) -defined bound_QC-variables f -defined f1 -valued Function-like Element of bool [:(bound_QC-variables f),f1:]
(b . (f | a)) . f is Element of f1
(b . (f | a)) . (x | a) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
a is Element of f1
x | a is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -defined f1 -valued Function-like one-to-one finite Element of bool [:(bound_QC-variables f),f1:]
{x} --> a is Relation-like {x} -defined f1 -valued {a} -valued Function-like constant non empty V14({x}) V30({x},{a}) finite Element of bool [:{x},{a}:]
{a} is non empty trivial finite 1 -element set
[:{x},{a}:] is Relation-like non empty finite set
bool [:{x},{a}:] is non empty finite V37() set
(b . (f | a)) . (x | a) is Relation-like bound_QC-variables f -defined f1 -valued Function-like V30( bound_QC-variables f,f1) Element of Valuations_in (f,f1)
still_not-bound_in p is Element of bool (bound_QC-variables f)
((b . (f | a)) . (x | a)) | (still_not-bound_in p) is Relation-like bound_QC-variables f -defined still_not-bound_in p -defined bound_QC-variables f -defined f1 -valued Function-like Element of bool [:(bound_QC-variables f),f1:]
(b . (x | a)) | (still_not-bound_in p) is Relation-like bound_QC-variables f -defined still_not-bound_in p -defined bound_QC-variables f -defined f1 -valued Function-like Element of bool [:(bound_QC-variables f),f1:]
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(p ^ <*(VERUM f)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(p ^ <*(VERUM f)*>)) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
x is non empty set
K291(x) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,x) is non empty M4( bound_QC-variables f,x)
f is Relation-like QC-pred_symbols f -defined K291(x) -valued Function-like V30( QC-pred_symbols f,K291(x)) interpretation of f,x
y0 is Relation-like bound_QC-variables f -defined x -valued Function-like V30( bound_QC-variables f,x) Element of Valuations_in (f,x)
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
p is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
p . x is set
(p . x) `2 is set
dom p is finite Element of bool NAT
rng p is Relation-like (f) -defined Proof_Step_Kinds -valued finite Element of bool [:(f),Proof_Step_Kinds:]
bool [:(f),Proof_Step_Kinds:] is non empty set
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x . p is set
(x . p) `1 is set
dom x is finite Element of bool NAT
rng x is Relation-like (f) -defined Proof_Step_Kinds -valued finite Element of bool [:(f),Proof_Step_Kinds:]
bool [:(f),Proof_Step_Kinds:] is non empty set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
bool (CQC-WFF f) is non empty set
p is Element of CQC-WFF f
x is Element of bool (CQC-WFF f)
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
rng ((CQC-WFF f),f) is finite Element of bool (CQC-WFF f)
(f,f) is Element of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . F is set
(y0 . F) `1 is set
b is set
(y0 . F) `2 is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
(y0 . F) `2 is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a ^ <*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),k) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,k) is Element of CQC-WFF f
(f,p) is Element of CQC-WFF f
y0 . a is set
(y0 . a) `1 is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),p)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),p)) is Element of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,p) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
y0 . k is set
(y0 . k) `1 is set
y0 . a is set
(y0 . a) `1 is set
<*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
y is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y) is Element of CQC-WFF f
c₁₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₅) is Element of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),p)) is Element of CQC-WFF f
y is Element of CQC-WFF f
'not' y is Element of CQC-WFF f
(f,p) is Element of CQC-WFF f
'not' (f,p) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
y0 . k is set
(y0 . k) `1 is set
y0 . a is set
(y0 . a) `1 is set
((CQC-WFF f),((CQC-WFF f),p)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*y*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) ^ <*y*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
c<sub>15</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>15</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>15</sub>) is Element of CQC-WFF f
c<sub>16</sub> is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c<sub>16</sub>) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c<sub>16</sub>) is Element of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 . k is set
(y0 . k) `1 is set
y0 . a is set
(y0 . a) `1 is set
(f,p) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f,p) '&' (f,x) is Element of CQC-WFF f
<*((f,p) '&' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
y is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y) is Element of CQC-WFF f
c₁₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₅) is Element of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Element of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
k is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,k) is Element of CQC-WFF f
y0 . a is set
(y0 . a) `1 is set
((CQC-WFF f),k) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),k) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
y is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y) is Element of CQC-WFF f
(y0 . F) `2 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p is Element of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
k is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,k) is Element of CQC-WFF f
y0 . a is set
(y0 . a) `1 is set
((CQC-WFF f),k) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),k) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
y is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y) is Element of CQC-WFF f
(y0 . F) `2 is set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,k) is Element of CQC-WFF f
x is Element of bound_QC-variables f
p is Element of CQC-WFF f
All (x,p) is Element of CQC-WFF f
y0 . a is set
(y0 . a) `1 is set
((CQC-WFF f),k) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y is Element of bound_QC-variables f
p . (x,y) is Element of CQC-WFF f
<*(p . (x,y))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),k) ^ <*(p . (x,y))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
c₁₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₅) is Element of CQC-WFF f
(y0 . F) `2 is set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,k) is Element of CQC-WFF f
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
y is Element of bound_QC-variables f
p . (x,y) is Element of CQC-WFF f
((CQC-WFF f),k) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),k)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
All (x,p) is Element of CQC-WFF f
still_not-bound_in (All (x,p)) is Element of bool (bound_QC-variables f)
y0 . a is set
(y0 . a) `1 is set
<*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),k) ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
c₁₅ is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),c₁₅) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,c₁₅) is Element of CQC-WFF f
(y0 . F) `2 is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,b) is Element of CQC-WFF f
a is set
a is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),a) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,a) is Element of CQC-WFF f
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . f1 is set
(y0 . f1) `1 is set
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
QC-pred_symbols f is non empty set
F is non empty set
K291(F) is set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
Valuations_in (f,F) is non empty M4( bound_QC-variables f,F)
b is Relation-like QC-pred_symbols f -defined K291(F) -valued Function-like V30( QC-pred_symbols f,K291(F)) interpretation of f,F
a is Relation-like bound_QC-variables f -defined F -valued Function-like V30( bound_QC-variables f,F) Element of Valuations_in (f,F)
a is Element of CQC-WFF f
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[p,0] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{p,0} is functional non empty finite V37() set
{p} is functional non empty trivial finite V37() 1 -element set
{{p,0},{p}} is non empty finite V37() set
<*[p,0]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[p,0]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[p,0]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
f is set
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . y0 is set
(f . y0) `1 is set
(f . y0) `2 is set
f . 1 is set
f . (len f) is set
(f . (len f)) `1 is set
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
p is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
p ^ x is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
dom p is finite Element of bool NAT
(p ^ x) . f is set
p . f is set
len (p ^ x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len p) + (len x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
p . y0 is set
(p . y0) `1 is set
(p ^ x) . y0 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),b)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),F)) is Element of CQC-WFF f
(f,((CQC-WFF f),b)) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
