:: SUBSTUT1 semantic presentation

REAL is V45() V46() V47() V51() set
NAT is non empty non trivial V21() V22() V23() V45() V46() V47() V48() V49() V50() V51() non finite cardinal limit_cardinal V94() V95() Element of bool REAL
bool REAL is non empty set
COMPLEX is V45() V51() set
RAT is V45() V46() V47() V48() V51() set
INT is V45() V46() V47() V48() V49() V51() set
NAT is non empty non trivial V21() V22() V23() V45() V46() V47() V48() V49() V50() V51() non finite cardinal limit_cardinal V94() V95() set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
[:COMPLEX,COMPLEX:] is set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is set
bool [:COMPLEX,REAL:] is non empty set
{} is Function-like functional empty ext-real non positive non negative V21() V22() V23() V25() V26() V27() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() set
1 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
2 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
3 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
Seg 1 is non empty trivial V45() V46() V47() V48() V49() V50() finite 1 -element V94() Element of bool NAT
0 is Function-like functional empty ext-real non positive non negative V21() V22() V23() V25() V26() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() Element of NAT
[0,0] is V15() set
{0,0} is non empty V45() V46() V47() V48() V49() V50() finite V56() V94() set
{0} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
{{0,0},{0}} is non empty finite V56() V94() set
<*[0,0]*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() set
[1,0] is V15() set
{1,0} is non empty V45() V46() V47() V48() V49() V50() finite V56() V94() set
{1} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
{{1,0},{1}} is non empty finite V56() V94() set
<*[1,0]*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() set
[2,0] is V15() set
{2,0} is non empty V45() V46() V47() V48() V49() V50() finite V56() V94() set
{2} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
{{2,0},{2}} is non empty finite V56() V94() set
<*[2,0]*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() set
[3,0] is V15() set
{3,0} is non empty V45() V46() V47() V48() V49() V50() finite V56() V94() set
{3} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
{{3,0},{3}} is non empty finite V56() V94() set
<*[3,0]*> is Relation-like NAT -defined Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() set
card NAT is non empty non trivial V21() V22() V23() non finite cardinal set
A is Relation-like non empty QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
6 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{6} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
[:{6},NAT:] is non empty non trivial non finite set
4 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
5 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{4,5} is non empty V45() V46() V47() V48() V49() V50() finite V56() V94() set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
{4} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
A is Relation-like non empty QC-alphabet
(A) is set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
A is Relation-like non empty QC-alphabet
(A) is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like Function-like Element of (A)
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is set
SQ is Relation-like Function-like Element of (A)
proj1 SQ is set
SQ . S is set
(A,SQ) is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
dom (A,SQ) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Relation-like Function-like Element of (A)
proj1 SQ is set
Seg (len S) is V45() V46() V47() V48() V49() V50() finite len S -element V94() Element of bool NAT
S9 is ext-real V21() V22() V23() V27() finite cardinal V94() set
S . S9 is set
SQ . (S . S9) is set
S9 is set
S9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
dom S9 is V45() V46() V47() V48() V49() V50() finite V94() Element of bool NAT
proj2 S9 is finite V94() set
S9 is set
l is set
S9 . l is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . l is set
S9 . l is set
SQ . (S . l) is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . l is set
dom S is V45() V46() V47() V48() V49() V50() finite V94() Element of bool NAT
rng S is finite V94() Element of bool (QC-variables A)
S9 . l is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . l is set
S9 . l is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . l is set
S9 . l is set
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . l is set
S9 . l is set
SQ . (S . l) is set
dom S is V45() V46() V47() V48() V49() V50() finite V94() Element of bool NAT
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l is ext-real V21() V22() V23() V27() finite cardinal V94() set
S . l is set
S9 . l is set
SQ . (S . l) is set
S9 . l is set
A is Relation-like non empty QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
S is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
rng S is finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
A is Relation-like non empty QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
(A,S) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
SQ is Relation-like Function-like Element of (A)
(A,(A,S),SQ) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len (A,(A,S),SQ) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
len (A,S) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
dom (A,(A,S),SQ) is V45() V46() V47() V48() V49() V50() finite V94() Element of bool NAT
Seg (len (A,S)) is V45() V46() V47() V48() V49() V50() finite len (A,S) -element V94() Element of bool NAT
proj1 SQ is set
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) . S9 is set
(A,(A,S),SQ) . S9 is set
SQ . ((A,S) . S9) is set
rng (A,(A,S),SQ) is finite V94() Element of bool (QC-variables A)
S9 is set
S9 is set
(A,(A,S),SQ) . S9 is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) . l is set
(A,(A,S),SQ) . l is set
SQ . ((A,S) . l) is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) . l is set
rng S is finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
dom (A,S) is V45() V46() V47() V48() V49() V50() finite V94() Element of bool NAT
rng (A,S) is finite V94() Element of bool (QC-variables A)
(A,(A,S),SQ) . l is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) . l is set
(A,(A,S),SQ) . l is set
l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) . l is set
(A,(A,S),SQ) . l is set
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like Function-like Element of (A)
SQ is set
S | SQ is Relation-like Function-like set
(A,S) is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
(A,S) | SQ is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Function-like functional empty ext-real non positive non negative V21() V22() V23() V25() V26() V27() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S9 is Relation-like Function-like Element of (A)
SQ is Element of QC-WFF A
still_not-bound_in SQ is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
proj1 S9 is set
S is Element of bound_QC-variables A
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in SQ & b₁ is Element of proj1 S9 & not b₁ = S & not b₁ = S9 . b₁ ) } is set
(A,S9, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in SQ & b₁ is Element of proj1 S9 & not b₁ = S & not b₁ = S9 . b₁ ) } ) is Relation-like Function-like Element of (A)
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ is Element of proj1 S9 & not b₁ = S & not b₁ = S9 . b₁ ) } is set
l is finite V94() set
l /\ { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ is Element of proj1 S9 & not b₁ = S & not b₁ = S9 . b₁ ) } is finite V94() set
s is set
P9 is Element of bound_QC-variables A
S9 . P9 is set
P9 is Element of bound_QC-variables A
S9 . P9 is set
s is finite V94() set
(A,S9,s) is Relation-like Function-like finite V94() Element of (A)
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
S is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
{ (S . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len S & S . b₁ in bound_QC-variables A ) } is set
bool (bound_QC-variables A) is non empty set
S9 is set
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . S9 is set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
[:(QC-WFF A),(bool (bound_QC-variables A)):] is non empty set
bool [:(QC-WFF A),(bool (bound_QC-variables A)):] is non empty set
S is Element of QC-WFF A
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
{} (bound_QC-variables A) is Function-like functional empty proper ext-real non positive non negative V21() V22() V23() V25() V26() V27() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
(A,(VERUM A)) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
{} (bound_QC-variables A) is Function-like functional empty proper ext-real non positive non negative V21() V22() V23() V25() V26() V27() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() Element of bool (bound_QC-variables A)
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
the_arguments_of S is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(A,(the_arguments_of S)) is Element of bool (bound_QC-variables A)
len (the_arguments_of S) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ ((the_arguments_of S) . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arguments_of S) & (the_arguments_of S) . b₁ in bound_QC-variables A ) } is set
the_argument_of S is Element of QC-WFF A
(A,(the_argument_of S)) is Element of bool (bound_QC-variables A)
the_left_argument_of S is Element of QC-WFF A
(A,(the_left_argument_of S)) is Element of bool (bound_QC-variables A)
the_right_argument_of S is Element of QC-WFF A
(A,(the_right_argument_of S)) is Element of bool (bound_QC-variables A)
(A,(the_left_argument_of S)) \/ (A,(the_right_argument_of S)) is Element of bool (bound_QC-variables A)
the_scope_of S is Element of QC-WFF A
(A,(the_scope_of S)) is Element of bool (bound_QC-variables A)
bound_in S is Element of bound_QC-variables A
{(bound_in S)} is non empty trivial finite 1 -element V94() Element of bool (bound_QC-variables A)
(A,(the_scope_of S)) \/ {(bound_in S)} is non empty Element of bool (bound_QC-variables A)
[:(QC-WFF A),(bool (bound_QC-variables A)):] is non empty set
bool [:(QC-WFF A),(bool (bound_QC-variables A)):] is non empty set
S9 is Element of bool (bound_QC-variables A)
S9 is Element of QC-WFF A
(A,S9) is Element of bool (bound_QC-variables A)
l is Element of bool (bound_QC-variables A)
s is Relation-like QC-WFF A -defined bool (bound_QC-variables A) -valued Function-like V29( QC-WFF A, bool (bound_QC-variables A)) Element of bool [:(QC-WFF A),(bool (bound_QC-variables A)):]
l is Element of QC-WFF A
s . l is Element of bool (bound_QC-variables A)
(A,l) is Element of bool (bound_QC-variables A)
H₂( the_scope_of S) \/ {(bound_in S)} is non empty Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
VERUM A is Element of CQC-WFF A
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
(A,(VERUM A)) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
{} (bound_QC-variables A) is Function-like functional empty proper ext-real non positive non negative V21() V22() V23() V25() V26() V27() V45() V46() V47() V48() V49() V50() V51() finite V56() cardinal {} -element FinSequence-membered V94() Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
the_arguments_of S is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(A,(the_arguments_of S)) is Element of bool (bound_QC-variables A)
len (the_arguments_of S) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ ((the_arguments_of S) . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arguments_of S) & (the_arguments_of S) . b₁ in bound_QC-variables A ) } is set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
the_argument_of S is Element of QC-WFF A
(A,(the_argument_of S)) is Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
the_left_argument_of S is Element of QC-WFF A
(A,(the_left_argument_of S)) is Element of bool (bound_QC-variables A)
the_right_argument_of S is Element of QC-WFF A
(A,(the_right_argument_of S)) is Element of bool (bound_QC-variables A)
(A,(the_left_argument_of S)) \/ (A,(the_right_argument_of S)) is Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
the_scope_of S is Element of QC-WFF A
(A,(the_scope_of S)) is Element of bool (bound_QC-variables A)
bound_in S is Element of bound_QC-variables A
{(bound_in S)} is non empty trivial finite 1 -element V94() Element of bool (bound_QC-variables A)
(A,(the_scope_of S)) \/ {(bound_in S)} is non empty Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
S is Element of QC-WFF A
(A,S) is Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
(A,(VERUM A)) is Element of bool (bound_QC-variables A)
SQ is Element of QC-WFF A
(A,SQ) is Element of bool (bound_QC-variables A)
the_argument_of SQ is Element of QC-WFF A
(A,(the_argument_of SQ)) is Element of bool (bound_QC-variables A)
the_left_argument_of SQ is Element of QC-WFF A
(A,(the_left_argument_of SQ)) is Element of bool (bound_QC-variables A)
the_right_argument_of SQ is Element of QC-WFF A
(A,(the_right_argument_of SQ)) is Element of bool (bound_QC-variables A)
the_scope_of SQ is Element of QC-WFF A
(A,(the_scope_of SQ)) is Element of bool (bound_QC-variables A)
the_arguments_of SQ is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len (the_arguments_of SQ) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(the_arguments_of SQ) . S9 is set
{ H₁(b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : S₃[b₁] } is set
{ H₁(b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : S₂[b₁] } is set
(A,(the_arguments_of SQ)) is Element of bool (bound_QC-variables A)
{ ((the_arguments_of SQ) . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arguments_of SQ) & (the_arguments_of SQ) . b₁ in bound_QC-variables A ) } is set
rng (the_arguments_of SQ) is finite V94() Element of bool (QC-variables A)
(A,(the_left_argument_of SQ)) \/ (A,(the_right_argument_of SQ)) is Element of bool (bound_QC-variables A)
bound_in SQ is Element of bound_QC-variables A
{(bound_in SQ)} is non empty trivial finite 1 -element V94() Element of bool (bound_QC-variables A)
(A,(the_scope_of SQ)) \/ {(bound_in SQ)} is non empty Element of bool (bound_QC-variables A)
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
QC-symbols A is non empty set
proj2 A is set
S is Element of QC-WFF A
(A,S) is finite V94() Element of bool (bound_QC-variables A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
bool (bound_QC-variables A) is non empty set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } is set
bool (QC-symbols A) is non empty set
S9 is set
S9 is Element of QC-symbols A
x. S9 is Element of bound_QC-variables A
[4,S9] is V15() set
{4,S9} is non empty finite V94() set
{{4,S9},{4}} is non empty finite V56() V94() set
S9 is set
S9 is Element of QC-symbols A
x. S9 is Element of bound_QC-variables A
[4,S9] is V15() set
{4,S9} is non empty finite V94() set
{{4,S9},{4}} is non empty finite V56() V94() set
S9 is Relation-like Function-like set
proj1 S9 is set
S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } is Relation-like Function-like set
proj2 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } ) is set
S9 is set
proj1 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } ) is set
l is set
(S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } ) . l is set
S9 . l is set
l is Element of QC-symbols A
x. l is Element of bound_QC-variables A
[4,l] is V15() set
{4,l} is non empty finite V94() set
{{4,l},{4}} is non empty finite V56() V94() set
s is Element of QC-symbols A
x. s is Element of bound_QC-variables A
[4,s] is V15() set
{4,s} is non empty finite V94() set
{{4,s},{4}} is non empty finite V56() V94() set
S9 is set
l is set
S9 . S9 is set
S9 . l is set
l is Element of QC-symbols A
x. l is Element of bound_QC-variables A
[4,l] is V15() set
{4,l} is non empty finite V94() set
{{4,l},{4}} is non empty finite V56() V94() set
s is Element of QC-symbols A
x. s is Element of bound_QC-variables A
[4,s] is V15() set
{4,s} is non empty finite V94() set
{{4,s},{4}} is non empty finite V56() V94() set
proj1 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } ) is set
S9 is Element of bool (QC-symbols A)
S9 | S9 is Relation-like Function-like set
proj1 (S9 | S9) is set
l is set
l is set
S9 /\ (QC-symbols A) is Element of bool (QC-symbols A)
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like Function-like finite V94() Element of (A)
proj2 S is finite V94() set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } is set
bool (QC-symbols A) is non empty set
S9 is set
S9 is Element of QC-symbols A
x. S9 is Element of bound_QC-variables A
[4,S9] is V15() set
{4,S9} is non empty finite V94() set
{{4,S9},{4}} is non empty finite V56() V94() set
S9 is set
S9 is Element of QC-symbols A
x. S9 is Element of bound_QC-variables A
[4,S9] is V15() set
{4,S9} is non empty finite V94() set
{{4,S9},{4}} is non empty finite V56() V94() set
S9 is Relation-like Function-like set
proj1 S9 is set
S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } is Relation-like Function-like set
proj2 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } ) is set
S9 is set
proj1 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } ) is set
l is set
(S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } ) . l is set
S9 . l is set
l is Element of QC-symbols A
x. l is Element of bound_QC-variables A
[4,l] is V15() set
{4,l} is non empty finite V94() set
{{4,l},{4}} is non empty finite V56() V94() set
s is Element of QC-symbols A
x. s is Element of bound_QC-variables A
[4,s] is V15() set
{4,s} is non empty finite V94() set
{{4,s},{4}} is non empty finite V56() V94() set
S9 is set
l is set
S9 . S9 is set
S9 . l is set
l is Element of QC-symbols A
x. l is Element of bound_QC-variables A
[4,l] is V15() set
{4,l} is non empty finite V94() set
{{4,l},{4}} is non empty finite V56() V94() set
s is Element of QC-symbols A
x. s is Element of bound_QC-variables A
[4,s] is V15() set
{4,s} is non empty finite V94() set
{{4,s},{4}} is non empty finite V56() V94() set
proj1 (S9 | { b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } ) is set
S9 is Element of bool (QC-symbols A)
S9 | S9 is Relation-like Function-like set
proj1 (S9 | S9) is set
l is set
l is set
S9 /\ (QC-symbols A) is Element of bool (QC-symbols A)
A is set
card A is V21() V22() V23() cardinal set
S is set
card S is V21() V22() V23() cardinal set
S \ A is Element of bool S
bool S is non empty set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Element of QC-WFF A
(A,S) is finite V94() Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty set
(A,S) is finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,S) } is set
SQ is Relation-like Function-like finite V94() Element of (A)
(A,SQ) is finite V94() Element of bool (QC-symbols A)
proj2 SQ is finite V94() set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 SQ } is set
(A,S) \/ (A,SQ) is finite V94() Element of bool (QC-symbols A)
NAT \ ((A,S) \/ (A,SQ)) is V45() V46() V47() V48() V49() V50() Element of bool REAL
card ((A,S) \/ (A,SQ)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
card NAT is non empty non trivial V21() V22() V23() non finite cardinal set
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
QC-WFF A is non empty set
SQ is Element of QC-WFF A
S is Relation-like Function-like finite V94() Element of (A)
(A,SQ,S) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty set
(A,SQ) is finite V94() Element of bool (QC-symbols A)
(A,SQ) is finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,SQ) } is set
(A,S) is finite V94() Element of bool (QC-symbols A)
proj2 S is finite V94() set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S } is set
(A,SQ) \/ (A,S) is finite V94() Element of bool (QC-symbols A)
NAT \ ((A,SQ) \/ (A,S)) is V45() V46() V47() V48() V49() V50() Element of bool REAL
the Element of (A,SQ,S) is Element of (A,SQ,S)
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S9 is Relation-like Function-like finite V94() Element of (A)
S is Element of bound_QC-variables A
SQ is Element of QC-WFF A
All (S,SQ) is Element of QC-WFF A
<*S*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*S*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
1 + 1 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
@ SQ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*S*>) ^ (@ SQ) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
proj2 S9 is finite V94() set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
(A,S9,SQ) is Element of QC-symbols A
(A,SQ,S9) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty set
(A,SQ) is finite V94() Element of bool (QC-symbols A)
(A,SQ) is finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,SQ) } is set
(A,S9) is finite V94() Element of bool (QC-symbols A)
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 S9 } is set
(A,SQ) \/ (A,S9) is finite V94() Element of bool (QC-symbols A)
NAT \ ((A,SQ) \/ (A,S9)) is V45() V46() V47() V48() V49() V50() Element of bool REAL
the Element of (A,SQ,S9) is Element of (A,SQ,S9)
x. (A,S9,SQ) is Element of bound_QC-variables A
[4,(A,S9,SQ)] is V15() set
{4,(A,S9,SQ)} is non empty finite V94() set
{{4,(A,S9,SQ)},{4}} is non empty finite V56() V94() set
[S,(x. (A,S9,SQ))] is V15() Element of [:(bound_QC-variables A),(bound_QC-variables A):]
{S,(x. (A,S9,SQ))} is non empty finite V94() set
{S} is non empty trivial finite 1 -element V94() set
{{S,(x. (A,S9,SQ))},{S}} is non empty finite V56() V94() set
{[S,(x. (A,S9,SQ))]} is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element V94() Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
S9 \/ {[S,(x. (A,S9,SQ))]} is non empty finite V94() set
[S,S] is V15() Element of [:(bound_QC-variables A),(bound_QC-variables A):]
{S,S} is non empty finite V94() set
{{S,S},{S}} is non empty finite V56() V94() set
{[S,S]} is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element V94() Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
S9 \/ {[S,S]} is non empty finite V94() set
l is Relation-like Function-like Element of (A)
(A,S,(All (S,SQ)),l) is Relation-like Function-like finite V94() Element of (A)
still_not-bound_in (All (S,SQ)) is Element of bool (bound_QC-variables A)
proj1 l is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } is set
(A,l, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } ) is Relation-like Function-like Element of (A)
l is Relation-like Function-like Element of (A)
(A,S,(All (S,SQ)),l) is Relation-like Function-like finite V94() Element of (A)
still_not-bound_in (All (S,SQ)) is Element of bool (bound_QC-variables A)
proj1 l is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } is set
(A,l, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } ) is Relation-like Function-like Element of (A)
proj1 S9 is finite V94() set
S9 is Relation-like set
proj1 S9 is set
(proj1 S9) /\ (proj1 S9) is finite V94() set
s is set
{S} is non empty trivial finite 1 -element V94() Element of bool (bound_QC-variables A)
P9 is Element of bound_QC-variables A
l . P9 is set
(A,S9) is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
dom (A,S9) is Element of bool (bound_QC-variables A)
l is Relation-like Function-like set
proj1 l is set
(dom (A,S9)) /\ (proj1 l) is Element of bool (bound_QC-variables A)
l is set
(A,S9) . l is set
l . l is set
(A,S9) \/ l is set
l is Relation-like Function-like set
s is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
(A,S9) \/ s is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
l is Relation-like Function-like Element of (A)
(A,S,(All (S,SQ)),l) is Relation-like Function-like finite V94() Element of (A)
proj1 l is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } is set
(A,l, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } ) is Relation-like Function-like Element of (A)
l is Relation-like Function-like Element of (A)
(A,S,(All (S,SQ)),l) is Relation-like Function-like finite V94() Element of (A)
proj1 l is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } is set
(A,l, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (All (S,SQ)) & b₁ is Element of proj1 l & not b₁ = S & not b₁ = l . b₁ ) } ) is Relation-like Function-like Element of (A)
S9 is Relation-like set
proj1 S9 is set
(proj1 S9) /\ (proj1 S9) is finite V94() set
s is set
P9 is Element of bound_QC-variables A
l . P9 is set
l is Relation-like Function-like set
proj1 l is set
(dom (A,S9)) /\ (proj1 l) is Element of bool (bound_QC-variables A)
l is set
(A,S9) . l is set
l . l is set
(A,S9) \/ l is set
l is Relation-like Function-like set
s is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
(A,S9) \/ s is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is set
SQ is set
S9 is set
S9 is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
S9 is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
l is Element of QC-WFF A
s is Relation-like Function-like Element of (A)
[l,s] is V15() Element of [:(QC-WFF A),(A):]
{l,s} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,s},{l}} is non empty finite V56() V94() set
l is Element of QC-WFF A
s is Relation-like Function-like Element of (A)
[l,s] is V15() Element of [:(QC-WFF A),(A):]
{l,s} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,s},{l}} is non empty finite V56() V94() set
bound_in S9 is Element of bound_QC-variables A
the_scope_of S9 is Element of QC-WFF A
(A,(bound_in S9),S9,l) is Relation-like Function-like finite V94() Element of (A)
still_not-bound_in S9 is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
proj1 l is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in S9 & b₁ is Element of proj1 l & not b₁ = bound_in S9 & not b₁ = l . b₁ ) } is set
(A,l, { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in S9 & b₁ is Element of proj1 l & not b₁ = bound_in S9 & not b₁ = l . b₁ ) } ) is Relation-like Function-like Element of (A)
(A,(bound_in S9),(the_scope_of S9),(A,(bound_in S9),S9,l)) is Relation-like Function-like Element of (A)
[:(QC-WFF A),(A):] is non empty set
S is Relation-like Function-like set
SQ is set
S9 is set
S9 is set
[S9,S9] is V15() set
{S9,S9} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,S9},{S9}} is non empty finite V56() V94() set
l is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[l,l] is V15() Element of [:(QC-WFF A),(A):]
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
S9 is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[S9,S9] is V15() Element of [:(QC-WFF A),(A):]
{S9,S9} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,S9},{S9}} is non empty finite V56() V94() set
l is set
[[S9,S9],l] is V15() set
{[S9,S9],l} is non empty finite V94() set
{[S9,S9]} is Function-like non empty trivial finite 1 -element V94() set
{{[S9,S9],l},{[S9,S9]}} is non empty finite V56() V94() set
SQ is set
S9 is set
S9 is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(QC-WFF A),(A):]
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
l is set
[[S9,l],l] is V15() set
{[S9,l],l} is non empty finite V94() set
{[S9,l]} is Function-like non empty trivial finite 1 -element V94() set
{{[S9,l],l},{[S9,l]}} is non empty finite V56() V94() set
S is Relation-like Function-like set
SQ is Relation-like Function-like set
S9 is set
S9 is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
l is set
[[S9,l],l] is V15() set
{[S9,l],l} is non empty finite V94() set
{[S9,l]} is Function-like non empty trivial finite 1 -element V94() set
{{[S9,l],l},{[S9,l]}} is non empty finite V56() V94() set
S9 is Element of QC-WFF A
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
l is set
[[S9,l],l] is V15() set
{[S9,l],l} is non empty finite V94() set
{[S9,l]} is Function-like non empty trivial finite 1 -element V94() set
{{[S9,l],l},{[S9,l]}} is non empty finite V56() V94() set
[:NAT,NAT:] is non empty non trivial non finite set
[:NAT,[:NAT,NAT:]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,NAT:]:] is non empty non trivial non finite set
[0,0] is V15() Element of [:NAT,NAT:]
<*[0,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,NAT:]
[1,0] is V15() Element of [:NAT,NAT:]
<*[1,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,NAT:]
[2,0] is V15() Element of [:NAT,NAT:]
<*[2,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,NAT:]
[3,0] is V15() Element of [:NAT,NAT:]
<*[3,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,NAT:]
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
bool [:([:NAT,(QC-symbols A):] *),(A):] is non empty set
QC-pred_symbols A is non empty set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
[:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
(A) is Relation-like Function-like set
bool ([:NAT,(QC-symbols A):] *) is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
<*SQ*> is Relation-like NAT -defined S -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
<*SQ*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + S -element FinSequence-like FinSubsequence-like V94() set
1 + S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is Relation-like Function-like Element of (A)
[(<*SQ*> ^ S9),S9] is V15() set
{(<*SQ*> ^ S9),S9} is functional non empty finite V94() set
{(<*SQ*> ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*SQ*> ^ S9),S9},{(<*SQ*> ^ S9)}} is non empty finite V56() V94() set
SQ ! S9 is Element of QC-WFF A
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Relation-like Function-like Element of (A)
[<*[0,0]*>,S] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(A):]
[:(bool [:NAT,[:NAT,NAT:]:]),(A):] is non empty non trivial non finite set
{<*[0,0]*>,S} is functional non empty finite V94() set
{<*[0,0]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[0,0]*>,S},{<*[0,0]*>}} is non empty finite V56() V94() set
S is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ S is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
SQ is Relation-like Function-like Element of (A)
[S,SQ] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{S,SQ} is functional non empty finite V94() set
{S} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S,SQ},{S}} is non empty finite V56() V94() set
[(<*[1,0]*> ^ S),SQ] is V15() set
{(<*[1,0]*> ^ S),SQ} is functional non empty finite V94() set
{(<*[1,0]*> ^ S)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*[1,0]*> ^ S),SQ},{(<*[1,0]*> ^ S)}} is non empty finite V56() V94() set
S9 is set
l is set
[S9,l] is V15() set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
S9 is Element of QC-WFF A
'not' S9 is Element of QC-WFF A
@ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
<*[1,0]*> ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
SQ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ S is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ S) ^ SQ is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like Function-like Element of (A)
[S,S9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{S,S9} is functional non empty finite V94() set
{S} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S,S9},{S}} is non empty finite V56() V94() set
[SQ,S9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{SQ,S9} is functional non empty finite V94() set
{SQ} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
[((<*[2,0]*> ^ S) ^ SQ),S9] is V15() set
{((<*[2,0]*> ^ S) ^ SQ),S9} is functional non empty finite V94() set
{((<*[2,0]*> ^ S) ^ SQ)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[2,0]*> ^ S) ^ SQ),S9},{((<*[2,0]*> ^ S) ^ SQ)}} is non empty finite V56() V94() set
l is set
l is set
[l,l] is V15() set
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
l is set
s is set
[l,s] is V15() set
{l,s} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,s},{l}} is non empty finite V56() V94() set
l is Element of QC-WFF A
S9 is Element of QC-WFF A
l '&' S9 is Element of QC-WFF A
@ l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ l) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ l)) ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
<*[2,0]*> ^ (@ l) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ (@ l)) ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S is Element of bound_QC-variables A
<*S*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*S*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
SQ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*S*>) ^ SQ is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like Function-like Element of (A)
[((<*[3,0]*> ^ <*S*>) ^ SQ),S9] is V15() set
{((<*[3,0]*> ^ <*S*>) ^ SQ),S9} is functional non empty finite V94() set
{((<*[3,0]*> ^ <*S*>) ^ SQ)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[3,0]*> ^ <*S*>) ^ SQ),S9},{((<*[3,0]*> ^ <*S*>) ^ SQ)}} is non empty finite V56() V94() set
(A) . [((<*[3,0]*> ^ <*S*>) ^ SQ),S9] is set
[SQ,((A) . [((<*[3,0]*> ^ <*S*>) ^ SQ),S9])] is V15() set
{SQ,((A) . [((<*[3,0]*> ^ <*S*>) ^ SQ),S9])} is non empty finite V94() set
{SQ} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{SQ,((A) . [((<*[3,0]*> ^ <*S*>) ^ SQ),S9])},{SQ}} is non empty finite V56() V94() set
l is set
l is set
[l,l] is V15() set
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
S9 is Element of QC-WFF A
All (S,S9) is Element of QC-WFF A
<*[3,0]*> ^ <*S*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*S*>) ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[3,0]*> ^ <*S*>) ^ (@ S9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
bool [:([:NAT,(QC-symbols A):] *),(A):] is non empty set
QC-pred_symbols A is non empty set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
[:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
(A) is Relation-like Function-like set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
<*SQ*> is Relation-like NAT -defined S -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
<*SQ*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + S -element FinSequence-like FinSubsequence-like V94() set
1 + S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is Relation-like Function-like Element of (A)
[(<*SQ*> ^ S9),S9] is V15() set
{(<*SQ*> ^ S9),S9} is functional non empty finite V94() set
{(<*SQ*> ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*SQ*> ^ S9),S9},{(<*SQ*> ^ S9)}} is non empty finite V56() V94() set