p . f1 is set
(p . f1) `1 is set
p . y0 is set
(p . y0) `1 is set
<*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
(p ^ x) . y0 is set
(p ^ x) . f1 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
a is Element of CQC-WFF f
'not' a is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
'not' (f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
p . f1 is set
(p . f1) `1 is set
p . y0 is set
(p . y0) `1 is set
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
(p ^ x) . y0 is set
(p ^ x) . f1 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . f1 is set
(p . f1) `1 is set
p . y0 is set
(p . y0) `1 is set
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
(f,F) '&' (f,b) is Element of CQC-WFF f
<*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) ^ <*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
(p ^ x) . y0 is set
(p ^ x) . f1 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
p . y0 is set
(p . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
p . y0 is set
(p . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
b is Element of bound_QC-variables f
F is Element of CQC-WFF f
All (b,F) is Element of CQC-WFF f
p . y0 is set
(p . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
<*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
((p ^ x) . f) `1 is set
(p . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
F is Element of CQC-WFF f
b is Element of bound_QC-variables f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),f1)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
All (b,F) is Element of CQC-WFF f
still_not-bound_in (All (b,F)) is Element of bool (bound_QC-variables f)
p . y0 is set
(p . y0) `1 is set
<*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . f) `2 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
p . y0 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),b)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),F)) is Element of CQC-WFF f
(f,((CQC-WFF f),b)) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
(p ^ x) . f1 is set
((p ^ x) . f1) `1 is set
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
<*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
p . y0 is set
p . f1 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
a is Element of CQC-WFF f
'not' a is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
'not' (f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
(p ^ x) . f1 is set
((p ^ x) . f1) `1 is set
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
p . y0 is set
p . f1 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(p ^ x) . f1 is set
((p ^ x) . f1) `1 is set
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
(f,F) '&' (f,b) is Element of CQC-WFF f
<*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) ^ <*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Seg (len p) is finite len p -element Element of bool NAT
p . y0 is set
p . f1 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . y0 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . y0 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
b is Element of bound_QC-variables f
F is Element of CQC-WFF f
All (b,F) is Element of CQC-WFF f
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
<*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . y0 is set
(p . f) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
(p . f) `1 is set
((p ^ x) . f) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
F is Element of CQC-WFF f
b is Element of bound_QC-variables f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),f1)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
All (b,F) is Element of CQC-WFF f
still_not-bound_in (All (b,F)) is Element of bool (bound_QC-variables f)
(p ^ x) . y0 is set
((p ^ x) . y0) `1 is set
<*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . y0 is set
(p . f) `2 is set
f is Relation-like non empty QC-alphabet
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
f ^ x is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom x is finite Element of bool NAT
x . p is set
(f ^ x) . (p + (len f)) is set
(len f) + (len x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
len (f ^ x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
VERUM f is Element of CQC-WFF f
<*(VERUM f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
x . y0 is set
(x . y0) `1 is set
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),b)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),F)) is Element of CQC-WFF f
(f,((CQC-WFF f),b)) is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
x . f1 is set
(x . f1) `1 is set
x . y0 is set
(x . y0) `1 is set
<*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*(f,F)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
(f ^ x) . ((len f) + f1) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),F)) is Element of CQC-WFF f
a is Element of CQC-WFF f
'not' a is Element of CQC-WFF f
(f,F) is Element of CQC-WFF f
'not' (f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
x . f1 is set
(x . f1) `1 is set
x . y0 is set
(x . y0) `1 is set
((CQC-WFF f),((CQC-WFF f),F)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),F)) ^ <*a*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
(f ^ x) . ((len f) + f1) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
b is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),b) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x . f1 is set
(x . f1) `1 is set
x . y0 is set
(x . y0) `1 is set
(f,F) is Element of CQC-WFF f
(f,b) is Element of CQC-WFF f
(f,F) '&' (f,b) is Element of CQC-WFF f
<*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),F) ^ <*((f,F) '&' (f,b))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
(f ^ x) . ((len f) + f1) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
x . y0 is set
(x . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*F*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is Element of CQC-WFF f
b is Element of CQC-WFF f
F '&' b is Element of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
x . y0 is set
(x . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*b*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
b is Element of bound_QC-variables f
F is Element of CQC-WFF f
All (b,F) is Element of CQC-WFF f
x . y0 is set
(x . y0) `1 is set
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
<*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(F . (b,a))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
((f ^ x) . (p + (len f))) `2 is set
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
((f ^ x) . (p + (len f))) `1 is set
(x . p) `1 is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f1) is Element of CQC-WFF f
F is Element of CQC-WFF f
b is Element of bound_QC-variables f
a is Element of bound_QC-variables f
F . (b,a) is Element of CQC-WFF f
((CQC-WFF f),f1) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),f1)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
All (b,F) is Element of CQC-WFF f
still_not-bound_in (All (b,F)) is Element of bool (bound_QC-variables f)
x . y0 is set
(x . y0) `1 is set
<*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f1) ^ <*(All (b,F))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(len f) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f ^ x) . ((len f) + y0) is set
((f ^ x) . (p + (len f))) `2 is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . (len f) is set
(f . (len f)) `1 is set
y0 is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[x,2] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{x,2} is non empty finite V37() set
{x} is functional non empty trivial finite V37() 1 -element set
{{x,2},{x}} is non empty finite V37() set
<*[x,2]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[x,2]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[x,2]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom y0 is finite Element of bool NAT
f ^ y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom F is finite Element of bool NAT
dom f is finite Element of bool NAT
F . (len f) is set
(F . (len f)) `1 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len f) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . a is set
(y0 . a) `1 is set
F . b is set
(F . b) `1 is set
(y0 . a) `2 is set
(F . b) `2 is set
F . (len F) is set
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + (len y0) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F . ((len f) + (len y0)) is set
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
F . ((len f) + 1) is set
y0 . 1 is set
(F . (len F)) `1 is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),p)) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),p)) is Element of CQC-WFF f
(f,p) is Element of CQC-WFF f
<*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . (len f) is set
(f . (len f)) `1 is set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3} is non empty finite V37() set
{(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3},{(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),((CQC-WFF f),p)) ^ <*(f,p)*>),3]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom f1 is finite Element of bool NAT
y0 ^ f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
(y0 ^ f) ^ f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
b is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom b is finite Element of bool NAT