l is Relation-like Function-like Element of (A)
[<*[0,0]*>,l] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(A):]
[:(bool [:NAT,[:NAT,NAT:]:]),(A):] is non empty non trivial non finite set
{<*[0,0]*>,l} is functional non empty finite V94() set
{<*[0,0]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[0,0]*>,l},{<*[0,0]*>}} is non empty finite V56() V94() set
l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
s is Relation-like Function-like Element of (A)
[l,s] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{l,s} is functional non empty finite V94() set
{l} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{l,s},{l}} is non empty finite V56() V94() set
<*[1,0]*> ^ l is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(<*[1,0]*> ^ l),s] is V15() set
{(<*[1,0]*> ^ l),s} is functional non empty finite V94() set
{(<*[1,0]*> ^ l)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*[1,0]*> ^ l),s},{(<*[1,0]*> ^ l)}} is non empty finite V56() V94() set
P9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
k9 is Relation-like Function-like Element of (A)
[P9,k9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{P9,k9} is functional non empty finite V94() set
{P9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{P9,k9},{P9}} is non empty finite V56() V94() set
s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[s,k9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{s,k9} is functional non empty finite V94() set
{s} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{s,k9},{s}} is non empty finite V56() V94() set
<*[2,0]*> ^ P9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ P9) ^ s is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((<*[2,0]*> ^ P9) ^ s),k9] is V15() set
{((<*[2,0]*> ^ P9) ^ s),k9} is functional non empty finite V94() set
{((<*[2,0]*> ^ P9) ^ s)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[2,0]*> ^ P9) ^ s),k9},{((<*[2,0]*> ^ P9) ^ s)}} is non empty finite V56() V94() set
c₁₃ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
k99 is Element of bound_QC-variables A
<*k99*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*k99*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
(<*[3,0]*> ^ <*k99*>) ^ c₁₃ is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
c₁₄ is Relation-like Function-like Element of (A)
[((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄] is V15() set
{((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄} is functional non empty finite V94() set
{((<*[3,0]*> ^ <*k99*>) ^ c₁₃)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄},{((<*[3,0]*> ^ <*k99*>) ^ c₁₃)}} is non empty finite V56() V94() set
(A) . [((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄] is set
[c₁₃,((A) . [((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄])] is V15() set
{c₁₃,((A) . [((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄])} is non empty finite V94() set
{c₁₃} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{c₁₃,((A) . [((<*[3,0]*> ^ <*k99*>) ^ c₁₃),c₁₄])},{c₁₃}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
rng <*[3,0]*> is Relation-like NAT -defined NAT -valued trivial finite V94() Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
{[3,0]} is Relation-like NAT -defined NAT -valued Function-like constant non empty trivial finite 1 -element V94() Element of bool [:NAT,NAT:]
SQ is Element of bound_QC-variables A
<*SQ*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*SQ*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*SQ*>) ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
rng <*SQ*> is trivial finite V94() Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
S is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
S ^ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(S ^ S9) ^ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
A is Relation-like non empty QC-alphabet
QC-symbols A is non empty set
proj2 A is set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Element of QC-symbols A
[S,SQ] is V15() Element of [:NAT,(QC-symbols A):]
{S,SQ} is non empty finite V94() set
{S} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
{{S,SQ},{S}} is non empty finite V56() V94() set
<*[S,SQ]*> is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
S9 is Relation-like Function-like Element of (A)
[<*[S,SQ]*>,S9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{<*[S,SQ]*>,S9} is functional non empty finite V94() set
{<*[S,SQ]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[S,SQ]*>,S9},{<*[S,SQ]*>}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
<*SQ*> is Relation-like NAT -defined S -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
<*SQ*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + S -element FinSequence-like FinSubsequence-like V94() set
1 + S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
rng <*SQ*> is trivial finite V94() Element of bool (S -ary_QC-pred_symbols A)
bool (S -ary_QC-pred_symbols A) is non empty set
rng S9 is finite V94() Element of bool (QC-variables A)
(rng <*SQ*>) \/ (rng S9) is finite V94() set
proj2 (<*SQ*> ^ S9) is finite V94() set
S9 is Relation-like Function-like Element of (A)
[(<*SQ*> ^ S9),S9] is V15() set
{(<*SQ*> ^ S9),S9} is functional non empty finite V94() set
{(<*SQ*> ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*SQ*> ^ S9),S9},{(<*SQ*> ^ S9)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
the Relation-like Function-like Element of (A) is Relation-like Function-like Element of (A)
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
SQ is set
[<*[0,0]*>, the Relation-like Function-like Element of (A)] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(A):]
[:(bool [:NAT,[:NAT,NAT:]:]),(A):] is non empty non trivial non finite set
{<*[0,0]*>, the Relation-like Function-like Element of (A)} is functional non empty finite V94() set
{<*[0,0]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[0,0]*>, the Relation-like Function-like Element of (A)},{<*[0,0]*>}} is non empty finite V56() V94() set
S9 is non empty set
S9 is non empty set
S9 is set
bool [:([:NAT,(QC-symbols A):] *),(A):] is non empty set
QC-pred_symbols A is non empty set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
[:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
(A) is Relation-like Function-like set
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S9 } is set
l is Element of S9 -ary_QC-pred_symbols A
<*l*> is Relation-like NAT -defined S9 -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S9 -ary_QC-pred_symbols A
l is Relation-like NAT -defined QC-variables A -valued Function-like finite S9 -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
<*l*> ^ l is Relation-like NAT -defined Function-like non empty finite 1 + S9 -element FinSequence-like FinSubsequence-like V94() set
1 + S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
s is Relation-like Function-like Element of (A)
[(<*l*> ^ l),s] is V15() set
{(<*l*> ^ l),s} is functional non empty finite V94() set
{(<*l*> ^ l)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*l*> ^ l),s},{(<*l*> ^ l)}} is non empty finite V56() V94() set
P9 is non empty set
S9 is Relation-like Function-like Element of (A)
[<*[0,0]*>,S9] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(A):]
{<*[0,0]*>,S9} is functional non empty finite V94() set
{{<*[0,0]*>,S9},{<*[0,0]*>}} is non empty finite V56() V94() set
l is non empty set
S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{S9,l} is functional non empty finite V94() set
{S9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
[(<*[1,0]*> ^ S9),l] is V15() set
{(<*[1,0]*> ^ S9),l} is functional non empty finite V94() set
{(<*[1,0]*> ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*[1,0]*> ^ S9),l},{(<*[1,0]*> ^ S9)}} is non empty finite V56() V94() set
l is non empty set
rng <*[1,0]*> is Relation-like NAT -defined NAT -valued trivial finite V94() Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
{[1,0]} is Relation-like NAT -defined NAT -valued Function-like constant non empty trivial finite 1 -element V94() Element of bool [:NAT,NAT:]
l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
l ^ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ S9) ^ l is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Relation-like Function-like Element of (A)
[S9,l] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{S9,l} is functional non empty finite V94() set
{S9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
[l,l] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{l,l} is functional non empty finite V94() set
{l} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{l,l},{l}} is non empty finite V56() V94() set
[((<*[2,0]*> ^ S9) ^ l),l] is V15() set
{((<*[2,0]*> ^ S9) ^ l),l} is functional non empty finite V94() set
{((<*[2,0]*> ^ S9) ^ l)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[2,0]*> ^ S9) ^ l),l},{((<*[2,0]*> ^ S9) ^ l)}} is non empty finite V56() V94() set
s is non empty set
rng <*[2,0]*> is Relation-like NAT -defined NAT -valued trivial finite V94() Element of bool [:NAT,NAT:]
bool [:NAT,NAT:] is non empty non trivial non finite set
{[2,0]} is Relation-like NAT -defined NAT -valued Function-like constant non empty trivial finite 1 -element V94() Element of bool [:NAT,NAT:]
s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
s ^ S9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(s ^ S9) ^ l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
S9 is Element of bound_QC-variables A
<*S9*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*S9*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*S9*>) ^ l is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Relation-like Function-like Element of (A)
[((<*[3,0]*> ^ <*S9*>) ^ l),l] is V15() set
{((<*[3,0]*> ^ <*S9*>) ^ l),l} is functional non empty finite V94() set
{((<*[3,0]*> ^ <*S9*>) ^ l)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[3,0]*> ^ <*S9*>) ^ l),l},{((<*[3,0]*> ^ <*S9*>) ^ l)}} is non empty finite V56() V94() set
(A) . [((<*[3,0]*> ^ <*S9*>) ^ l),l] is set
[l,((A) . [((<*[3,0]*> ^ <*S9*>) ^ l),l])] is V15() set
{l,((A) . [((<*[3,0]*> ^ <*S9*>) ^ l),l])} is non empty finite V94() set
{l} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{l,((A) . [((<*[3,0]*> ^ <*S9*>) ^ l),l])},{l}} is non empty finite V56() V94() set
s is non empty set
S9 is non empty set
l is set
S is non empty set
SQ is non empty set
A is Relation-like non empty QC-alphabet
(A) is non empty set
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Element of (A)
[:(QC-WFF A),(A):] is non empty set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
[:NAT,(QC-symbols A):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols A):] *),(A):] is non empty set
bool [:([:NAT,(QC-symbols A):] *),(A):] is non empty set
QC-pred_symbols A is non empty set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
[:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols A):]:] is non empty non trivial non finite set
(A) is Relation-like Function-like set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
S9 is Element of SQ -ary_QC-pred_symbols A
<*S9*> is Relation-like NAT -defined SQ -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
<*S9*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + SQ -element FinSequence-like FinSubsequence-like V94() set
1 + SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l is Relation-like Function-like Element of (A)
[(<*S9*> ^ S9),l] is V15() set
{(<*S9*> ^ S9),l} is functional non empty finite V94() set
{(<*S9*> ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*S9*> ^ S9),l},{(<*S9*> ^ S9)}} is non empty finite V56() V94() set
l is Relation-like Function-like Element of (A)
[<*[0,0]*>,l] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(A):]
[:(bool [:NAT,[:NAT,NAT:]:]),(A):] is non empty non trivial non finite set
{<*[0,0]*>,l} is functional non empty finite V94() set
{<*[0,0]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[0,0]*>,l},{<*[0,0]*>}} is non empty finite V56() V94() set
s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
P9 is Relation-like Function-like Element of (A)
[s,P9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
[:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):] is non empty non trivial non finite set
{s,P9} is functional non empty finite V94() set
{s} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{s,P9},{s}} is non empty finite V56() V94() set
<*[1,0]*> ^ s is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(<*[1,0]*> ^ s),P9] is V15() set
{(<*[1,0]*> ^ s),P9} is functional non empty finite V94() set
{(<*[1,0]*> ^ s)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*[1,0]*> ^ s),P9},{(<*[1,0]*> ^ s)}} is non empty finite V56() V94() set
s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
k99 is Relation-like Function-like Element of (A)
[s,k99] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{s,k99} is functional non empty finite V94() set
{s} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{s,k99},{s}} is non empty finite V56() V94() set
k9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[k9,k99] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols A):]:]),(A):]
{k9,k99} is functional non empty finite V94() set
{k9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{k9,k99},{k9}} is non empty finite V56() V94() set
<*[2,0]*> ^ s is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ s) ^ k9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((<*[2,0]*> ^ s) ^ k9),k99] is V15() set
{((<*[2,0]*> ^ s) ^ k9),k99} is functional non empty finite V94() set
{((<*[2,0]*> ^ s) ^ k9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[2,0]*> ^ s) ^ k9),k99},{((<*[2,0]*> ^ s) ^ k9)}} is non empty finite V56() V94() set
c₁₄ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
c₁₃ is Element of bound_QC-variables A
<*c₁₃*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*c₁₃*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
(<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄ is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
c₁₅ is Relation-like Function-like Element of (A)
[((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅] is V15() set
{((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅} is functional non empty finite V94() set
{((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅},{((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄)}} is non empty finite V56() V94() set
(A) . [((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅] is set
[c₁₄,((A) . [((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅])] is V15() set
{c₁₄,((A) . [((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅])} is non empty finite V94() set
{c₁₄} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{c₁₄,((A) . [((<*[3,0]*> ^ <*c₁₃*>) ^ c₁₄),c₁₅])},{c₁₄}} is non empty finite V56() V94() set
SQ is set
S9 is set
[SQ,S9] is V15() set
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
l is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[l,S9] is V15() Element of [:(QC-WFF A),(A):]
{l,S9} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,S9},{l}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty set
A is Relation-like non empty QC-alphabet
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
7 is non empty ext-real positive non negative V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Element of QC-pred_symbols A
the_arity_of S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
QC-WFF A is non empty set
S ! SQ is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[(S ! SQ),S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(S ! SQ),S9} is non empty finite V94() set
{(S ! SQ)} is non empty trivial finite 1 -element V94() set
{{(S ! SQ),S9},{(S ! SQ)}} is non empty finite V56() V94() set
(A) is non empty (A) set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = len SQ } is set
(len SQ) -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
l is Element of (len SQ) -ary_QC-pred_symbols A
s is Relation-like NAT -defined QC-variables A -valued Function-like finite len SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l ! s is Element of QC-WFF A
<*l*> is Relation-like NAT -defined (len SQ) -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of (len SQ) -ary_QC-pred_symbols A
<*l*> ^ s is Relation-like NAT -defined Function-like non empty finite 1 + (len SQ) -element FinSequence-like FinSubsequence-like V94() set
1 + (len SQ) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
QC-pred_symbols A is non empty set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
QC-WFF A is non empty set
S is Relation-like Function-like Element of (A)
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
S9 is Element of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(A,S9,S9,S) is Element of (A)
(A) is non empty (A) set
S9 ! S9 is Element of QC-WFF A
[(S9 ! S9),S] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(S9 ! S9),S} is non empty finite V94() set
{(S9 ! S9)} is non empty trivial finite 1 -element V94() set
{{(S9 ! S9),S},{(S9 ! S9)}} is non empty finite V56() V94() set
len S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l is Element of QC-pred_symbols A
the_arity_of l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
S `1 is set
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[SQ,S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
S `2 is set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[SQ,S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Element of (A)
(A,S) is Element of QC-WFF A
(A,S) is Relation-like Function-like Element of (A)
[(A,S),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
SQ is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[SQ,S9] is V15() Element of [:(QC-WFF A),(A):]
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Element of (A)
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
[(A,S),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
QC-WFF A is non empty set
(A,S) is Element of QC-WFF A
(A,SQ) is Element of QC-WFF A
(A,S) '&' (A,SQ) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S))) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,S) '&' (A,SQ)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{((A,S) '&' (A,SQ)),(A,S)} is non empty finite V94() set
{((A,S) '&' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{((A,S) '&' (A,SQ)),(A,S)},{((A,S) '&' (A,SQ))}} is non empty finite V56() V94() set
[(A,S),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
S `1 is set
S `2 is set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of (A)
(A,(A,S)) is Relation-like Function-like Element of (A)
(A) is Relation-like Function-like set
QC-WFF A is non empty set
(A,S) is Element of bound_QC-variables A
(A,(A,S)) is Element of QC-WFF A
All ((A,S),(A,(A,S))) is Element of QC-WFF A
<*(A,S)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,S)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,S)*>) ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of bound_QC-variables A
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
All ((A,S),(A,(A,S))) is Element of QC-WFF A
<*(A,S)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,S)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,S)*>) ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
SQ is Relation-like Function-like (A,S)
[(All ((A,S),(A,(A,S)))),SQ] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,S),(A,(A,S)))),SQ} is non empty finite V94() set
{(All ((A,S),(A,(A,S))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,S),(A,(A,S)))),SQ},{(All ((A,S),(A,(A,S))))}} is non empty finite V56() V94() set
(A,(A,S)) is Relation-like Function-like Element of (A)
(A) is Relation-like Function-like set
(A) . [(All ((A,S),(A,(A,S)))),SQ] is set
[(A,(A,S)),((A) . [(All ((A,S),(A,(A,S)))),SQ])] is V15() set
{(A,(A,S)),((A) . [(All ((A,S),(A,(A,S)))),SQ])} is non empty finite V94() set
{(A,(A,S))} is non empty trivial finite 1 -element V94() set
{{(A,(A,S)),((A) . [(All ((A,S),(A,(A,S)))),SQ])},{(A,(A,S))}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
S is Element of (A)
SQ is Element of bound_QC-variables A
[S,SQ] is V15() set
{S,SQ} is non empty finite V94() set
{S} is non empty trivial finite 1 -element V94() set
{{S,SQ},{S}} is non empty finite V56() V94() set
[:(A),(bound_QC-variables A):] is non empty set
[S,SQ] is V15() Element of [:(A),(bound_QC-variables A):]
F₁() is Relation-like non empty QC-alphabet
(F₁()) is non empty (F₁()) set
QC-pred_symbols F₁() is non empty set
QC-symbols F₁() is non empty set
proj2 F₁() is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols F₁() : 7 <= b₁ } is set
QC-variables F₁() is non empty set
[:{4,5},(QC-symbols F₁()):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols F₁()):] is non empty set
(F₁()) is functional non empty set
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
bool (QC-variables F₁()) is non empty set
[:{4},(QC-symbols F₁()):] is non empty set
PFuncs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is functional non empty set
{ b₁ where b₁ is Element of (F₁()) : P₁[b₁] } is set
the Relation-like Function-like Element of (F₁()) is Relation-like Function-like Element of (F₁())
CQC-WFF F₁() is non empty Element of bool (QC-WFF F₁())
QC-WFF F₁() is non empty set
bool (QC-WFF F₁()) is non empty set
VERUM F₁() is Element of CQC-WFF F₁()
[(VERUM F₁()), the Relation-like Function-like Element of (F₁())] is V15() Element of [:(CQC-WFF F₁()),(F₁()):]
[:(CQC-WFF F₁()),(F₁()):] is non empty set
{(VERUM F₁()), the Relation-like Function-like Element of (F₁())} is non empty finite V94() set
{(VERUM F₁())} is non empty trivial finite 1 -element V94() set
{{(VERUM F₁()), the Relation-like Function-like Element of (F₁())},{(VERUM F₁())}} is non empty finite V56() V94() set
SQ is Element of (F₁())
CQC-WFF F₁() is non empty Element of bool (QC-WFF F₁())
QC-WFF F₁() is non empty set
bool (QC-WFF F₁()) is non empty set
VERUM F₁() is Element of CQC-WFF F₁()
S is non empty set
SQ is Relation-like Function-like Element of (F₁())
[(VERUM F₁()),SQ] is V15() Element of [:(CQC-WFF F₁()),(F₁()):]
[:(CQC-WFF F₁()),(F₁()):] is non empty set
{(VERUM F₁()),SQ} is non empty finite V94() set
{(VERUM F₁())} is non empty trivial finite 1 -element V94() set
{{(VERUM F₁()),SQ},{(VERUM F₁())}} is non empty finite V56() V94() set
S9 is Element of (F₁())
SQ is Relation-like Function-like Element of (F₁())
[<*[0,0]*>,SQ] is V15() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(F₁()):]
[:(bool [:NAT,[:NAT,NAT:]:]),(F₁()):] is non empty non trivial non finite set
{<*[0,0]*>,SQ} is functional non empty finite V94() set
{<*[0,0]*>} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{<*[0,0]*>,SQ},{<*[0,0]*>}} is non empty finite V56() V94() set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
[:NAT,[:NAT,(QC-symbols F₁()):]:] is non empty non trivial non finite set
bool [:NAT,[:NAT,(QC-symbols F₁()):]:] is non empty non trivial non finite set
SQ is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
<*[1,0]*> ^ SQ is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like Function-like Element of (F₁())
[SQ,S9] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols F₁()):]:]),(F₁()):]
[:(bool [:NAT,[:NAT,(QC-symbols F₁()):]:]),(F₁()):] is non empty non trivial non finite set
{SQ,S9} is functional non empty finite V94() set
{SQ} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
[(<*[1,0]*> ^ SQ),S9] is V15() set
{(<*[1,0]*> ^ SQ),S9} is functional non empty finite V94() set
{(<*[1,0]*> ^ SQ)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*[1,0]*> ^ SQ),S9},{(<*[1,0]*> ^ SQ)}} is non empty finite V56() V94() set
S9 is Element of (F₁())
(F₁(),S9) is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
'not' (F₁(),S9) is Element of QC-WFF F₁()
@ (F₁(),S9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
<*[1,0]*> ^ (@ (F₁(),S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(F₁(),S9) is Relation-like Function-like Element of (F₁())
[('not' (F₁(),S9)),(F₁(),S9)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{('not' (F₁(),S9)),(F₁(),S9)} is non empty finite V94() set
{('not' (F₁(),S9))} is non empty trivial finite 1 -element V94() set
{{('not' (F₁(),S9)),(F₁(),S9)},{('not' (F₁(),S9))}} is non empty finite V56() V94() set
l is Element of QC-WFF F₁()
l is Relation-like Function-like Element of (F₁())
[l,l] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
(F₁()) is Relation-like Function-like set
SQ is Element of bound_QC-variables F₁()
<*SQ*> is Relation-like NAT -defined bound_QC-variables F₁() -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables F₁()
<*[3,0]*> ^ <*SQ*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
(<*[3,0]*> ^ <*SQ*>) ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S9 is Relation-like Function-like Element of (F₁())
[((<*[3,0]*> ^ <*SQ*>) ^ S9),S9] is V15() set
{((<*[3,0]*> ^ <*SQ*>) ^ S9),S9} is functional non empty finite V94() set
{((<*[3,0]*> ^ <*SQ*>) ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[3,0]*> ^ <*SQ*>) ^ S9),S9},{((<*[3,0]*> ^ <*SQ*>) ^ S9)}} is non empty finite V56() V94() set
(F₁()) . [((<*[3,0]*> ^ <*SQ*>) ^ S9),S9] is set
[S9,((F₁()) . [((<*[3,0]*> ^ <*SQ*>) ^ S9),S9])] is V15() set
{S9,((F₁()) . [((<*[3,0]*> ^ <*SQ*>) ^ S9),S9])} is non empty finite V94() set
{S9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S9,((F₁()) . [((<*[3,0]*> ^ <*SQ*>) ^ S9),S9])},{S9}} is non empty finite V56() V94() set
l is Element of (F₁())
(F₁(),l,SQ) is V15() Element of [:(F₁()),(bound_QC-variables F₁()):]
[:(F₁()),(bound_QC-variables F₁()):] is non empty set
{l,SQ} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,SQ},{l}} is non empty finite V56() V94() set
l is set
s is Element of [:(F₁()),(bound_QC-variables F₁()):]
(F₁(),s) is Element of (F₁())
(F₁(),s) is Element of bound_QC-variables F₁()
(F₁(),l) is Element of QC-WFF F₁()
(F₁(),l) is Relation-like Function-like Element of (F₁())
All (SQ,(F₁(),l)) is Element of QC-WFF F₁()
<*[3,0]*> ^ <*SQ*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (F₁(),l) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
(<*[3,0]*> ^ <*SQ*>) ^ (@ (F₁(),l)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All (SQ,(F₁(),l))),S9] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{(All (SQ,(F₁(),l))),S9} is non empty finite V94() set
{(All (SQ,(F₁(),l)))} is non empty trivial finite 1 -element V94() set
{{(All (SQ,(F₁(),l))),S9},{(All (SQ,(F₁(),l)))}} is non empty finite V56() V94() set
(F₁()) . [(All (SQ,(F₁(),l))),S9] is set
P9 is Relation-like Function-like (F₁(),s)
(F₁(),s,P9) is Element of (F₁())
(F₁(),(F₁(),s)) is Element of QC-WFF F₁()
All ((F₁(),s),(F₁(),(F₁(),s))) is Element of QC-WFF F₁()
<*(F₁(),s)*> is Relation-like NAT -defined bound_QC-variables F₁() -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables F₁()
<*[3,0]*> ^ <*(F₁(),s)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (F₁(),(F₁(),s)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
(<*[3,0]*> ^ <*(F₁(),s)*>) ^ (@ (F₁(),(F₁(),s))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((F₁(),s),(F₁(),(F₁(),s)))),P9] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
{(All ((F₁(),s),(F₁(),(F₁(),s)))),P9} is non empty finite V94() set
{(All ((F₁(),s),(F₁(),(F₁(),s))))} is non empty trivial finite 1 -element V94() set
{{(All ((F₁(),s),(F₁(),(F₁(),s)))),P9},{(All ((F₁(),s),(F₁(),(F₁(),s))))}} is non empty finite V56() V94() set
SQ is Element of (F₁())
[:NAT,(QC-symbols F₁()):] * is functional non empty FinSequence-membered set
[:([:NAT,(QC-symbols F₁()):] *),(F₁()):] is non empty set
S9 is set
S9 is Element of (F₁())
S9 is Element of QC-WFF F₁()
l is Relation-like Function-like Element of (F₁())
[S9,l] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{S9,l} is non empty finite V94() set
{S9} is non empty trivial finite 1 -element V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
@ S9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
S9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
S9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
<*[2,0]*> ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(<*[2,0]*> ^ S9) ^ S9 is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Relation-like Function-like Element of (F₁())
[S9,l] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols F₁()):]:]),(F₁()):]
[:(bool [:NAT,[:NAT,(QC-symbols F₁()):]:]),(F₁()):] is non empty non trivial non finite set
{S9,l} is functional non empty finite V94() set
{S9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
[S9,l] is V15() Element of [:(bool [:NAT,[:NAT,(QC-symbols F₁()):]:]),(F₁()):]
{S9,l} is functional non empty finite V94() set
{S9} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{S9,l},{S9}} is non empty finite V56() V94() set
[((<*[2,0]*> ^ S9) ^ S9),l] is V15() set
{((<*[2,0]*> ^ S9) ^ S9),l} is functional non empty finite V94() set
{((<*[2,0]*> ^ S9) ^ S9)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{((<*[2,0]*> ^ S9) ^ S9),l},{((<*[2,0]*> ^ S9) ^ S9)}} is non empty finite V56() V94() set
l is Element of (F₁())
s is Element of (F₁())
P9 is Element of QC-WFF F₁()
s is Relation-like Function-like Element of (F₁())
[P9,s] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{P9,s} is non empty finite V94() set
{P9} is non empty trivial finite 1 -element V94() set
{{P9,s},{P9}} is non empty finite V56() V94() set
(F₁(),l) is Relation-like Function-like Element of (F₁())
(F₁(),s) is Relation-like Function-like Element of (F₁())
(F₁(),l,s) is Element of (F₁())
(F₁(),l) is Element of QC-WFF F₁()
(F₁(),s) is Element of QC-WFF F₁()
(F₁(),l) '&' (F₁(),s) is Element of QC-WFF F₁()
@ (F₁(),l) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
<*[2,0]*> ^ (@ (F₁(),l)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (F₁(),s) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
(<*[2,0]*> ^ (@ (F₁(),l))) ^ (@ (F₁(),s)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((F₁(),l) '&' (F₁(),s)),(F₁(),l)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
{((F₁(),l) '&' (F₁(),s)),(F₁(),l)} is non empty finite V94() set
{((F₁(),l) '&' (F₁(),s))} is non empty trivial finite 1 -element V94() set
{{((F₁(),l) '&' (F₁(),s)),(F₁(),l)},{((F₁(),l) '&' (F₁(),s))}} is non empty finite V56() V94() set
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols F₁() : the_arity_of b₁ = S9 } is set
S9 is Element of S9 -ary_QC-pred_symbols F₁()
<*S9*> is Relation-like NAT -defined S9 -ary_QC-pred_symbols F₁() -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S9 -ary_QC-pred_symbols F₁()
l is Relation-like NAT -defined QC-variables F₁() -valued Function-like finite S9 -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables F₁()
<*S9*> ^ l is Relation-like NAT -defined Function-like non empty finite 1 + S9 -element FinSequence-like FinSubsequence-like V94() set
1 + S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l is Relation-like Function-like Element of (F₁())
[(<*S9*> ^ l),l] is V15() set
{(<*S9*> ^ l),l} is functional non empty finite V94() set
{(<*S9*> ^ l)} is functional non empty trivial finite V56() 1 -element V92() V94() set
{{(<*S9*> ^ l),l},{(<*S9*> ^ l)}} is non empty finite V56() V94() set
(F₁(),S9,l,l) is Element of (F₁())
S9 ! l is Element of QC-WFF F₁()
[(S9 ! l),l] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{(S9 ! l),l} is non empty finite V94() set
{(S9 ! l)} is non empty trivial finite 1 -element V94() set
{{(S9 ! l),l},{(S9 ! l)}} is non empty finite V56() V94() set
S9 is Element of (F₁())
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
S9 is Element of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Relation-like Function-like Element of (A)
(A,S9,S9,l) is Element of (A)
S9 ! S9 is Element of QC-WFF A
[(S9 ! S9),l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(S9 ! S9),l} is non empty finite V94() set
{(S9 ! S9)} is non empty trivial finite 1 -element V94() set
{{(S9 ! S9),l},{(S9 ! S9)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
S9 is Relation-like Function-like Element of (A)
(A,SQ,S9,S9) is Element of (A)
(A) is non empty (A) set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
S9 is Relation-like Function-like Element of (A)
(A,SQ,S9,S9) is (A) Element of (A)
S is Element of (A)
SQ is Element of (A)
S is Element of bound_QC-variables A
(A,SQ,S) is V15() Element of [:(A),(bound_QC-variables A):]
[:(A),(bound_QC-variables A):] is non empty set
{SQ,S} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S},{SQ}} is non empty finite V56() V94() set
S9 is Relation-like Function-like (A,(A,SQ,S))
(A,(A,SQ,S),S9) is Element of (A)
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
S is Element of (A)
(A,S) is Element of (A)
QC-WFF A is non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
QC-pred_symbols A is non empty set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
S9 is Element of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Relation-like Function-like Element of (A)
(A,S9,S9,l) is (A) Element of (A)
l is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
SQ is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S9 } is set
l is Relation-like NAT -defined QC-variables A -valued Function-like finite S9 -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Element of S9 -ary_QC-pred_symbols A
s is Relation-like Function-like Element of (A)
(A,l,l,s) is (A) Element of (A)
QC-WFF A is non empty set
l ! l is Element of QC-WFF A
[(l ! l),s] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(l ! l),s} is non empty finite V94() set
{(l ! l)} is non empty trivial finite 1 -element V94() set
{{(l ! l),s},{(l ! l)}} is non empty finite V56() V94() set
P9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
P9 -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = P9 } is set
k9 is Relation-like NAT -defined QC-variables A -valued Function-like finite P9 -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
s is Element of P9 -ary_QC-pred_symbols A
k99 is Relation-like Function-like Element of (A)
(A,s,k9,k99) is (A) Element of (A)
<*l*> is Relation-like NAT -defined S9 -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S9 -ary_QC-pred_symbols A