len (y0 ^ f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len (y0 ^ f)) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . a is set
(f1 . a) `1 is set
b . a is set
(b . a) `1 is set
(f1 . a) `2 is set
(b . a) `2 is set
dom y0 is finite Element of bool NAT
(y0 ^ f) . (len y0) is set
((y0 ^ f) . (len y0)) `1 is set
dom (y0 ^ f) is finite Element of bool NAT
b . (len y0) is set
(b . (len y0)) `1 is set
dom f is finite Element of bool NAT
(len y0) + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(y0 ^ f) . ((len y0) + (len f)) is set
((y0 ^ f) . ((len y0) + (len f))) `1 is set
(y0 ^ f) . (len (y0 ^ f)) is set
((y0 ^ f) . (len (y0 ^ f))) `1 is set
b . (len (y0 ^ f)) is set
(b . (len (y0 ^ f))) `1 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len y0) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + (len y0) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . (len b) is set
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len (y0 ^ f)) + (len f1) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . ((len (y0 ^ f)) + (len f1)) is set
(len (y0 ^ f)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
b . ((len (y0 ^ f)) + 1) is set
f1 . 1 is set
(b . (len b)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),x)) is Element of CQC-WFF f
(f,x) is Element of CQC-WFF f
'not' (f,x) is Element of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . (len f1) is set
(f1 . (len f1)) `1 is set
F is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4} is non empty finite V37() set
{(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4},{(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),((CQC-WFF f),x)) ^ <*p*>),4]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom F is finite Element of bool NAT
f1 ^ y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
(f1 ^ y0) ^ F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
a is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom a is finite Element of bool NAT
len (f1 ^ y0) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len (f1 ^ y0)) + k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F . k is set
(F . k) `1 is set
a . a is set
(a . a) `1 is set
(F . k) `2 is set
(a . a) `2 is set
dom f1 is finite Element of bool NAT
(f1 ^ y0) . (len f1) is set
((f1 ^ y0) . (len f1)) `1 is set
dom (f1 ^ y0) is finite Element of bool NAT
a . (len f1) is set
(a . (len f1)) `1 is set
dom y0 is finite Element of bool NAT
(len f1) + (len y0) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(f1 ^ y0) . ((len f1) + (len y0)) is set
((f1 ^ y0) . ((len f1) + (len y0))) `1 is set
(f1 ^ y0) . (len (f1 ^ y0)) is set
((f1 ^ y0) . (len (f1 ^ y0))) `1 is set
a . (len (f1 ^ y0)) is set
(a . (len (f1 ^ y0))) `1 is set
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len f1) + k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len y0) + (len f1) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a . (len a) is set
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len (f1 ^ y0)) + (len F) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a . ((len (f1 ^ y0)) + (len F)) is set
(len (f1 ^ y0)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
a . ((len (f1 ^ y0)) + 1) is set
F . 1 is set
(a . (len a)) `1 is set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
(f,p) '&' (f,x) is Element of CQC-WFF f
<*((f,p) '&' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . (len f) is set
(f . (len f)) `1 is set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5} is non empty finite V37() set
{(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5},{(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),p) ^ <*((f,p) '&' (f,x))*>),5]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom f1 is finite Element of bool NAT
y0 ^ f is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
(y0 ^ f) ^ f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
b is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom b is finite Element of bool NAT
len (y0 ^ f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len (y0 ^ f)) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . a is set
(f1 . a) `1 is set
b . a is set
(b . a) `1 is set
(f1 . a) `2 is set
(b . a) `2 is set
dom y0 is finite Element of bool NAT
(y0 ^ f) . (len y0) is set
((y0 ^ f) . (len y0)) `1 is set
dom (y0 ^ f) is finite Element of bool NAT
b . (len y0) is set
(b . (len y0)) `1 is set
dom f is finite Element of bool NAT
(len y0) + (len f) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(y0 ^ f) . ((len y0) + (len f)) is set
((y0 ^ f) . ((len y0) + (len f))) `1 is set
(y0 ^ f) . (len (y0 ^ f)) is set
((y0 ^ f) . (len (y0 ^ f))) `1 is set
b . (len (y0 ^ f)) is set
(b . (len (y0 ^ f))) `1 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len y0) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + (len y0) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . (len b) is set
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len (y0 ^ f)) + (len f1) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . ((len (y0 ^ f)) + (len f1)) is set
(len (y0 ^ f)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
b . ((len (y0 ^ f)) + 1) is set
f1 . 1 is set
(b . (len b)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),f) ^ <*p*>),6] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),f) ^ <*p*>),6} is non empty finite V37() set
{(((CQC-WFF f),f) ^ <*p*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),f) ^ <*p*>),6},{(((CQC-WFF f),f) ^ <*p*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),f) ^ <*p*>),6]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),f) ^ <*p*>),6]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),f) ^ <*p*>),6]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom f1 is finite Element of bool NAT
y0 ^ f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
b is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom b is finite Element of bool NAT
dom y0 is finite Element of bool NAT
b . (len y0) is set
(b . (len y0)) `1 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len y0) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . a is set
(f1 . a) `1 is set
b . a is set
(b . a) `1 is set
(f1 . a) `2 is set
(b . a) `2 is set
b . (len b) is set
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len y0) + (len f1) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . ((len y0) + (len f1)) is set
(len y0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
b . ((len y0) + 1) is set
f1 . 1 is set
(b . (len b)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
x is Element of CQC-WFF f
p '&' x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of CQC-WFF f
((CQC-WFF f),f) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),f) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
y0 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 . (len y0) is set
(y0 . (len y0)) `1 is set
f1 is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),f) ^ <*x*>),7] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),f) ^ <*x*>),7} is non empty finite V37() set
{(((CQC-WFF f),f) ^ <*x*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),f) ^ <*x*>),7},{(((CQC-WFF f),f) ^ <*x*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),f) ^ <*x*>),7]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),f) ^ <*x*>),7]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),f) ^ <*x*>),7]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom f1 is finite Element of bool NAT
y0 ^ f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
b is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom b is finite Element of bool NAT
dom y0 is finite Element of bool NAT
b . (len y0) is set
(b . (len y0)) `1 is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len y0) + a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . a is set
(f1 . a) `1 is set
b . a is set
(b . a) `1 is set
(f1 . a) `2 is set
(b . a) `2 is set
b . (len b) is set
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len y0) + (len f1) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
b . ((len y0) + (len f1)) is set
(len y0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
b . ((len y0) + 1) is set
f1 . 1 is set
(b . (len b)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
f is Element of bound_QC-variables f
p . (x,f) is Element of CQC-WFF f
<*(p . (x,f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y0) is Element of CQC-WFF f
((CQC-WFF f),y0) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),y0) ^ <*(p . (x,f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . (len f1) is set
(f1 . (len f1)) `1 is set
F is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8} is non empty finite V37() set
{(((CQC-WFF f),y0) ^ <*(p . (x,f))*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8},{(((CQC-WFF f),y0) ^ <*(p . (x,f))*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),y0) ^ <*(p . (x,f))*>),8]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom F is finite Element of bool NAT
f1 ^ F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
a is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom a is finite Element of bool NAT
dom f1 is finite Element of bool NAT
a . (len f1) is set
(a . (len f1)) `1 is set
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len f1) + k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F . k is set
(F . k) `1 is set
a . a is set
(a . a) `1 is set
(F . k) `2 is set
(a . a) `2 is set
a . (len a) is set
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f1) + (len F) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a . ((len f1) + (len F)) is set
(len f1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
a . ((len f1) + 1) is set
F . 1 is set
(a . (len a)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
still_not-bound_in (All (x,p)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
<*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Element of bound_QC-variables f
p . (x,f) is Element of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,y0) is Element of CQC-WFF f
((CQC-WFF f),y0) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),y0)) is Element of bool (bound_QC-variables f)
((CQC-WFF f),y0) ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f) is set
[:(f),Proof_Step_Kinds:] is Relation-like set
f1 is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len f1 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . (len f1) is set
(f1 . (len f1)) `1 is set
F is set
[:NAT,(CQC-WFF f):] is Relation-like non empty non trivial non finite set
bool [:NAT,(CQC-WFF f):] is non empty non trivial non finite set
[:(bool [:NAT,(CQC-WFF f):]),NAT:] is Relation-like non empty non trivial non finite set
[(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9] is V22() Element of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
{(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9} is non empty finite V37() set
{(((CQC-WFF f),y0) ^ <*(All (x,p))*>)} is functional non empty trivial finite V37() 1 -element set
{{(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9},{(((CQC-WFF f),y0) ^ <*(All (x,p))*>)}} is non empty finite V37() set
<*[(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9]*> is Relation-like NAT -defined [:(bool [:NAT,(CQC-WFF f):]),NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of [:(bool [:NAT,(CQC-WFF f):]),NAT:]
rng <*[(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9]*> is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
bool [:(bool [:NAT,(CQC-WFF f):]),NAT:] is non empty non trivial non finite set
{[(((CQC-WFF f),y0) ^ <*(All (x,p))*>),9]} is Relation-like bool [:NAT,(CQC-WFF f):] -defined NAT -valued Function-like constant non empty trivial finite 1 -element Element of bool [:(bool [:NAT,(CQC-WFF f):]),NAT:]
F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
dom F is finite Element of bool NAT
f1 ^ F is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
a is Relation-like NAT -defined [:(f),Proof_Step_Kinds:] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:(f),Proof_Step_Kinds:]
len a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom a is finite Element of bool NAT
dom f1 is finite Element of bool NAT
a . (len f1) is set
(a . (len f1)) `1 is set
k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len f1) + k is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F . k is set
(F . k) `1 is set
a . a is set
(a . a) `1 is set
(F . k) `2 is set
(a . a) `2 is set
a . (len a) is set
len F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f1) + (len F) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
a . ((len f1) + (len F)) is set
(len f1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
a . ((len f1) + 1) is set
F . 1 is set
(a . (len a)) `1 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
'not' (f,x) is Element of CQC-WFF f
<*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>)) is Element of CQC-WFF f
(((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((CQC-WFF f),x) ^ <*('not' (f,x))*>)) is Element of CQC-WFF f
(f,((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*('not' (f,x))*>)) is Element of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*('not' (f,x))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((CQC-WFF f),x) ^ <*('not' (f,x))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (f,((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>)) is Element of CQC-WFF f
len ((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f,((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>))) is Element of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' p)*>) ^ <*(f,x)*>))) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,x) is Element of CQC-WFF f
'not' (f,x) is Element of CQC-WFF f
<*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) is finite Element of bool NAT
len ((CQC-WFF f),x) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),x)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(((CQC-WFF f),x) ^ <*('not' (f,x))*>) . ((len ((CQC-WFF f),x)) + 1) is set
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) . ((len ((CQC-WFF f),x)) + 1) is set
(f,((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) is Element of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>)) . (len ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*('not' (f,x))*>))) is set
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*('not' (f,x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) is Element of CQC-WFF f
'not' (f,((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) is Element of CQC-WFF f
<*('not' (f,((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*('not' (f,((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*p*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (x ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f,((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>))) is Element of CQC-WFF f
((CQC-WFF f),(x ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(x ^ <*p*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(x ^ <*p*>))) is Element of CQC-WFF f
((CQC-WFF f),(((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*>))) is Element of CQC-WFF f
len ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len ((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>))) + (len <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(x ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((CQC-WFF f),((((CQC-WFF f),x) ^ <*('not' (f,x))*>) ^ <*(f,x)*>)) ^ <*p*>)) is Element of CQC-WFF f
(f,(x ^ <*p*>)) is Element of CQC-WFF f
<*(f,(x ^ <*p*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(x ^ <*p*>))) ^ <*(f,(x ^ <*p*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),x) ^ <*(f,(x ^ <*p*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' x)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*p*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x)*> ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ (<*('not' x)*> ^ <*p*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x),p*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x),p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*('not' x)*>)) . ((len f) + 1) is set
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,((f ^ <*p*>) ^ <*x*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) is Element of CQC-WFF f
len (((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f,((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*p*>) ^ <*x*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom <*('not' x),p*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*('not' x)*>)) is finite Element of bool NAT
'not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) is Element of CQC-WFF f
<*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x)*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ (<*('not' x)*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x),('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x),('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(len f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) . ((len f) + 2) is set
dom <*('not' x),('not' p)*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is finite Element of bool NAT
((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>))) is Element of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' p)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' p)*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*x*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((f ^ <*('not' p)*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*x*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ (<*x*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x,('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x,('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) . ((len f) + 1) is set
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) is Element of CQC-WFF f
dom <*x,('not' p)*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) is finite Element of bool NAT
(f,(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>)) is Element of CQC-WFF f
'not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) is Element of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ (<*x*> ^ <*p*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x,p*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x,p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(len f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>)) . ((len f) + 2) is set
dom <*x,p*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>)) is finite Element of bool NAT