<*l*> ^ l is Relation-like NAT -defined Function-like non empty finite 1 + S9 -element FinSequence-like FinSubsequence-like V94() set
1 + S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
<*s*> is Relation-like NAT -defined P9 -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of P9 -ary_QC-pred_symbols A
<*s*> ^ k9 is Relation-like NAT -defined Function-like non empty finite 1 + P9 -element FinSequence-like FinSubsequence-like V94() set
1 + P9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
s ! k9 is Element of QC-WFF A
(A,S) is Element of QC-WFF A
[(s ! k9),k99] is V15() Element of [:(QC-WFF A),(A):]
{(s ! k9),k99} is non empty finite V94() set
{(s ! k9)} is non empty trivial finite 1 -element V94() set
{{(s ! k9),k99},{(s ! k9)}} is non empty finite V56() V94() set
the_pred_symbol_of (A,S) is Element of QC-pred_symbols A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
SQ is Element of (A)
(A,SQ) is Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,SQ) is Element of QC-WFF A
'not' (A,SQ) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,SQ) is Relation-like Function-like Element of (A)
[('not' (A,SQ)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,SQ)),(A,SQ)} is non empty finite V94() set
{('not' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{('not' (A,SQ)),(A,SQ)},{('not' (A,SQ))}} is non empty finite V56() V94() set
S9 is Element of (A)
(A,S9) is Element of (A)
(A,S9) is Element of QC-WFF A
'not' (A,S9) is Element of QC-WFF A
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S9) is Relation-like Function-like Element of (A)
[('not' (A,S9)),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{('not' (A,S9)),(A,S9)} is non empty finite V94() set
{('not' (A,S9))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S9)),(A,S9)},{('not' (A,S9))}} is non empty finite V56() V94() set
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
[(A,S9),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S9),(A,S9)} is non empty finite V94() set
{(A,S9)} is non empty trivial finite 1 -element V94() set
{{(A,S9),(A,S9)},{(A,S9)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S9 is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
S9 is Element of (A)
(A,SQ,S9) is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
l is Element of (A)
(A,S9,l) is Element of (A)
(A,l) is Relation-like Function-like Element of (A)
(A,SQ) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
len (@ (A,SQ)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S9) is Element of QC-WFF A
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (A,S9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,l) is Element of QC-WFF A
(A,S9) '&' (A,l) is Element of QC-WFF A
<*[2,0]*> ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,l) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S9))) ^ (@ (A,l)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,S9) '&' (A,l)),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{((A,S9) '&' (A,l)),(A,S9)} is non empty finite V94() set
{((A,S9) '&' (A,l))} is non empty trivial finite 1 -element V94() set
{{((A,S9) '&' (A,l)),(A,S9)},{((A,S9) '&' (A,l))}} is non empty finite V56() V94() set
(A,S9) is Element of QC-WFF A
(A,SQ) '&' (A,S9) is Element of QC-WFF A
<*[2,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,SQ))) ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,SQ) '&' (A,S9)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{((A,SQ) '&' (A,S9)),(A,SQ)} is non empty finite V94() set
{((A,SQ) '&' (A,S9))} is non empty trivial finite 1 -element V94() set
{{((A,SQ) '&' (A,S9)),(A,SQ)},{((A,SQ) '&' (A,S9))}} is non empty finite V56() V94() set
(@ (A,SQ)) ^ (@ (A,S9)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ ((@ (A,SQ)) ^ (@ (A,S9))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(@ (A,S9)) ^ (@ (A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ ((@ (A,S9)) ^ (@ (A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
s is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
len l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
len s is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
l ^ P9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
s is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
s ^ s is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
[(A,S9),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S9),(A,S9)} is non empty finite V94() set
{(A,S9)} is non empty trivial finite 1 -element V94() set
{{(A,S9),(A,S9)},{(A,S9)}} is non empty finite V56() V94() set
k9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
l ^ k9 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
SQ is Element of (A)
S9 is Element of (A)
(A,SQ,S9) is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S9) is Relation-like Function-like Element of (A)
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S9 is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
S9 is Element of (A)
(A,S9,SQ) is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
QC-WFF A is non empty set
(A,SQ) is Element of QC-WFF A
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
(A,S9) is Element of QC-WFF A
[(A,S9),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S9),(A,S9)} is non empty finite V94() set
{(A,S9)} is non empty trivial finite 1 -element V94() set
{{(A,S9),(A,S9)},{(A,S9)}} is non empty finite V56() V94() set
l is Element of (A)
(A,l,S9) is Element of (A)
(A,l) is Relation-like Function-like Element of (A)
(A,S9) is Element of QC-WFF A
(A,S9) '&' (A,SQ) is Element of QC-WFF A
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S9))) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,S9) '&' (A,SQ)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{((A,S9) '&' (A,SQ)),(A,SQ)} is non empty finite V94() set
{((A,S9) '&' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{((A,S9) '&' (A,SQ)),(A,SQ)},{((A,S9) '&' (A,SQ))}} is non empty finite V56() V94() set
(A,l) is Element of QC-WFF A
(A,l) '&' (A,S9) is Element of QC-WFF A
@ (A,l) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ (A,l)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,l))) ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,l) '&' (A,S9)),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{((A,l) '&' (A,S9)),(A,S9)} is non empty finite V94() set
{((A,l) '&' (A,S9))} is non empty trivial finite 1 -element V94() set
{{((A,l) '&' (A,S9)),(A,S9)},{((A,l) '&' (A,S9))}} is non empty finite V56() V94() set
(@ (A,S9)) ^ (@ (A,SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ ((@ (A,S9)) ^ (@ (A,SQ))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(@ (A,l)) ^ (@ (A,S9)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ ((@ (A,l)) ^ (@ (A,S9))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
SQ is Element of [:(A),(bound_QC-variables A):]
S9 is Relation-like Function-like (A,SQ)
(A,SQ,S9) is Element of (A)
(A,SQ) is Element of bound_QC-variables A
SQ is Element of bound_QC-variables A
S9 is Element of bound_QC-variables A
S9 is Element of [:(A),(bound_QC-variables A):]
l is Relation-like Function-like (A,S9)
(A,S9,l) is Element of (A)
(A,S9) is Element of bound_QC-variables A
S9 is Element of [:(A),(bound_QC-variables A):]
l is Relation-like Function-like (A,S9)
(A,S9,l) is Element of (A)
(A,S9) is Element of bound_QC-variables A
l is Element of [:(A),(bound_QC-variables A):]
s is Relation-like Function-like (A,l)
(A,l,s) is Element of (A)
(A,l) is Element of bound_QC-variables A
l is Element of [:(A),(bound_QC-variables A):]
s is Relation-like Function-like (A,l)
(A,l,s) is Element of (A)
(A,l) is Element of bound_QC-variables A
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,l) is Element of (A)
(A,(A,l)) is Element of QC-WFF A
All ((A,l),(A,(A,l))) is Element of QC-WFF A
<*(A,l)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,l)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,l)*>) ^ (@ (A,(A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,l),(A,(A,l)))),s] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,l),(A,(A,l)))),s} is non empty finite V94() set
{(All ((A,l),(A,(A,l))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,l),(A,(A,l)))),s},{(All ((A,l),(A,(A,l))))}} is non empty finite V56() V94() set
(A,S9) is Element of (A)
(A,(A,S9)) is Element of QC-WFF A
All ((A,S9),(A,(A,S9))) is Element of QC-WFF A
<*(A,S9)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,S9)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S9)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,S9)*>) ^ (@ (A,(A,S9))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,S9),(A,(A,S9)))),l] is V15() Element of [:(QC-WFF A),(A):]
{(All ((A,S9),(A,(A,S9)))),l} is non empty finite V94() set
{(All ((A,S9),(A,(A,S9))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,S9),(A,(A,S9)))),l},{(All ((A,S9),(A,(A,S9))))}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
SQ is Element of [:(A),(bound_QC-variables A):]
S9 is Relation-like Function-like (A,SQ)
(A,SQ,S9) is Element of (A)
(A,SQ) is Element of (A)
SQ is Element of (A)
S9 is Element of (A)
S9 is Element of [:(A),(bound_QC-variables A):]
l is Relation-like Function-like (A,S9)
(A,S9,l) is Element of (A)
(A,S9) is Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S9) is Element of bound_QC-variables A
(A,(A,S9)) is Element of QC-WFF A
All ((A,S9),(A,(A,S9))) is Element of QC-WFF A
<*(A,S9)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,S9)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S9)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,S9)*>) ^ (@ (A,(A,S9))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,S9),(A,(A,S9)))),l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,S9),(A,(A,S9)))),l} is non empty finite V94() set
{(All ((A,S9),(A,(A,S9))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,S9),(A,(A,S9)))),l},{(All ((A,S9),(A,(A,S9))))}} is non empty finite V56() V94() set
(A,(A,S9)) is Relation-like Function-like Element of (A)
(A) is Relation-like Function-like set
(A) . [(All ((A,S9),(A,(A,S9)))),l] is set
l is Element of [:(A),(bound_QC-variables A):]
s is Relation-like Function-like (A,l)
(A,l,s) is Element of (A)
(A,l) is Element of (A)
[(A,(A,S9)),(A,(A,S9))] is V15() Element of [:(QC-WFF A),(A):]
{(A,(A,S9)),(A,(A,S9))} is non empty finite V94() set
{(A,(A,S9))} is non empty trivial finite 1 -element V94() set
{{(A,(A,S9)),(A,(A,S9))},{(A,(A,S9))}} is non empty finite V56() V94() set
(A,(A,l)) is Element of QC-WFF A
(A,(A,l)) is Relation-like Function-like Element of (A)
[(A,(A,l)),(A,(A,l))] is V15() Element of [:(QC-WFF A),(A):]
{(A,(A,l)),(A,(A,l))} is non empty finite V94() set
{(A,(A,l))} is non empty trivial finite 1 -element V94() set
{{(A,(A,l)),(A,(A,l))},{(A,(A,l))}} is non empty finite V56() V94() set
(A,l) is Element of bound_QC-variables A
All ((A,l),(A,(A,l))) is Element of QC-WFF A
<*(A,l)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,l)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,l)*>) ^ (@ (A,(A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,l),(A,(A,l)))),s] is V15() Element of [:(QC-WFF A),(A):]
{(All ((A,l),(A,(A,l)))),s} is non empty finite V94() set
{(All ((A,l),(A,(A,l))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,l),(A,(A,l)))),s},{(All ((A,l),(A,(A,l))))}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
SQ is Relation-like Function-like (A,S)
(A,S,SQ) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is (A) Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
SQ is Element of (A)
(A,SQ) is (A) Element of (A)
(A,SQ) is Element of QC-WFF A
'not' (A,SQ) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,SQ) is Relation-like Function-like Element of (A)
[('not' (A,SQ)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{('not' (A,SQ)),(A,SQ)} is non empty finite V94() set
{('not' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{('not' (A,SQ)),(A,SQ)},{('not' (A,SQ))}} is non empty finite V56() V94() set
[(A,S),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is (A) Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
(A,(A,S)) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
S9 is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
S9 is Element of (A)
(A,S9) is Relation-like Function-like Element of (A)
(A,S9,S9) is Element of (A)
QC-WFF A is non empty set
(A,S) is Element of QC-WFF A
(A,SQ) is Element of QC-WFF A
(A,S) '&' (A,SQ) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S))) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,S) '&' (A,SQ)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{((A,S) '&' (A,SQ)),(A,S)} is non empty finite V94() set
{((A,S) '&' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{((A,S) '&' (A,SQ)),(A,S)},{((A,S) '&' (A,SQ))}} is non empty finite V56() V94() set
(A,S9) is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
(A,S9) '&' (A,S9) is Element of QC-WFF A
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S9))) ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,S9) '&' (A,S9)),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{((A,S9) '&' (A,S9)),(A,S9)} is non empty finite V94() set
{((A,S9) '&' (A,S9))} is non empty trivial finite 1 -element V94() set
{{((A,S9) '&' (A,S9)),(A,S9)},{((A,S9) '&' (A,S9))}} is non empty finite V56() V94() set
[(A,SQ),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
[(A,S9),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S9),(A,S9)} is non empty finite V94() set
{(A,S9)} is non empty trivial finite 1 -element V94() set
{{(A,S9),(A,S9)},{(A,S9)}} is non empty finite V56() V94() set
[(A,S),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
[(A,S9),(A,S9)] is V15() Element of [:(QC-WFF A),(A):]
{(A,S9),(A,S9)} is non empty finite V94() set
{(A,S9)} is non empty trivial finite 1 -element V94() set
{{(A,S9),(A,S9)},{(A,S9)}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
(A,(A,S,SQ)) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
(A,(A,S,SQ)) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
SQ is Element of [:(A),(bound_QC-variables A):]
S9 is Relation-like Function-like (A,S)
(A,S,S9) is Element of (A)
S9 is Relation-like Function-like (A,SQ)
(A,SQ,S9) is Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of bound_QC-variables A
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
All ((A,S),(A,(A,S))) is Element of QC-WFF A
<*(A,S)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,S)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,S)*>) ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,S),(A,(A,S)))),S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,S),(A,(A,S)))),S9} is non empty finite V94() set
{(All ((A,S),(A,(A,S))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,S),(A,(A,S)))),S9},{(All ((A,S),(A,(A,S))))}} is non empty finite V56() V94() set
(A,SQ) is Element of bound_QC-variables A
(A,SQ) is Element of (A)
(A,(A,SQ)) is Element of QC-WFF A
All ((A,SQ),(A,(A,SQ))) is Element of QC-WFF A
<*(A,SQ)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,SQ)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,SQ)*>) ^ (@ (A,(A,SQ))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,SQ),(A,(A,SQ)))),S9] is V15() Element of [:(QC-WFF A),(A):]
{(All ((A,SQ),(A,(A,SQ)))),S9} is non empty finite V94() set
{(All ((A,SQ),(A,(A,SQ))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,SQ),(A,(A,SQ)))),S9},{(All ((A,SQ),(A,(A,SQ))))}} is non empty finite V56() V94() set
(A,(A,SQ),(A,SQ)) is V15() Element of [:(A),(bound_QC-variables A):]
{(A,SQ),(A,SQ)} is non empty finite V94() set
{(A,SQ)} is non empty trivial finite 1 -element V94() set
{{(A,SQ),(A,SQ)},{(A,SQ)}} is non empty finite V56() V94() set
l is set
l is set
[l,l] is V15() set
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
(A,(A,S),(A,S)) is V15() Element of [:(A),(bound_QC-variables A):]
{(A,S),(A,S)} is non empty finite V94() set
{(A,S)} is non empty trivial finite 1 -element V94() set
{{(A,S),(A,S)},{(A,S)}} is non empty finite V56() V94() set
l is set
l is set
[l,l] is V15() set
{l,l} is non empty finite V94() set
{l} is non empty trivial finite 1 -element V94() set
{{l,l},{l}} is non empty finite V56() V94() set
(A,(A,S)) is Relation-like Function-like Element of (A)
[(A,(A,S)),(A,(A,S))] is V15() Element of [:(QC-WFF A),(A):]
{(A,(A,S)),(A,(A,S))} is non empty finite V94() set
{(A,(A,S))} is non empty trivial finite 1 -element V94() set
{{(A,(A,S)),(A,(A,S))},{(A,(A,S))}} is non empty finite V56() V94() set
(A,(A,SQ)) is Relation-like Function-like Element of (A)
[(A,(A,SQ)),(A,(A,SQ))] is V15() Element of [:(QC-WFF A),(A):]
{(A,(A,SQ)),(A,(A,SQ))} is non empty finite V94() set
{(A,(A,SQ))} is non empty trivial finite 1 -element V94() set
{{(A,(A,SQ)),(A,(A,SQ))},{(A,(A,SQ))}} is non empty finite V56() V94() set
(A) is Relation-like Function-like set
(A) . [(All ((A,S),(A,(A,S)))),S9] is set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
S is Element of [:(A),(bound_QC-variables A):]
(A,S) is Element of (A)
SQ is Relation-like Function-like (A,S)
(A,S,SQ) is Element of (A)
(A,(A,S,SQ)) is Element of (A)