((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' x)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' p)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' x)*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x)*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ (<*('not' x)*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x),('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x),('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) . ((len f) + 1) is set
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
dom <*('not' x),('not' p)*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*('not' x)*>)) is finite Element of bool NAT
(f,((f ^ <*('not' p)*>) ^ <*x*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) is Element of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f,((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
'not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) is Element of CQC-WFF f
<*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x)*> ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ (<*('not' x)*> ^ <*p*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x),p*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x),p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(len f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>)) . ((len f) + 2) is set
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>)) is Element of CQC-WFF f
dom <*('not' x),p*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>)) is finite Element of bool NAT
((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
(f,(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*('not' p)*>) ^ <*x*>)) ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*x*>))) ^ <*('not' x)*>) ^ <*p*>) ^ <*p*>))) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*x*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((f ^ <*p*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*x*> ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ (<*x*> ^ <*p*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x,p*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x,p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) . ((len f) + 1) is set
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) is Element of CQC-WFF f
dom <*x,p*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) is finite Element of bool NAT
(f,(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>)) is Element of CQC-WFF f
(f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
'not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) is Element of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ (<*x*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x,('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x,('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
(len f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) . ((len f) + 2) is set
dom <*x,('not' p)*> is non empty finite 2 -element Element of bool NAT
dom ((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is finite Element of bool NAT
((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>))) is Element of CQC-WFF f
len (((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*('not' x)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' (f,(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*p*>) ^ <*x*>)) ^ <*('not' p)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((((CQC-WFF f),((CQC-WFF f),((f ^ <*p*>) ^ <*('not' x)*>))) ^ <*x*>) ^ <*('not' p)*>) ^ <*('not' p)*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Element of CQC-WFF f
<*f*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p 'or' f is Element of CQC-WFF f
<*(p 'or' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*p*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*f*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*f*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*(p 'or' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*(p 'or' f)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' x)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' f is Element of CQC-WFF f
<*('not' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' x)*>) ^ <*('not' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((y0 ^ <*('not' x)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
(f,((y0 ^ <*('not' x)*>) ^ <*('not' f)*>)) is Element of CQC-WFF f
((CQC-WFF f),((y0 ^ <*('not' x)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((y0 ^ <*('not' x)*>) ^ <*('not' f)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' p) '&' ('not' f) is Element of CQC-WFF f
<*(('not' p) '&' ('not' f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' x)*>) ^ <*(('not' p) '&' ('not' f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (('not' p) '&' ('not' f)) is Element of CQC-WFF f
<*('not' (('not' p) '&' ('not' f)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*('not' (('not' p) '&' ('not' f)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' (('not' p) '&' ('not' f)))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
p 'or' x is Element of CQC-WFF f
<*(p 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(p 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
'not' x is Element of CQC-WFF f
('not' p) '&' ('not' x) is Element of CQC-WFF f
<*(('not' p) '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(('not' p) '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*(('not' p) '&' ('not' x))*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len f) + (len <*(('not' p) '&' ('not' x))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*>)) is finite Element of bool NAT
(f,((f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*>)) is Element of CQC-WFF f
((CQC-WFF f),((f ^ <*(('not' p) '&' ('not' x))*>) ^ <*(('not' p) '&' ('not' x))*>)) . ((len f) + 1) is set
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(('not' p) '&' ('not' x))*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (('not' p) '&' ('not' x)) is Element of CQC-WFF f
<*('not' (('not' p) '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*('not' (('not' p) '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*(p 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (f ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(f ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(f ^ <*p*>)) ^ <*(p 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
x 'or' p is Element of CQC-WFF f
<*(x 'or' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(x 'or' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' x is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
('not' x) '&' ('not' p) is Element of CQC-WFF f
<*(('not' x) '&' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(('not' x) '&' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*(('not' x) '&' ('not' p))*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len f) + (len <*(('not' x) '&' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*>)) is finite Element of bool NAT
(f,((f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*>)) is Element of CQC-WFF f
((CQC-WFF f),((f ^ <*(('not' x) '&' ('not' p))*>) ^ <*(('not' x) '&' ('not' p))*>)) . ((len f) + 1) is set
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(('not' x) '&' ('not' p))*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (('not' x) '&' ('not' p)) is Element of CQC-WFF f
<*('not' (('not' x) '&' ('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*('not' (('not' x) '&' ('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*p*>) ^ <*(x 'or' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (f ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(f ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(f ^ <*p*>)) ^ <*(x 'or' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Element of CQC-WFF f
<*f*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p 'or' f is Element of CQC-WFF f
<*(p 'or' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*p*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*f*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*f*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*(p 'or' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*(p 'or' f)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' x)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' f is Element of CQC-WFF f
<*('not' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' x)*>) ^ <*('not' f)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((y0 ^ <*('not' x)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((y0 ^ <*('not' x)*>) ^ <*('not' f)*>)) is Element of CQC-WFF f
(f,((y0 ^ <*('not' x)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
((CQC-WFF f),((y0 ^ <*('not' x)*>) ^ <*('not' f)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' p) '&' ('not' f) is Element of CQC-WFF f
<*(('not' p) '&' ('not' f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((y0 ^ <*('not' x)*>) ^ <*('not' p)*>)) ^ <*(('not' p) '&' ('not' f))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (('not' p) '&' ('not' f)) is Element of CQC-WFF f
<*('not' (('not' p) '&' ('not' f)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 ^ <*('not' (('not' p) '&' ('not' f)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(y0 ^ <*('not' (('not' p) '&' ('not' f)))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
<*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(x ^ <*p*>) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(x ^ <*p*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) is Element of CQC-WFF f
len (((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p*> ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
x ^ (<*p*> ^ <*('not' ('not' p))*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p,('not' ('not' p))*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
x ^ <*p,('not' ('not' p))*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
((CQC-WFF f),(((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>))) is Element of CQC-WFF f
<*p*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ (<*p*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p,('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
x ^ <*p,('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len x) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*p,('not' p)*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*p,('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) is finite Element of bool NAT
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) . ((len x) + 1) is set
len (((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
<*(f,(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*(f,(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (x ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*p,('not' ('not' p))*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*p,('not' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>)) is finite Element of bool NAT
len ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is finite Element of bool NAT
'not' (f,(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) . ((len x) + 2) is set
(f,(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>)) is Element of CQC-WFF f
(f,(((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>)) is Element of CQC-WFF f
((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>)) . ((len x) + 2) is set
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' ('not' p))*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((x ^ <*p*>) ^ <*('not' ('not' p))*>) ^ <*('not' ('not' p))*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(x ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(x ^ <*p*>)) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
<*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(x ^ <*('not' ('not' p))*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(x ^ <*('not' ('not' p))*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
len (((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
<*('not' ('not' p))*> ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
x ^ (<*('not' ('not' p))*> ^ <*('not' p)*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' ('not' p)),('not' p)*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
x ^ <*('not' ('not' p)),('not' p)*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
len x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len x) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*('not' ('not' p)),('not' p)*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*('not' ('not' p)),('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is finite Element of bool NAT
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) . ((len x) + 2) is set
len (((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len x) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) is finite Element of bool NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len (((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(f,(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) is Element of CQC-WFF f
<*(f,(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) ^ <*(f,(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (x ^ <*('not' ('not' p))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' ('not' p))*> ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x ^ (<*('not' ('not' p))*> ^ <*p*>) is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' ('not' p)),p*> is Relation-like NAT -defined Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
x ^ <*('not' ('not' p)),p*> is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like set
((CQC-WFF f),(((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*>))) is Element of CQC-WFF f
(f,((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
'not' (f,((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>))) is Element of CQC-WFF f
len <*('not' ('not' p)),p*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len x) + (len <*('not' ('not' p)),p*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>)) is finite Element of bool NAT
'not' (f,(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' ('not' p))*>)) . ((len x) + 1) is set
(f,(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>)) is Element of CQC-WFF f
(f,(((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>)) . ((len x) + 2) is set
((CQC-WFF f),((CQC-WFF f),(((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*('not' p)*>) ^ <*('not' p)*>)) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((CQC-WFF f),(((x ^ <*('not' ('not' p))*>) ^ <*p*>) ^ <*p*>))) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(x ^ <*('not' ('not' p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(x ^ <*('not' ('not' p))*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
x is Element of CQC-WFF f
p => x is Element of CQC-WFF f
<*(p => x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(p => x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*x*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
<*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' p)*>) ^ <*('not' p)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' p)*>) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f ^ <*p*>)) is Element of CQC-WFF f
(f,((f ^ <*('not' p)*>) ^ <*p*>)) is Element of CQC-WFF f
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((f ^ <*('not' p)*>) ^ <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((f ^ <*x*>) ^ <*x*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),((f ^ <*x*>) ^ <*x*>)) . ((len f) + 1) is set
len <*x*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len f) + (len <*x*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*x*>) ^ <*x*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((f ^ <*x*>) ^ <*x*>)) is finite Element of bool NAT
(f,((f ^ <*x*>) ^ <*x*>)) is Element of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' p)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len <*('not' p)*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len f) + (len <*('not' p)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' p)*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' p)*>)) is finite Element of bool NAT
(f,((f ^ <*('not' p)*>) ^ <*('not' p)*>)) is Element of CQC-WFF f
'not' (f,((f ^ <*('not' p)*>) ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*('not' p)*>)) . ((len f) + 1) is set
<*('not' (f,((f ^ <*('not' p)*>) ^ <*p*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*p*>)) ^ <*('not' (f,((f ^ <*('not' p)*>) ^ <*p*>)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(f ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' p)*>) ^ <*p*>)) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' p) 'or' x is Element of CQC-WFF f
<*(('not' p) 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(('not' p) 'or' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(('not' p) 'or' x)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
'not' x is Element of CQC-WFF f
('not' ('not' p)) '&' ('not' x) is Element of CQC-WFF f
'not' (('not' ('not' p)) '&' ('not' x)) is Element of CQC-WFF f
<*('not' (('not' ('not' p)) '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' (('not' ('not' p)) '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' (('not' ('not' p)) '&' ('not' x)))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*(('not' ('not' p)) '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*p*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*p*>)) is Element of CQC-WFF f
((CQC-WFF f),(((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*('not' x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*('not' x)*>)) is Element of CQC-WFF f
(f,((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) is Element of CQC-WFF f
<*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*('not' ('not' p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p '&' ('not' x) is Element of CQC-WFF f
<*(p '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*('not' x)*>) ^ <*(('not' ('not' p)) '&' ('not' x))*>)) ^ <*(p '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' x)*>) ^ <*(p '&' ('not' x))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (p '&' ('not' x)) is Element of CQC-WFF f
<*('not' (p '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' (p '&' ('not' x)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*('not' (p '&' ('not' x)))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(p => x)*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (f ^ <*(p => x)*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(f ^ <*(p => x)*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(f ^ <*(p => x)*>)) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
x is Element of bound_QC-variables f
f is Element of bound_QC-variables f
('not' p) . (x,f) is Element of CQC-WFF f
p . (x,f) is Element of CQC-WFF f
'not' (p . (x,f)) is Element of CQC-WFF f