F₁() is Relation-like non empty QC-alphabet
(F₁()) is non empty (F₁()) set
QC-variables F₁() is non empty set
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:{4,5},(QC-symbols F₁()):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols F₁()):] is non empty set
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
bool (QC-variables F₁()) is non empty set
[:{4},(QC-symbols F₁()):] is non empty set
S is Element of (F₁())
A is Element of bound_QC-variables F₁()
(F₁(),S,A) is V15() Element of [:(F₁()),(bound_QC-variables F₁()):]
[:(F₁()),(bound_QC-variables F₁()):] is non empty set
{S,A} is non empty finite V94() set
{S} is non empty trivial finite 1 -element V94() set
{{S,A},{S}} is non empty finite V56() V94() set
(F₁(),(F₁(),S,A)) is Element of (F₁())
SQ is Relation-like Function-like (F₁(),(F₁(),S,A))
(F₁(),(F₁(),S,A),SQ) is Element of (F₁())
(F₁(),(F₁(),(F₁(),S,A),SQ)) is Element of (F₁())
A is Element of (F₁())
(F₁(),A) is Relation-like Function-like Element of (F₁())
(F₁()) is functional non empty set
PFuncs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is functional non empty set
S is Element of (F₁())
(F₁(),S) is Relation-like Function-like Element of (F₁())
(F₁(),A,S) is Element of (F₁())
(F₁(),(F₁(),A,S)) is Element of (F₁())
(F₁(),(F₁(),A,S)) is Element of (F₁())
A is Element of (F₁())
(F₁(),A) is (F₁()) Element of (F₁())
QC-WFF F₁() is non empty set
(F₁(),A) is Element of QC-WFF F₁()
'not' (F₁(),A) is Element of QC-WFF F₁()
@ (F₁(),A) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (F₁(),A)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(F₁(),A) is Relation-like Function-like Element of (F₁())
[('not' (F₁(),A)),(F₁(),A)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{('not' (F₁(),A)),(F₁(),A)} is non empty finite V94() set
{('not' (F₁(),A))} is non empty trivial finite 1 -element V94() set
{{('not' (F₁(),A)),(F₁(),A)},{('not' (F₁(),A))}} is non empty finite V56() V94() set
(F₁(),(F₁(),A)) is Element of (F₁())
A is Element of (F₁())
QC-pred_symbols F₁() is non empty set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols F₁() : 7 <= b₁ } is set
A is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols F₁() : the_arity_of b₁ = A } is set
S is Element of A -ary_QC-pred_symbols F₁()
SQ is Relation-like NAT -defined QC-variables F₁() -valued Function-like finite A -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables F₁()
S9 is Relation-like Function-like Element of (F₁())
(F₁(),S,SQ,S9) is (F₁()) Element of (F₁())
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
len (@ (A,S)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (A,(A,S))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Element of (A)
(A,SQ) is (A) Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,SQ) is Element of QC-WFF A
'not' (A,SQ) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,SQ) is Relation-like Function-like Element of (A)
[('not' (A,SQ)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,SQ)),(A,SQ)} is non empty finite V94() set
{('not' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{('not' (A,SQ)),(A,SQ)},{('not' (A,SQ))}} is non empty finite V56() V94() set
the_argument_of ('not' (A,SQ)) is Element of QC-WFF A
@ (the_argument_of ('not' (A,SQ))) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (the_argument_of ('not' (A,SQ)))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
len (@ (A,S)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (A,(A,S))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (A,(A,S))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Element of (A)
S9 is Element of (A)
(A,SQ,S9) is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S9) is Relation-like Function-like Element of (A)
(A,SQ) is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
(A,SQ) '&' (A,S9) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,SQ))) ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,SQ) '&' (A,S9)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{((A,SQ) '&' (A,S9)),(A,SQ)} is non empty finite V94() set
{((A,SQ) '&' (A,S9))} is non empty trivial finite 1 -element V94() set
{{((A,SQ) '&' (A,S9)),(A,SQ)},{((A,SQ) '&' (A,S9))}} is non empty finite V56() V94() set
the_left_argument_of ((A,SQ) '&' (A,S9)) is Element of QC-WFF A
@ (the_left_argument_of ((A,SQ) '&' (A,S9))) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (the_left_argument_of ((A,SQ) '&' (A,S9)))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
the_right_argument_of ((A,SQ) '&' (A,S9)) is Element of QC-WFF A
@ (the_right_argument_of ((A,SQ) '&' (A,S9))) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (the_right_argument_of ((A,SQ) '&' (A,S9)))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
len (@ (A,S)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (A,(A,S))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
SQ is Element of [:(A),(bound_QC-variables A):]
S9 is Relation-like Function-like (A,SQ)
(A,SQ,S9) is Element of (A)
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,SQ) is Element of bound_QC-variables A
(A,SQ) is Element of (A)
(A,(A,SQ)) is Element of QC-WFF A
All ((A,SQ),(A,(A,SQ))) is Element of QC-WFF A
<*(A,SQ)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,SQ)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,SQ)*>) ^ (@ (A,(A,SQ))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,SQ),(A,(A,SQ)))),S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,SQ),(A,(A,SQ)))),S9} is non empty finite V94() set
{(All ((A,SQ),(A,(A,SQ))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,SQ),(A,(A,SQ)))),S9},{(All ((A,SQ),(A,(A,SQ))))}} is non empty finite V56() V94() set
the_scope_of (All ((A,SQ),(A,(A,SQ)))) is Element of QC-WFF A
@ (the_scope_of (All ((A,SQ),(A,(A,SQ))))) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
len (@ (the_scope_of (All ((A,SQ),(A,(A,SQ)))))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(@ (A,S)) . 1 is set
((@ (A,S)) . 1) `1 is set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
VERUM A is Element of CQC-WFF A
SQ is Relation-like Function-like Element of (A)
[(VERUM A),SQ] is V15() Element of [:(CQC-WFF A),(A):]
[:(CQC-WFF A),(A):] is non empty set
{(VERUM A),SQ} is non empty finite V94() set
{(VERUM A)} is non empty trivial finite 1 -element V94() set
{{(VERUM A),SQ},{(VERUM A)}} is non empty finite V56() V94() set
[0,0] `1 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
S9 is Element of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Relation-like Function-like Element of (A)
(A,S9,S9,l) is (A) Element of (A)
S9 ! S9 is Element of QC-WFF A
[(S9 ! S9),l] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(S9 ! S9),l} is non empty finite V94() set
{(S9 ! S9)} is non empty trivial finite 1 -element V94() set
{{(S9 ! S9),l},{(S9 ! S9)}} is non empty finite V56() V94() set
<*S9*> is Relation-like NAT -defined SQ -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of SQ -ary_QC-pred_symbols A
<*S9*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + SQ -element FinSequence-like FinSubsequence-like V94() set
1 + SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Element of (A)
(A,SQ) is (A) Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,SQ) is Element of QC-WFF A
'not' (A,SQ) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,SQ) is Relation-like Function-like Element of (A)
[('not' (A,SQ)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,SQ)),(A,SQ)} is non empty finite V94() set
{('not' (A,SQ))} is non empty trivial finite 1 -element V94() set
{{('not' (A,SQ)),(A,SQ)},{('not' (A,SQ))}} is non empty finite V56() V94() set
SQ is Element of (A)
S9 is Element of (A)
(A,SQ,S9) is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S9) is Relation-like Function-like Element of (A)
(A,SQ) is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
(A,SQ) '&' (A,S9) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,S9) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,SQ))) ^ (@ (A,S9)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((A,SQ) '&' (A,S9)),(A,SQ)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{((A,SQ) '&' (A,S9)),(A,SQ)} is non empty finite V94() set
{((A,SQ) '&' (A,S9))} is non empty trivial finite 1 -element V94() set
{{((A,SQ) '&' (A,S9)),(A,SQ)},{((A,SQ) '&' (A,S9))}} is non empty finite V56() V94() set
(@ (A,SQ)) ^ (@ (A,S9)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ ((@ (A,SQ)) ^ (@ (A,S9))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
[:(A),(bound_QC-variables A):] is non empty set
SQ is Element of [:(A),(bound_QC-variables A):]
S9 is Relation-like Function-like (A,SQ)
(A,SQ,S9) is Element of (A)
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,SQ) is Element of bound_QC-variables A
(A,SQ) is Element of (A)
(A,(A,SQ)) is Element of QC-WFF A
All ((A,SQ),(A,(A,SQ))) is Element of QC-WFF A
<*(A,SQ)*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,SQ)*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,SQ)*>) ^ (@ (A,(A,SQ))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((A,SQ),(A,(A,SQ)))),S9] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{(All ((A,SQ),(A,(A,SQ)))),S9} is non empty finite V94() set
{(All ((A,SQ),(A,(A,SQ))))} is non empty trivial finite 1 -element V94() set
{{(All ((A,SQ),(A,(A,SQ)))),S9},{(All ((A,SQ),(A,(A,SQ))))}} is non empty finite V56() V94() set
<*(A,SQ)*> ^ (@ (A,(A,SQ))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
<*[3,0]*> ^ (<*(A,SQ)*> ^ (@ (A,(A,SQ)))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(@ (A,S)) . 1 is set
((@ (A,S)) . 1) `1 is set
QC-pred_symbols A is non empty set
{ [b<sub>1</sub>,b<sub>2</sub>] where b<sub>1</sub> is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b<sub>2</sub> is Element of QC-symbols A : 7 <= b<sub>1</sub> } is set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of QC-pred_symbols A : the_arity_of b<sub>1</sub> = SQ } is set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(@ (A,S)) . 1 is set
((@ (A,S)) . 1) `1 is set
F₂() is non empty set
F₁() is Relation-like non empty QC-alphabet
(F₁()) is non empty (F₁()) set
[:(F₁()),F₂():] is non empty set
bool [:(F₁()),F₂():] is non empty set
F₃() is Element of F₂()
A is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A + 1 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
SQ is Element of (F₁())
(F₁(),SQ) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),SQ) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),SQ)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . SQ is Element of F₂()
F₄(SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
F₅((S . (F₁(),SQ))) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
F₆((S . (F₁(),SQ)),(S . (F₁(),SQ))) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
F₇(F₁(),SQ,(S . (F₁(),SQ))) is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
S9 is Element of F₂()
l is Element of F₂()
l is Element of F₂()
s is Element of F₂()
P9 is Element of F₂()
SQ is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
S9 is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),S9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),S9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 . S9 is Element of F₂()
F₄(S9) is Element of F₂()
(F₁(),S9) is Element of (F₁())
S9 . (F₁(),S9) is Element of F₂()
F₅((S9 . (F₁(),S9))) is Element of F₂()
(F₁(),S9) is Element of (F₁())
S9 . (F₁(),S9) is Element of F₂()
(F₁(),S9) is Element of (F₁())
S9 . (F₁(),S9) is Element of F₂()
F₆((S9 . (F₁(),S9)),(S9 . (F₁(),S9))) is Element of F₂()
(F₁(),S9) is Element of (F₁())
S9 . (F₁(),S9) is Element of F₂()
F₇(F₁(),S9,(S9 . (F₁(),S9))) is Element of F₂()
S . S9 is Element of F₂()
S . S9 is Element of F₂()
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . (F₁(),S9) is Element of F₂()
S . S9 is Element of F₂()
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . (F₁(),S9) is Element of F₂()
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . (F₁(),S9) is Element of F₂()
S . S9 is Element of F₂()
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S . (F₁(),S9) is Element of F₂()
S . S9 is Element of F₂()
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
S is Element of (F₁())
(F₁(),S) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),S) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),S)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . S is Element of F₂()
F₄(S) is Element of F₂()
(F₁(),S) is Element of (F₁())
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S) is Element of F₂()
F₅(( the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S))) is Element of F₂()
(F₁(),S) is Element of (F₁())
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S) is Element of F₂()
(F₁(),S) is Element of (F₁())
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S) is Element of F₂()
F₆(( the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S)),( the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S))) is Element of F₂()
(F₁(),S) is Element of (F₁())
the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S) is Element of F₂()
F₇(F₁(),S,( the Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():] . (F₁(),S))) is Element of F₂()
A is set
S is Element of (F₁())
(F₁(),S) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),S) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),S)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
SQ . A is set
S9 is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
S9 . S is Element of F₂()
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
@ (F₁(),S9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),S9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ . S9 is Element of F₂()
S9 . S9 is Element of F₂()
F₄(S9) is Element of F₂()
(F₁(),S9) is Element of (F₁())
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ . (F₁(),S9) is Element of F₂()
S9 . (F₁(),S9) is Element of F₂()
F₅((S9 . (F₁(),S9))) is Element of F₂()
(F₁(),S9) is Element of (F₁())
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ . (F₁(),S9) is Element of F₂()
S9 . (F₁(),S9) is Element of F₂()
(F₁(),S9) is Element of (F₁())
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ . (F₁(),S9) is Element of F₂()
S9 . (F₁(),S9) is Element of F₂()
F₆((S9 . (F₁(),S9)),(S9 . (F₁(),S9))) is Element of F₂()
(F₁(),S9) is Element of (F₁())
(F₁(),(F₁(),S9)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),S9)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),S9))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ . (F₁(),S9) is Element of F₂()
S9 . (F₁(),S9) is Element of F₂()
F₇(F₁(),S9,(S9 . (F₁(),S9))) is Element of F₂()
A is Relation-like Function-like set
proj1 A is set
proj2 A is set
S is set
SQ is set
A . SQ is set
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),S9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),S9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
S9 . S9 is Element of F₂()
S is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
SQ is Element of (F₁())
S . SQ is Element of F₂()
F₄(SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
(F₁(),SQ) is Element of (F₁())
S . (F₁(),SQ) is Element of F₂()
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
QC-WFF F₁() is non empty set
@ (F₁(),S9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
len (@ (F₁(),S9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 is Element of F₂()
F₅(S9) is Element of F₂()
l is Element of F₂()
F₆(S9,l) is Element of F₂()
F₇(F₁(),SQ,S9) is Element of F₂()
l is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
l . SQ is Element of F₂()
(F₁(),SQ) is Element of QC-WFF F₁()
@ (F₁(),SQ) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),SQ)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
P9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
s is Element of (F₁())
(F₁(),s) is Element of QC-WFF F₁()
@ (F₁(),s) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),s)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . s is Element of F₂()
F₄(s) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₅((l . (F₁(),s))) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₆((l . (F₁(),s)),(l . (F₁(),s))) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₇(F₁(),s,(l . (F₁(),s))) is Element of F₂()
(F₁(),(F₁(),SQ)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),SQ))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
k9 is Element of (F₁())
(F₁(),k9) is Element of QC-WFF F₁()
@ (F₁(),k9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),k9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . k9 is Element of F₂()
F₄(k9) is Element of F₂()
(F₁(),k9) is Element of (F₁())
l . (F₁(),k9) is Element of F₂()
F₅((l . (F₁(),k9))) is Element of F₂()
(F₁(),k9) is Element of (F₁())
l . (F₁(),k9) is Element of F₂()
(F₁(),k9) is Element of (F₁())
l . (F₁(),k9) is Element of F₂()
F₆((l . (F₁(),k9)),(l . (F₁(),k9))) is Element of F₂()
(F₁(),k9) is Element of (F₁())
l . (F₁(),k9) is Element of F₂()
F₇(F₁(),k9,(l . (F₁(),k9))) is Element of F₂()
l . (F₁(),SQ) is Element of F₂()
k9 is Element of (F₁())
(F₁(),k9) is Element of QC-WFF F₁()
@ (F₁(),k9) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),k9)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(F₁(),(F₁(),SQ)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),SQ))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(F₁(),(F₁(),SQ)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),SQ))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
c₁₃ is Element of (F₁())
(F₁(),c₁₃) is Element of QC-WFF F₁()
@ (F₁(),c₁₃) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),c₁₃)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . c₁₃ is Element of F₂()
F₄(c₁₃) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₅((l . (F₁(),c₁₃))) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₆((l . (F₁(),c₁₃)),(l . (F₁(),c₁₃))) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₇(F₁(),c₁₃,(l . (F₁(),c₁₃))) is Element of F₂()
c₁₃ is Element of (F₁())
(F₁(),c₁₃) is Element of QC-WFF F₁()
@ (F₁(),c₁₃) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),c₁₃)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . c₁₃ is Element of F₂()
F₄(c₁₃) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₅((l . (F₁(),c₁₃))) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₆((l . (F₁(),c₁₃)),(l . (F₁(),c₁₃))) is Element of F₂()
(F₁(),c₁₃) is Element of (F₁())
l . (F₁(),c₁₃) is Element of F₂()
F₇(F₁(),c₁₃,(l . (F₁(),c₁₃))) is Element of F₂()
l . (F₁(),SQ) is Element of F₂()
c₁₃ is Element of (F₁())
(F₁(),c₁₃) is Element of QC-WFF F₁()
@ (F₁(),c₁₃) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),c₁₃)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . (F₁(),SQ) is Element of F₂()
c₁₃ is Element of (F₁())
(F₁(),c₁₃) is Element of QC-WFF F₁()
@ (F₁(),c₁₃) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),c₁₃)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(F₁(),(F₁(),SQ)) is Element of QC-WFF F₁()
@ (F₁(),(F₁(),SQ)) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),(F₁(),SQ))) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
s is Element of (F₁())
(F₁(),s) is Element of QC-WFF F₁()
@ (F₁(),s) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),s)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
l . s is Element of F₂()
F₄(s) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₅((l . (F₁(),s))) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₆((l . (F₁(),s)),(l . (F₁(),s))) is Element of F₂()
(F₁(),s) is Element of (F₁())
l . (F₁(),s) is Element of F₂()
F₇(F₁(),s,(l . (F₁(),s))) is Element of F₂()
l . (F₁(),SQ) is Element of F₂()
s is Element of (F₁())
(F₁(),s) is Element of QC-WFF F₁()
@ (F₁(),s) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (F₁(),s)) is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
F₁() is Relation-like non empty QC-alphabet
(F₁()) is non empty (F₁()) set
F₂() is non empty set
[:(F₁()),F₂():] is non empty set
bool [:(F₁()),F₂():] is non empty set
F₃() is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
F₅() is Element of F₂()
F₄() is Relation-like (F₁()) -defined F₂() -valued Function-like V29((F₁()),F₂()) Element of bool [:(F₁()),F₂():]
QC-pred_symbols F₁() is non empty set
QC-symbols F₁() is non empty set
proj2 F₁() is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols F₁() : 7 <= b₁ } is set
QC-variables F₁() is non empty set
[:{4,5},(QC-symbols F₁()):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols F₁()):] is non empty set
(F₁()) is functional non empty set
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
bool (QC-variables F₁()) is non empty set
[:{4},(QC-symbols F₁()):] is non empty set
PFuncs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is functional non empty set
A is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols F₁() : the_arity_of b₁ = A } is set
S is Element of A -ary_QC-pred_symbols F₁()
SQ is Relation-like NAT -defined QC-variables F₁() -valued Function-like finite A -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables F₁()
S9 is Relation-like Function-like Element of (F₁())
(F₁(),S,SQ,S9) is (F₁()) Element of (F₁())
F₃() . (F₁(),S,SQ,S9) is Element of F₂()
F₄() . (F₁(),S,SQ,S9) is Element of F₂()
F₆((F₁(),S,SQ,S9)) is Element of F₂()
A is Element of bound_QC-variables F₁()
S is Element of (F₁())
(F₁(),S,A) is V15() Element of [:(F₁()),(bound_QC-variables F₁()):]
[:(F₁()),(bound_QC-variables F₁()):] is non empty set
{S,A} is non empty finite V94() set
{S} is non empty trivial finite 1 -element V94() set
{{S,A},{S}} is non empty finite V56() V94() set
F₃() . S is Element of F₂()
F₄() . S is Element of F₂()
SQ is Relation-like Function-like (F₁(),(F₁(),S,A))
(F₁(),(F₁(),S,A),SQ) is Element of (F₁())
F₃() . (F₁(),(F₁(),S,A),SQ) is Element of F₂()
F₄() . (F₁(),(F₁(),S,A),SQ) is Element of F₂()
(F₁(),(F₁(),(F₁(),S,A),SQ)) is Element of (F₁())
(F₁(),(F₁(),S,A)) is Element of (F₁())
F₄() . (F₁(),(F₁(),(F₁(),S,A),SQ)) is Element of F₂()
F₉(F₁(),(F₁(),(F₁(),S,A),SQ),(F₄() . (F₁(),(F₁(),(F₁(),S,A),SQ)))) is Element of F₂()
A is Element of (F₁())
F₃() . A is Element of F₂()
F₄() . A is Element of F₂()
A is Element of (F₁())
(F₁(),A) is Relation-like Function-like Element of (F₁())
S is Element of (F₁())
(F₁(),S) is Relation-like Function-like Element of (F₁())
F₃() . A is Element of F₂()
F₄() . A is Element of F₂()
F₃() . S is Element of F₂()
F₄() . S is Element of F₂()
(F₁(),A,S) is Element of (F₁())
F₃() . (F₁(),A,S) is Element of F₂()
F₄() . (F₁(),A,S) is Element of F₂()
(F₁(),(F₁(),A,S)) is Element of (F₁())
(F₁(),(F₁(),A,S)) is Element of (F₁())
F₈((F₄() . A),(F₄() . S)) is Element of F₂()
A is Element of (F₁())
F₃() . A is Element of F₂()
F₄() . A is Element of F₂()
(F₁(),A) is (F₁()) Element of (F₁())
QC-WFF F₁() is non empty set
(F₁(),A) is Element of QC-WFF F₁()
'not' (F₁(),A) is Element of QC-WFF F₁()
@ (F₁(),A) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (F₁(),A)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(F₁(),A) is Relation-like Function-like Element of (F₁())
[('not' (F₁(),A)),(F₁(),A)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{('not' (F₁(),A)),(F₁(),A)} is non empty finite V94() set
{('not' (F₁(),A))} is non empty trivial finite 1 -element V94() set
{{('not' (F₁(),A)),(F₁(),A)},{('not' (F₁(),A))}} is non empty finite V56() V94() set
F₃() . (F₁(),A) is Element of F₂()
F₄() . (F₁(),A) is Element of F₂()
(F₁(),(F₁(),A)) is Element of (F₁())
F₇((F₄() . A)) is Element of F₂()
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
SQ is Element of QC-WFF A
S9 is Relation-like Function-like Element of (A)
[SQ,S9] is V15() Element of [:(QC-WFF A),(A):]
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
S is Element of [:(QC-WFF A),(A):]
S `1 is set
SQ is set
S9 is set
[SQ,S9] is V15() set
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
S `2 is set
SQ is set
S9 is set
[SQ,S9] is V15() set
{SQ,S9} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S9},{SQ}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
S is Element of [:(QC-WFF A),(A):]
(A,S) is Element of QC-WFF A
bound_in (A,S) is Element of bound_QC-variables A
(A,S) is Relation-like Function-like Element of (A)
(A,(bound_in (A,S)),(A,S),(A,S)) is Relation-like Function-like finite V94() Element of (A)
still_not-bound_in (A,S) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set
proj1 (A,S) is set
{ b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (A,S) & b₁ is Element of proj1 (A,S) & not b₁ = bound_in (A,S) & not b₁ = (A,S) . b₁ ) } is set
(A,(A,S), { b₁ where b₁ is Element of bound_QC-variables A : ( b₁ in still_not-bound_in (A,S) & b₁ is Element of proj1 (A,S) & not b₁ = bound_in (A,S) & not b₁ = (A,S) . b₁ ) } ) is Relation-like Function-like Element of (A)
proj2 (A,(bound_in (A,S)),(A,S),(A,S)) is finite V94() set
the_scope_of (A,S) is Element of QC-WFF A
(A,(A,(bound_in (A,S)),(A,S),(A,S)),(the_scope_of (A,S))) is Element of QC-symbols A
(A,(the_scope_of (A,S)),(A,(bound_in (A,S)),(A,S),(A,S))) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty set
(A,(the_scope_of (A,S))) is finite V94() Element of bool (QC-symbols A)
(A,(the_scope_of (A,S))) is finite V94() Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in (A,(the_scope_of (A,S))) } is set
(A,(A,(bound_in (A,S)),(A,S),(A,S))) is finite V94() Element of bool (QC-symbols A)
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in proj2 (A,(bound_in (A,S)),(A,S),(A,S)) } is set
(A,(the_scope_of (A,S))) \/ (A,(A,(bound_in (A,S)),(A,S),(A,S))) is finite V94() Element of bool (QC-symbols A)
NAT \ ((A,(the_scope_of (A,S))) \/ (A,(A,(bound_in (A,S)),(A,S),(A,S)))) is V45() V46() V47() V48() V49() V50() Element of bool REAL
the Element of (A,(the_scope_of (A,S)),(A,(bound_in (A,S)),(A,S),(A,S))) is Element of (A,(the_scope_of (A,S)),(A,(bound_in (A,S)),(A,S),(A,S)))
x. (A,(A,(bound_in (A,S)),(A,S),(A,S)),(the_scope_of (A,S))) is Element of bound_QC-variables A
[4,(A,(A,(bound_in (A,S)),(A,S),(A,S)),(the_scope_of (A,S)))] is V15() set
{4,(A,(A,(bound_in (A,S)),(A,S),(A,S)),(the_scope_of (A,S)))} is non empty finite V94() set
{{4,(A,(A,(bound_in (A,S)),(A,S),(A,S)),(the_scope_of (A,S)))},{4}} is non empty finite V56() V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
S is Element of (A)
(A,S) is Element of [:(QC-WFF A),(A):]
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
(A,(A,S)) is Element of bound_QC-variables A
SQ is Element of QC-WFF A
All ((A,(A,S)),SQ) is Element of QC-WFF A
<*(A,(A,S))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,S))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ SQ is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,(A,S))*>) ^ (@ SQ) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 is Element of (A)
S . S9 is Element of QC-WFF A
S9 is Element of (A)
S . S9 is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
the_pred_symbol_of (A,S9) is Element of QC-pred_symbols A
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
(A,S9) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A,S9) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,(A,S9),(A,S9)) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(the_pred_symbol_of (A,S9)) ! (A,(A,S9),(A,S9)) is Element of QC-WFF A
l is Element of (A)
l is Element of QC-WFF A
(A,l) is Element of (A)
S . (A,l) is Element of QC-WFF A
S . l is Element of QC-WFF A
'not' l is Element of QC-WFF A
@ l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ l) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
s is Element of (A)
P9 is Element of QC-WFF A
(A,s) is Element of (A)
S . (A,s) is Element of QC-WFF A
s is Element of QC-WFF A
(A,s) is Element of (A)
S . (A,s) is Element of QC-WFF A
S . s is Element of QC-WFF A
P9 '&' s is Element of QC-WFF A
@ P9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ P9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ P9)) ^ (@ s) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
k9 is Element of (A)
k99 is Element of QC-WFF A
(A,k9) is Element of (A)
S . (A,k9) is Element of QC-WFF A
S . k9 is Element of QC-WFF A
(A,k9,k99) is Element of QC-WFF A
(A,k9) is Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
(A,(A,k9)) is Element of bound_QC-variables A
All ((A,(A,k9)),k99) is Element of QC-WFF A
<*(A,(A,k9))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,k9))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ k99 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,(A,k9))*>) ^ (@ k99) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
S9 is Element of (A)
SQ . S9 is Element of QC-WFF A
S9 is Element of (A)
SQ . S9 is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
the_pred_symbol_of (A,S9) is Element of QC-pred_symbols A
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
(A,S9) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A,S9) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,(A,S9),(A,S9)) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(the_pred_symbol_of (A,S9)) ! (A,(A,S9),(A,S9)) is Element of QC-WFF A
l is Element of (A)
l is Element of QC-WFF A
(A,l) is Element of (A)
SQ . (A,l) is Element of QC-WFF A
SQ . l is Element of QC-WFF A
'not' l is Element of QC-WFF A
@ l is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ l) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
s is Element of (A)
P9 is Element of QC-WFF A
(A,s) is Element of (A)
SQ . (A,s) is Element of QC-WFF A
s is Element of QC-WFF A
(A,s) is Element of (A)
SQ . (A,s) is Element of QC-WFF A
SQ . s is Element of QC-WFF A
P9 '&' s is Element of QC-WFF A
@ P9 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ P9) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ s is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ P9)) ^ (@ s) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
k9 is Element of (A)
k99 is Element of QC-WFF A
(A,k9) is Element of (A)
SQ . (A,k9) is Element of QC-WFF A
SQ . k9 is Element of QC-WFF A
(A,k9,k99) is Element of QC-WFF A
(A,k9) is Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
(A,(A,k9)) is Element of bound_QC-variables A
All ((A,(A,k9)),k99) is Element of QC-WFF A
<*(A,(A,k9))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,k9))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ k99 is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,(A,k9))*>) ^ (@ k99) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
S is Element of (A)
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ . S is Element of QC-WFF A
S9 is Element of (A)
SQ . S9 is Element of QC-WFF A
S9 is Element of (A)
SQ . S9 is Element of QC-WFF A
(A,S9) is Element of QC-WFF A
the_pred_symbol_of (A,S9) is Element of QC-pred_symbols A
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
(A,S9) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
(A,S9) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,(A,S9),(A,S9)) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(the_pred_symbol_of (A,S9)) ! (A,(A,S9),(A,S9)) is Element of QC-WFF A
l is Element of (A)
SQ . l is Element of QC-WFF A
(A,l) is Element of (A)
SQ . (A,l) is Element of QC-WFF A
'not' (SQ . (A,l)) is Element of QC-WFF A
@ (SQ . (A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (SQ . (A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
l is Element of (A)
SQ . l is Element of QC-WFF A
(A,l) is Element of (A)
SQ . (A,l) is Element of QC-WFF A
(A,l) is Element of (A)
SQ . (A,l) is Element of QC-WFF A
(SQ . (A,l)) '&' (SQ . (A,l)) is Element of QC-WFF A
@ (SQ . (A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[2,0]*> ^ (@ (SQ . (A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (SQ . (A,l)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (SQ . (A,l)))) ^ (@ (SQ . (A,l))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
s is Element of (A)
SQ . s is Element of QC-WFF A
(A,s) is Element of (A)
SQ . (A,s) is Element of QC-WFF A
(A,s,(SQ . (A,s))) is Element of QC-WFF A
(A,s) is Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
(A,(A,s)) is Element of bound_QC-variables A
All ((A,(A,s)),(SQ . (A,s))) is Element of QC-WFF A
<*(A,(A,s))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,s))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (SQ . (A,s)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,(A,s))*>) ^ (@ (SQ . (A,s))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
SQ is Element of QC-WFF A
S9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 . S is Element of QC-WFF A
S9 is Element of QC-WFF A
l is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
l . S is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
'not' (A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ . S is Element of QC-WFF A
S9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 . (A,S) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is (A) Element of (A)
QC-WFF A is non empty set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
(A,(A,S)) is Element of QC-WFF A
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,(A,S)) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
(A,(A,S)) '&' (A,(A,S)) is Element of QC-WFF A
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
QC-symbols A is non empty set
proj2 A is set
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,(A,S)))) ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ . S is Element of QC-WFF A
S9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 . (A,S) is Element of QC-WFF A
S9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 . (A,S) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,S,SQ) is Element of (A)
(A,(A,S,SQ)) is Element of QC-WFF A
(A,SQ) is Element of QC-WFF A
(A,S) '&' (A,SQ) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S))) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,(A,S,SQ)) is Element of (A)
(A,(A,S,SQ)) is Element of (A)
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-WFF A is non empty set
(A,S) is Element of (A)
(A,(A,S)) is Element of QC-WFF A
(A,S,(A,(A,S))) is Element of QC-WFF A
(A,S) is Element of [:(QC-WFF A),(A):]
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
(A,(A,S)) is Element of bound_QC-variables A
All ((A,(A,S)),(A,(A,S))) is Element of QC-WFF A