Sbst (x,f) is Relation-like bound_QC-variables f -defined {x} -defined bound_QC-variables f -valued Function-like one-to-one finite Element of vSUB f
{x} is non empty trivial finite 1 -element set
vSUB f is set
{x} --> f is Relation-like {x} -defined bound_QC-variables f -valued {f} -valued Function-like constant non empty V14({x}) V30({x},{f}) finite Element of bool [:{x},{f}:]
{f} is non empty trivial finite 1 -element set
[:{x},{f}:] is Relation-like non empty finite set
bool [:{x},{f}:] is non empty finite V37() set
[p,(Sbst (x,f))] is V22() Element of CQC-Sub-WFF f
QC-Sub-WFF f is non empty set
CQC-Sub-WFF f is Element of bool (QC-Sub-WFF f)
bool (QC-Sub-WFF f) is non empty set
{p,(Sbst (x,f))} is non empty finite set
{p} is non empty trivial finite 1 -element set
{{p,(Sbst (x,f))},{p}} is non empty finite V37() set
[p,(Sbst (x,f))] `1 is Element of CQC-WFF f
[p,(Sbst (x,f))] `2 is Element of vSUB f
[('not' p),(Sbst (x,f))] is V22() Element of CQC-Sub-WFF f
{('not' p),(Sbst (x,f))} is non empty finite set
{('not' p)} is non empty trivial finite 1 -element set
{{('not' p),(Sbst (x,f))},{('not' p)}} is non empty finite V37() set
CQC_Sub [('not' p),(Sbst (x,f))] is Element of CQC-WFF f
Sub_not [p,(Sbst (x,f))] is Element of CQC-Sub-WFF f
CQC_Sub [p,(Sbst (x,f))] is Element of CQC-WFF f
'not' (CQC_Sub [p,(Sbst (x,f))]) is Element of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of bound_QC-variables f
Ex (x,p) is Element of CQC-WFF f
<*(Ex (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(Ex (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Element of bound_QC-variables f
p . (x,y0) is Element of CQC-WFF f
<*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
All (x,('not' p)) is Element of CQC-WFF f
<*(All (x,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len <*(All (x,('not' p)))*> is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
(len f) + (len <*(All (x,('not' p)))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
len ((CQC-WFF f),((f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*>)) is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom ((CQC-WFF f),((f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*>)) is finite Element of bool NAT
(f,((f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*>)) is Element of CQC-WFF f
((CQC-WFF f),((f ^ <*(All (x,('not' p)))*>) ^ <*(All (x,('not' p)))*>)) . ((len f) + 1) is set
('not' p) . (x,y0) is Element of CQC-WFF f
<*(('not' p) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(All (x,('not' p)))*>) ^ <*(('not' p) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (p . (x,y0)) is Element of CQC-WFF f
<*('not' (p . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(All (x,('not' p)))*>) ^ <*('not' (p . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (All (x,('not' p))) is Element of CQC-WFF f
<*('not' (All (x,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(p . (x,y0))*>) ^ <*('not' (All (x,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f ^ <*(p . (x,y0))*>) ^ <*(Ex (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
len (f ^ <*(p . (x,y0))*>) is non empty epsilon-transitive epsilon-connected ordinal natural ext-real positive non negative V28() V29() finite cardinal Element of NAT
((CQC-WFF f),(f ^ <*(p . (x,y0))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),(f ^ <*(p . (x,y0))*>)) ^ <*(Ex (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p ^ x is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(p ^ x)) is Element of bool (bound_QC-variables f)
(f,x) is Element of bool (bound_QC-variables f)
(f,p) \/ (f,x) is Element of bool (bound_QC-variables f)
f is set
dom (p ^ x) is finite Element of bool NAT
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Element of CQC-WFF f
(p ^ x) . y0 is set
still_not-bound_in f1 is Element of bool (bound_QC-variables f)
dom x is finite Element of bool NAT
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
(len p) + F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
x . F is set
dom p is finite Element of bool NAT
p . y0 is set
f is set
dom x is finite Element of bool NAT
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Element of CQC-WFF f
x . y0 is set
still_not-bound_in f1 is Element of bool (bound_QC-variables f)
len p is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
(len p) + y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
dom (p ^ x) is finite Element of bool NAT
(p ^ x) . ((len p) + y0) is set
dom p is finite Element of bool NAT
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Element of CQC-WFF f
p . y0 is set
still_not-bound_in f1 is Element of bool (bound_QC-variables f)
(p ^ x) . y0 is set
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
p is Element of CQC-WFF f
<*p*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,<*p*>) is Element of bool (bound_QC-variables f)
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
bool (bound_QC-variables f) is non empty set
still_not-bound_in p is Element of bool (bound_QC-variables f)
dom <*p*> is non empty trivial finite 1 -element Element of bool NAT
<*p*> . 1 is set
x is set
x is set
f is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
y0 is Element of CQC-WFF f
<*p*> . f is set
still_not-bound_in y0 is Element of bool (bound_QC-variables f)
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
x is Element of CQC-WFF f
<*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Element of bound_QC-variables f
Ex (f,p) is Element of CQC-WFF f
<*(Ex (f,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
y0 is Element of bound_QC-variables f
p . (f,y0) is Element of CQC-WFF f
<*(p . (f,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 ^ <*(p . (f,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*(p . (f,y0))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 ^ <*(Ex (f,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*(Ex (f,p))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((f1 ^ <*(Ex (f,p))*>) ^ <*x*>)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
'not' x is Element of CQC-WFF f
<*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 ^ <*('not' x)*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' p is Element of CQC-WFF f
('not' p) . (f,y0) is Element of CQC-WFF f
<*(('not' p) . (f,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*('not' x)*>) ^ <*(('not' p) . (f,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (p . (f,y0)) is Element of CQC-WFF f
<*('not' (p . (f,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*('not' x)*>) ^ <*('not' (p . (f,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f1 ^ <*(Ex (f,p))*>)) is Element of bool (bound_QC-variables f)
(f,<*x*>) is Element of bool (bound_QC-variables f)
(f,(f1 ^ <*(Ex (f,p))*>)) \/ (f,<*x*>) is Element of bool (bound_QC-variables f)
(f,f1) is Element of bool (bound_QC-variables f)
(f,<*(Ex (f,p))*>) is Element of bool (bound_QC-variables f)
(f,f1) \/ (f,<*(Ex (f,p))*>) is Element of bool (bound_QC-variables f)
still_not-bound_in (Ex (f,p)) is Element of bool (bound_QC-variables f)
still_not-bound_in p is Element of bool (bound_QC-variables f)
{f} is non empty trivial finite 1 -element Element of bool (bound_QC-variables f)
(still_not-bound_in p) \ {f} is Element of bool (bound_QC-variables f)
still_not-bound_in ('not' p) is Element of bool (bound_QC-variables f)
(still_not-bound_in ('not' p)) \ {f} is Element of bool (bound_QC-variables f)
All (f,('not' p)) is Element of CQC-WFF f
still_not-bound_in (All (f,('not' p))) is Element of bool (bound_QC-variables f)
still_not-bound_in x is Element of bool (bound_QC-variables f)
still_not-bound_in ('not' x) is Element of bool (bound_QC-variables f)
(f,<*('not' x)*>) is Element of bool (bound_QC-variables f)
(f,f1) \/ (f,<*('not' x)*>) is Element of bool (bound_QC-variables f)
(f,(f1 ^ <*('not' x)*>)) is Element of bool (bound_QC-variables f)
((CQC-WFF f),((f1 ^ <*('not' x)*>) ^ <*(('not' p) . (f,y0))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),((f1 ^ <*('not' x)*>) ^ <*(('not' p) . (f,y0))*>))) is Element of bool (bound_QC-variables f)
(f,((f1 ^ <*('not' x)*>) ^ <*(('not' p) . (f,y0))*>)) is Element of CQC-WFF f
<*(All (f,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
((CQC-WFF f),((f1 ^ <*('not' x)*>) ^ <*(('not' p) . (f,y0))*>)) ^ <*(All (f,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*('not' x)*>) ^ <*(All (f,('not' p)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (All (f,('not' p))) is Element of CQC-WFF f
<*('not' (All (f,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f1 ^ <*('not' (All (f,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f1 ^ <*('not' (All (f,('not' p))))*>) ^ <*x*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of bool (bound_QC-variables f)
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
bool (bound_QC-variables f) is non empty set
dom p is finite Element of bool NAT
{ (still_not-bound_in b₁) where b₁ is Element of CQC-WFF f : ex b₂ being epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT st
( b₂ in dom p & b₁ = p . b₂ ) } is set
union { (still_not-bound_in b₁) where b₁ is Element of CQC-WFF f : ex b₂ being epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT st
( b₂ in dom p & b₁ = p . b₂ ) } is set
f is set
y0 is set
f1 is Element of CQC-WFF f
still_not-bound_in f1 is Element of bool (bound_QC-variables f)
F is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p . F is set
f is set
y0 is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 is Element of CQC-WFF f
p . y0 is set
still_not-bound_in f1 is Element of bool (bound_QC-variables f)
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of bool (bound_QC-variables f)
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
bool (bound_QC-variables f) is non empty set
dom p is finite Element of bool NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal set
Seg x is finite x -element Element of bool NAT
{ (still_not-bound_in b₁) where b₁ is Element of CQC-WFF f : ex b₂ being epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT st
( b₂ in dom p & b₁ = p . b₂ ) } is set
y0 is Relation-like Function-like set
proj2 y0 is set
proj1 y0 is set
f1 is set
F is Element of CQC-WFF f
still_not-bound_in F is Element of bool (bound_QC-variables f)
b is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p . b is set
f1 is set
p . f1 is set
rng p is finite Element of bool (CQC-WFF f)
bool (CQC-WFF f) is non empty set
F is Element of CQC-WFF f
still_not-bound_in F is Element of bool (bound_QC-variables f)
f1 is Relation-like Function-like set
proj1 f1 is set
y0 * f1 is Relation-like Function-like set
b is set
a is Element of CQC-WFF f
still_not-bound_in a is Element of bool (bound_QC-variables f)
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p . a is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
p . a is set
f1 . a is set
proj2 f1 is set
k is Element of CQC-WFF f
still_not-bound_in k is Element of bool (bound_QC-variables f)
proj2 (y0 * f1) is set
b is set
a is set
f1 . a is set
a is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f1 . a is set
p . a is set
k is Element of CQC-WFF f
still_not-bound_in k is Element of bool (bound_QC-variables f)
proj1 (y0 * f1) is set
union { (still_not-bound_in b₁) where b₁ is Element of CQC-WFF f : ex b₂ being epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT st
( b₂ in dom p & b₁ = p . b₂ ) } is set
f is Relation-like non empty QC-alphabet
bound_QC-variables f is non empty Element of bool (QC-variables f)
QC-variables f is non empty set
bool (QC-variables f) is non empty set
len (bound_QC-variables f) is non empty epsilon-transitive epsilon-connected ordinal cardinal set
QC-symbols f is non empty set
len (QC-symbols f) is non empty epsilon-transitive epsilon-connected ordinal cardinal set
{4} is non empty trivial finite V37() 1 -element Element of bool NAT
[:{4},(QC-symbols f):] is Relation-like non empty set
[:(QC-symbols f),{4}:] is Relation-like non empty set
len [:(QC-symbols f),{4}:] is non empty epsilon-transitive epsilon-connected ordinal cardinal set
f is Relation-like non empty QC-alphabet
CQC-WFF f is non empty Element of bool (QC-WFF f)
QC-WFF f is non empty set
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,p) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
x is set
f is set
x is set
f is Element of bound_QC-variables f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
<*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
All (x,('not' ('not' p))) is Element of CQC-WFF f
<*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f ^ <*(All (x,p))*>)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
y0 is Element of bound_QC-variables f
((CQC-WFF f),(f ^ <*(All (x,p))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f ^ <*(All (x,p))*>)) is Element of CQC-WFF f
p . (x,y0) is Element of CQC-WFF f
<*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (p . (x,y0)) is Element of CQC-WFF f
'not' ('not' (p . (x,y0))) is Element of CQC-WFF f
<*('not' ('not' (p . (x,y0))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' ('not' (p . (x,y0))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' p) . (x,y0) is Element of CQC-WFF f
'not' (('not' p) . (x,y0)) is Element of CQC-WFF f
<*('not' (('not' p) . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' (('not' p) . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' ('not' p)) . (x,y0) is Element of CQC-WFF f
<*(('not' ('not' p)) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(('not' ('not' p)) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of bool (bound_QC-variables f)
(f,<*(All (x,p))*>) is Element of bool (bound_QC-variables f)
(f,f) \/ (f,<*(All (x,p))*>) is Element of bool (bound_QC-variables f)
((CQC-WFF f),(f ^ <*(('not' ('not' p)) . (x,y0))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(f ^ <*(('not' ('not' p)) . (x,y0))*>))) is Element of bool (bound_QC-variables f)
still_not-bound_in (All (x,p)) is Element of bool (bound_QC-variables f)
still_not-bound_in p is Element of bool (bound_QC-variables f)
{x} is non empty trivial finite 1 -element Element of bool (bound_QC-variables f)
(still_not-bound_in p) \ {x} is Element of bool (bound_QC-variables f)
still_not-bound_in ('not' p) is Element of bool (bound_QC-variables f)
(still_not-bound_in ('not' p)) \ {x} is Element of bool (bound_QC-variables f)
still_not-bound_in ('not' ('not' p)) is Element of bool (bound_QC-variables f)
(still_not-bound_in ('not' ('not' p))) \ {x} is Element of bool (bound_QC-variables f)
still_not-bound_in (All (x,('not' ('not' p)))) is Element of bool (bound_QC-variables f)
(f,(f ^ <*(('not' ('not' p)) . (x,y0))*>)) is Element of CQC-WFF f
((CQC-WFF f),(f ^ <*(('not' ('not' p)) . (x,y0))*>)) ^ <*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,('not' ('not' p))) is Element of CQC-WFF f
<*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
All (x,p) is Element of CQC-WFF f
<*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f ^ <*(All (x,p))*>)) is Element of bool (bound_QC-variables f)
bool (bound_QC-variables f) is non empty set
y0 is Element of bound_QC-variables f
((CQC-WFF f),(f ^ <*(All (x,('not' ('not' p))))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,(f ^ <*(All (x,('not' ('not' p))))*>)) is Element of CQC-WFF f
('not' ('not' p)) . (x,y0) is Element of CQC-WFF f
<*(('not' ('not' p)) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(('not' ('not' p)) . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
('not' p) . (x,y0) is Element of CQC-WFF f
'not' (('not' p) . (x,y0)) is Element of CQC-WFF f
<*('not' (('not' p) . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' (('not' p) . (x,y0)))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
p . (x,y0) is Element of CQC-WFF f
'not' (p . (x,y0)) is Element of CQC-WFF f
'not' ('not' (p . (x,y0))) is Element of CQC-WFF f
<*('not' ('not' (p . (x,y0))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' ('not' (p . (x,y0))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(p . (x,y0))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,f) is Element of bool (bound_QC-variables f)
(f,<*(All (x,p))*>) is Element of bool (bound_QC-variables f)
(f,f) \/ (f,<*(All (x,p))*>) is Element of bool (bound_QC-variables f)
((CQC-WFF f),(f ^ <*(p . (x,y0))*>)) is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
(f,((CQC-WFF f),(f ^ <*(p . (x,y0))*>))) is Element of bool (bound_QC-variables f)
still_not-bound_in (All (x,p)) is Element of bool (bound_QC-variables f)
(f,(f ^ <*(p . (x,y0))*>)) is Element of CQC-WFF f
((CQC-WFF f),(f ^ <*(p . (x,y0))*>)) ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like non empty QC-alphabet
QC-WFF f is non empty set
CQC-WFF f is non empty Element of bool (QC-WFF f)
bool (QC-WFF f) is non empty set
QC-variables f is non empty set
bound_QC-variables f is non empty Element of bool (QC-variables f)
bool (QC-variables f) is non empty set
p is Element of CQC-WFF f
'not' p is Element of CQC-WFF f
x is Element of bound_QC-variables f
All (x,p) is Element of CQC-WFF f
<*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
Ex (x,('not' p)) is Element of CQC-WFF f
'not' (Ex (x,('not' p))) is Element of CQC-WFF f
<*('not' (Ex (x,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined CQC-WFF f -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,p))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' (Ex (x,('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
All (x,('not' ('not' p))) is Element of CQC-WFF f
<*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' (All (x,('not' ('not' p)))) is Element of CQC-WFF f
'not' ('not' (All (x,('not' ('not' p))))) is Element of CQC-WFF f
<*('not' ('not' (All (x,('not' ('not' p))))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' ('not' (All (x,('not' ('not' p))))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
'not' ('not' p) is Element of CQC-WFF f
All (x,('not' ('not' p))) is Element of CQC-WFF f
'not' (All (x,('not' ('not' p)))) is Element of CQC-WFF f
'not' ('not' (All (x,('not' ('not' p))))) is Element of CQC-WFF f
<*('not' ('not' (All (x,('not' ('not' p))))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*('not' ('not' (All (x,('not' ('not' p))))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
<*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f ^ <*(All (x,('not' ('not' p))))*> is Relation-like NAT -defined CQC-WFF f -valued Function-like non empty finite FinSequence-like FinSubsequence-like FinSequence of CQC-WFF f
f is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
p is set
dom f is finite Element of bool NAT
x is epsilon-transitive epsilon-connected ordinal natural ext-real non negative V28() V29() finite cardinal Element of NAT
f . x is set