<*(A,(A,S))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,S))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,S)) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,(A,S))*>) ^ (@ (A,(A,S))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ . S is Element of QC-WFF A
S9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
S9 . (A,S) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
{ b₁ where b₁ is Element of (A) : (A,b₁) is Element of CQC-WFF A } is set
bool (A) is non empty set
SQ is set
S9 is Element of (A)
(A,S9) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is Element of bool (A)
(A) is non empty (A) set
bool (A) is non empty set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
{ b₁ where b₁ is Element of (A) : (A,b₁) is Element of CQC-WFF A } is set
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
the Relation-like Function-like Element of (A) is Relation-like Function-like Element of (A)
VERUM A is Element of CQC-WFF A
[(VERUM A), the Relation-like Function-like Element of (A)] is V15() Element of [:(CQC-WFF A),(A):]
[:(CQC-WFF A),(A):] is non empty set
{(VERUM A), the Relation-like Function-like Element of (A)} is non empty finite V94() set
{(VERUM A)} is non empty trivial finite 1 -element V94() set
{{(VERUM A), the Relation-like Function-like Element of (A)},{(VERUM A)}} is non empty finite V56() V94() set
SQ is Element of (A)
(A,SQ) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Element of (A)
(A,S) is Element of QC-WFF A
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
SQ is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
SQ . S is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
SQ ! S9 is Element of CQC-WFF A
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
the_pred_symbol_of (SQ ! S9) is Element of QC-pred_symbols A
<*SQ*> is Relation-like NAT -defined S -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S -ary_QC-pred_symbols A
<*SQ*> ^ S9 is Relation-like NAT -defined Function-like non empty finite 1 + S -element FinSequence-like FinSubsequence-like V94() set
1 + S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
(<*SQ*> ^ S9) . 1 is set
S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S9 -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S9 } is set
l is Element of S9 -ary_QC-pred_symbols A
l is Relation-like NAT -defined QC-variables A -valued Function-like finite S9 -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l ! l is Element of QC-WFF A
<*l*> is Relation-like NAT -defined S9 -ary_QC-pred_symbols A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of S9 -ary_QC-pred_symbols A
<*l*> ^ l is Relation-like NAT -defined Function-like non empty finite 1 + S9 -element FinSequence-like FinSubsequence-like V94() set
1 + S9 is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A is Relation-like non empty QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like V94() set
len SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
proj2 SQ is finite V94() set
proj2 SQ is finite V94() set
A is Relation-like non empty QC-alphabet
QC-pred_symbols A is non empty set
QC-symbols A is non empty set
proj2 A is set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
S -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = S } is set
SQ is Element of S -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
S9 is Relation-like Function-like Element of (A)
(A,SQ,S9,S9) is (A) Element of (A)
(A) is non empty (A) set
(A,(A,SQ,S9,S9)) is Element of QC-WFF A
(A,(A,SQ,S9,S9)) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
(A,(A,SQ,S9,S9)) is Relation-like Function-like Element of (A)
(A,l,(A,(A,SQ,S9,S9))) is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
(A,l) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
(A,(A,l),(A,(A,SQ,S9,S9))) is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
len l is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
s is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
len s is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ ! S9 is Element of CQC-WFF A
[(SQ ! S9),S9] is V15() Element of [:(CQC-WFF A),(A):]
[:(CQC-WFF A),(A):] is non empty set
{(SQ ! S9),S9} is non empty finite V94() set
{(SQ ! S9)} is non empty trivial finite 1 -element V94() set
{{(SQ ! S9),S9},{(SQ ! S9)}} is non empty finite V56() V94() set
(A,(A,SQ,S9,S9)) is Element of QC-WFF A
the_pred_symbol_of (A,(A,SQ,S9,S9)) is Element of QC-pred_symbols A
[:(A),(QC-WFF A):] is non empty set
bool [:(A),(QC-WFF A):] is non empty set
VERUM A is Element of CQC-WFF A
P9 is Element of S -ary_QC-pred_symbols A
s is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite S -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
P9 ! s is Element of CQC-WFF A
k9 is Relation-like (A) -defined QC-WFF A -valued Function-like V29((A), QC-WFF A) Element of bool [:(A),(QC-WFF A):]
k9 . (A,SQ,S9,S9) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Element of (A)
(A,S) is Element of QC-WFF A
(A,S) is (A) Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,S) is Relation-like Function-like Element of (A)
[('not' (A,S)),(A,S)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,S)),(A,S)} is non empty finite V94() set
{('not' (A,S))} is non empty trivial finite 1 -element V94() set
{{('not' (A,S)),(A,S)},{('not' (A,S))}} is non empty finite V56() V94() set
(A,(A,S)) is Element of QC-WFF A
'not' (A,S) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
<*[1,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Element of (A)
(A,S) is Relation-like Function-like Element of (A)
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
(A,S) is Element of QC-WFF A
SQ is Element of (A)
(A,SQ) is Relation-like Function-like Element of (A)
(A,SQ) is Element of QC-WFF A
(A,S,SQ) is Element of (A)
(A,(A,S,SQ)) is Element of QC-WFF A
(A,S) '&' (A,SQ) is Element of QC-WFF A
@ (A,S) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (A,S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[2,0]*> ^ (@ (A,S))) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
A is Relation-like non empty QC-alphabet
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
(A) is non empty (A) set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
S is Element of bound_QC-variables A
SQ is Element of (A)
(A,SQ,S) is V15() Element of [:(A),(bound_QC-variables A):]
[:(A),(bound_QC-variables A):] is non empty set
{SQ,S} is non empty finite V94() set
{SQ} is non empty trivial finite 1 -element V94() set
{{SQ,S},{SQ}} is non empty finite V56() V94() set
(A,SQ) is Element of QC-WFF A
S9 is Relation-like Function-like (A,(A,SQ,S))
(A,(A,SQ,S),S9) is Element of (A)
(A,(A,(A,SQ,S),S9)) is Element of QC-WFF A
(A,(A,(A,SQ,S),S9)) is Element of (A)
(A,(A,SQ,S)) is Element of (A)
(A,(A,(A,(A,SQ,S),S9))) is Element of QC-WFF A
(A,(A,(A,SQ,S),S9),(A,(A,(A,(A,SQ,S),S9)))) is Element of QC-WFF A
(A,(A,(A,SQ,S),S9)) is Element of [:(QC-WFF A),(A):]
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
[:(QC-WFF A),(A):] is non empty set
(A,(A,(A,(A,SQ,S),S9))) is Element of bound_QC-variables A
All ((A,(A,(A,(A,SQ,S),S9))),(A,(A,(A,(A,SQ,S),S9)))) is Element of QC-WFF A
<*(A,(A,(A,(A,SQ,S),S9)))*> is Relation-like NAT -defined bound_QC-variables A -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables A
<*[3,0]*> ^ <*(A,(A,(A,(A,SQ,S),S9)))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (A,(A,(A,(A,SQ,S),S9))) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(A,(A,(A,(A,SQ,S),S9)))*>) ^ (@ (A,(A,(A,(A,SQ,S),S9)))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
All ((A,(A,(A,(A,SQ,S),S9))),(A,SQ)) is Element of QC-WFF A
@ (A,SQ) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
(<*[3,0]*> ^ <*(A,(A,(A,(A,SQ,S),S9)))*>) ^ (@ (A,SQ)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
F₁() is Relation-like non empty QC-alphabet
(F₁()) is non empty (F₁()) set
(F₁()) is non empty Element of bool (F₁())
bool (F₁()) is non empty set
QC-WFF F₁() is non empty set
CQC-WFF F₁() is non empty Element of bool (QC-WFF F₁())
bool (QC-WFF F₁()) is non empty set
{ b₁ where b₁ is Element of (F₁()) : (F₁(),b₁) is Element of CQC-WFF F₁() } is set
QC-variables F₁() is non empty set
QC-symbols F₁() is non empty set
proj2 F₁() is set
[:{4,5},(QC-symbols F₁()):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols F₁()):] is non empty set
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
bool (QC-variables F₁()) is non empty set
[:{4},(QC-symbols F₁()):] is non empty set
QC-pred_symbols F₁() is non empty set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols F₁() : 7 <= b₁ } is set
(F₁()) is functional non empty set
PFuncs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is functional non empty set
A is Element of (F₁())
(F₁(),A) is (F₁()) Element of (F₁())
(F₁(),A) is Element of QC-WFF F₁()
'not' (F₁(),A) is Element of QC-WFF F₁()
@ (F₁(),A) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (F₁(),A)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(F₁(),A) is Relation-like Function-like Element of (F₁())
[('not' (F₁(),A)),(F₁(),A)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{('not' (F₁(),A)),(F₁(),A)} is non empty finite V94() set
{('not' (F₁(),A))} is non empty trivial finite 1 -element V94() set
{{('not' (F₁(),A)),(F₁(),A)},{('not' (F₁(),A))}} is non empty finite V56() V94() set
S is Element of (F₁())
(F₁(),S) is Element of QC-WFF F₁()
A is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
A -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols F₁() : the_arity_of b₁ = A } is set
S is Element of A -ary_QC-pred_symbols F₁()
SQ is Relation-like NAT -defined QC-variables F₁() -valued Function-like finite A -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables F₁()
S9 is Relation-like Function-like Element of (F₁())
(F₁(),S,SQ,S9) is (F₁()) Element of (F₁())
S ! SQ is Element of QC-WFF F₁()
[(S ! SQ),S9] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{(S ! SQ),S9} is non empty finite V94() set
{(S ! SQ)} is non empty trivial finite 1 -element V94() set
{{(S ! SQ),S9},{(S ! SQ)}} is non empty finite V56() V94() set
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
len SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
fixed_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
{5} is non empty trivial V45() V46() V47() V48() V49() V50() finite V56() 1 -element V94() set
[:{5},(QC-symbols F₁()):] is non empty set
{ (SQ . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len SQ & SQ . b₁ in fixed_QC-variables F₁() ) } is set
free_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
{ (SQ . b₁) where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT : ( 1 <= b₁ & b₁ <= len SQ & SQ . b₁ in free_QC-variables F₁() ) } is set
A is Element of (F₁())
(F₁(),A) is Relation-like Function-like Element of (F₁())
S is Element of (F₁())
(F₁(),S) is Relation-like Function-like Element of (F₁())
(F₁(),A,S) is Element of (F₁())
SQ is Element of (F₁())
(F₁(),SQ) is Element of QC-WFF F₁()
(F₁(),A) is Element of QC-WFF F₁()
(F₁(),S) is Element of QC-WFF F₁()
(F₁(),A) '&' (F₁(),S) is Element of QC-WFF F₁()
@ (F₁(),A) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
<*[2,0]*> ^ (@ (F₁(),A)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
@ (F₁(),S) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
(<*[2,0]*> ^ (@ (F₁(),A))) ^ (@ (F₁(),S)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[((F₁(),A) '&' (F₁(),S)),(F₁(),A)] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{((F₁(),A) '&' (F₁(),S)),(F₁(),A)} is non empty finite V94() set
{((F₁(),A) '&' (F₁(),S))} is non empty trivial finite 1 -element V94() set
{{((F₁(),A) '&' (F₁(),S)),(F₁(),A)},{((F₁(),A) '&' (F₁(),S))}} is non empty finite V56() V94() set
A is Element of bound_QC-variables F₁()
S is Element of (F₁())
(F₁(),S,A) is V15() Element of [:(F₁()),(bound_QC-variables F₁()):]
[:(F₁()),(bound_QC-variables F₁()):] is non empty set
{S,A} is non empty finite V94() set
{S} is non empty trivial finite 1 -element V94() set
{{S,A},{S}} is non empty finite V56() V94() set
SQ is Relation-like Function-like (F₁(),(F₁(),S,A))
(F₁(),(F₁(),S,A),SQ) is Element of (F₁())
S9 is Element of (F₁())
(F₁(),S9) is Element of QC-WFF F₁()
(F₁(),(F₁(),S,A)) is Element of bound_QC-variables F₁()
(F₁(),(F₁(),S,A)) is Element of (F₁())
(F₁(),(F₁(),(F₁(),S,A))) is Element of QC-WFF F₁()
All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A)))) is Element of QC-WFF F₁()
<*(F₁(),(F₁(),S,A))*> is Relation-like NAT -defined bound_QC-variables F₁() -valued Function-like constant non empty trivial finite 1 -element FinSequence-like FinSubsequence-like V94() FinSequence of bound_QC-variables F₁()
<*[3,0]*> ^ <*(F₁(),(F₁(),S,A))*> is Relation-like NAT -defined Function-like non empty finite 1 + 1 -element FinSequence-like FinSubsequence-like V94() set
@ (F₁(),(F₁(),(F₁(),S,A))) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols F₁()):]
[:NAT,(QC-symbols F₁()):] is non empty non trivial non finite set
(<*[3,0]*> ^ <*(F₁(),(F₁(),S,A))*>) ^ (@ (F₁(),(F₁(),(F₁(),S,A)))) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
[(All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A))))),SQ] is V15() Element of [:(QC-WFF F₁()),(F₁()):]
[:(QC-WFF F₁()),(F₁()):] is non empty set
{(All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A))))),SQ} is non empty finite V94() set
{(All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A)))))} is non empty trivial finite 1 -element V94() set
{{(All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A))))),SQ},{(All ((F₁(),(F₁(),S,A)),(F₁(),(F₁(),(F₁(),S,A)))))}} is non empty finite V56() V94() set
A is Element of (F₁())
A is Element of (F₁())
A is Relation-like non empty QC-alphabet
(A) is non empty (A) set
(A) is non empty Element of bool (A)
bool (A) is non empty set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
{ b₁ where b₁ is Element of (A) : (A,b₁) is Element of CQC-WFF A } is set
S is Element of (A)
(A,S) is Element of QC-WFF A
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
QC-pred_symbols A is non empty set
{ [b₁,b₂] where b₁ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT , b₂ is Element of QC-symbols A : 7 <= b₁ } is set
(A) is functional non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
SQ is ext-real V21() V22() V23() V27() V28() V32() V43() V44() V45() V46() V47() V48() V49() V50() finite cardinal V94() Element of NAT
SQ -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty set
{ b₁ where b₁ is Element of QC-pred_symbols A : the_arity_of b₁ = SQ } is set
k9 is Element of (A)
k99 is Element of bound_QC-variables A
(A,k9,k99) is V15() Element of [:(A),(bound_QC-variables A):]
[:(A),(bound_QC-variables A):] is non empty set
{k9,k99} is non empty finite V94() set
{k9} is non empty trivial finite 1 -element V94() set
{{k9,k99},{k9}} is non empty finite V56() V94() set
S9 is Element of SQ -ary_QC-pred_symbols A
S9 is Relation-like NAT -defined QC-variables A -valued bound_QC-variables A -valued Function-like finite SQ -element FinSequence-like FinSubsequence-like V94() FinSequence of QC-variables A
l is Relation-like Function-like Element of (A)
(A,S9,S9,l) is (A) Element of (A)
(A,(A,S9,S9,l)) is Element of QC-WFF A
l is Element of (A)
(A,l) is Element of QC-WFF A
s is Element of (A)
(A,s) is Element of QC-WFF A
(A,s) is (A) Element of (A)
(A,s) is Element of QC-WFF A
'not' (A,s) is Element of QC-WFF A
@ (A,s) is Relation-like NAT -defined [:NAT,(QC-symbols A):] -valued Function-like finite FinSequence-like FinSubsequence-like V94() FinSequence of [:NAT,(QC-symbols A):]
[:NAT,(QC-symbols A):] is non empty non trivial non finite set
<*[1,0]*> ^ (@ (A,s)) is Relation-like NAT -defined Function-like non empty finite FinSequence-like FinSubsequence-like V94() set
(A,s) is Relation-like Function-like Element of (A)
[('not' (A,s)),(A,s)] is V15() Element of [:(QC-WFF A),(A):]
[:(QC-WFF A),(A):] is non empty set
{('not' (A,s)),(A,s)} is non empty finite V94() set
{('not' (A,s))} is non empty trivial finite 1 -element V94() set
{{('not' (A,s)),(A,s)},{('not' (A,s))}} is non empty finite V56() V94() set
(A,(A,s)) is Element of QC-WFF A
P9 is Element of (A)
(A,P9) is Relation-like Function-like Element of (A)
s is Element of (A)
(A,s) is Relation-like Function-like Element of (A)
(A,P9) is Element of QC-WFF A
(A,s) is Element of QC-WFF A
(A,P9,s) is Element of (A)
(A,(A,P9,s)) is Element of QC-WFF A
(A,k9) is Element of QC-WFF A
c₁₃ is Relation-like Function-like (A,(A,k9,k99))
(A,(A,k9,k99),c₁₃) is Element of (A)
(A,(A,(A,k9,k99),c₁₃)) is Element of QC-WFF A
A is Relation-like non empty QC-alphabet
(A) is functional non empty set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
QC-symbols A is non empty set
proj2 A is set
[:{4,5},(QC-symbols A):] is non empty set
[:{6},NAT:] \/ [:{4,5},(QC-symbols A):] is non empty set
bool (QC-variables A) is non empty set
[:{4},(QC-symbols A):] is non empty set
PFuncs ((bound_QC-variables A),(bound_QC-variables A)) is functional non empty set
S is Relation-like Function-like Element of (A)
(A,S) is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty set
rng (A,S) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty set