:: CQC_SIM1 semantic presentation

REAL is V56() V57() V58() V62() V74() V75() V77() set
NAT is non empty non trivial V35() V36() V37() V56() V57() V58() V59() V60() V61() V62() non finite V72() V74() V78() V79() Element of bool REAL
bool REAL is non empty cup-closed diff-closed preBoolean set
RAT is V56() V57() V58() V59() V62() set
{} is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() set
the empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() set is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() set
COMPLEX is V56() V62() set
INT is V56() V57() V58() V59() V60() V62() set
NAT is non empty non trivial V35() V36() V37() V56() V57() V58() V59() V60() V61() V62() non finite V72() V74() V78() V79() set
bool NAT is non empty non trivial cup-closed diff-closed preBoolean non finite set
bool NAT is non empty non trivial cup-closed diff-closed preBoolean non finite set
[:COMPLEX,COMPLEX:] is Relation-like V43() set
bool [:COMPLEX,COMPLEX:] is non empty cup-closed diff-closed preBoolean set
[:COMPLEX,REAL:] is Relation-like V43() V44() V45() set
bool [:COMPLEX,REAL:] is non empty cup-closed diff-closed preBoolean set
1 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
2 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
3 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
QC-variables 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 cup-closed diff-closed preBoolean set
QC-symbols A is non empty set
p is Element of bound_QC-variables A
q is Element of QC-symbols A
x. q is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,q] is V18() set
{4,q} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,q},{4}} is non empty finite V67() set
r is Element of QC-symbols A
x. r is Element of bound_QC-variables A
[4,r] is V18() set
{4,r} is non empty finite set
{{4,r},{4}} is non empty finite V67() set
A is set
p is set
A .--> p is Relation-like {A} -defined Function-like one-to-one finite set
{A} is non empty trivial finite V80(1) set
{A} --> p is non empty Relation-like {A} -defined {p} -valued Function-like constant total quasi_total finite Element of bool [:{A},{p}:]
{p} is non empty trivial finite V80(1) set
[:{A},{p}:] is non empty Relation-like finite set
bool [:{A},{p}:] is non empty cup-closed diff-closed preBoolean finite V67() set
q is Relation-like Function-like set
q +* (A .--> p) is Relation-like Function-like set
Im ((q +* (A .--> p)),A) is set
(q +* (A .--> p)) .: {A} is finite set
r is set
proj1 (q +* (A .--> p)) is set
f is set
(q +* (A .--> p)) . f is set
proj1 (A .--> p) is finite set
(A .--> p) . f is set
proj1 (A .--> p) is finite set
proj1 (q +* (A .--> p)) is set
(A .--> p) . A is set
(q +* (A .--> p)) . A is set
p is set
A is set
r is set
p --> r is Relation-like p -defined {r} -valued Function-like constant total quasi_total Element of bool [:p,{r}:]
{r} is non empty trivial finite V80(1) set
[:p,{r}:] is Relation-like set
bool [:p,{r}:] is non empty cup-closed diff-closed preBoolean set
f is Relation-like Function-like set
f +* (p --> r) is Relation-like Function-like set
(f +* (p --> r)) .: A is set
f .: A is set
(f .: A) \/ {r} is non empty set
h is set
proj1 (f +* (p --> r)) is set
u is set
(f +* (p --> r)) . u is set
proj1 (p --> r) is set
(p --> r) . u is set
f . u is set
proj1 f is set
A is set
p is set
A .--> p is Relation-like {A} -defined Function-like one-to-one finite set
{A} is non empty trivial finite V80(1) set
{A} --> p is non empty Relation-like {A} -defined {p} -valued Function-like constant total quasi_total finite Element of bool [:{A},{p}:]
{p} is non empty trivial finite V80(1) set
[:{A},{p}:] is non empty Relation-like finite set
bool [:{A},{p}:] is non empty cup-closed diff-closed preBoolean finite V67() set
q is Relation-like Function-like set
q +* (A .--> p) is Relation-like Function-like set
r is set
r \ {A} is Element of bool r
bool r is non empty cup-closed diff-closed preBoolean set
(q +* (A .--> p)) .: (r \ {A}) is set
q .: (r \ {A}) is set
f is set
proj1 (A .--> p) is finite set
proj1 (q +* (A .--> p)) is set
h is set
(q +* (A .--> p)) . h is set
proj1 q is set
q . h is set
f is set
proj1 q is set
h is set
q . h is set
proj1 (A .--> p) is finite set
(q +* (A .--> p)) . h is set
proj1 (q +* (A .--> p)) is set
p is set
A is set
{A} is non empty trivial finite V80(1) set
A .--> p is Relation-like {A} -defined Function-like one-to-one finite set
{A} --> p is non empty Relation-like {A} -defined {p} -valued Function-like constant total quasi_total finite Element of bool [:{A},{p}:]
{p} is non empty trivial finite V80(1) set
[:{A},{p}:] is non empty Relation-like finite set
bool [:{A},{p}:] is non empty cup-closed diff-closed preBoolean finite V67() set
q is Relation-like Function-like set
q +* (A .--> p) is Relation-like Function-like set
r is set
r \ {A} is Element of bool r
bool r is non empty cup-closed diff-closed preBoolean set
q .: (r \ {A}) is set
(q +* (A .--> p)) .: (r \ {A}) is set
(q +* (A .--> p)) .: r is set
((q +* (A .--> p)) .: r) \ {p} is Element of bool ((q +* (A .--> p)) .: r)
bool ((q +* (A .--> p)) .: r) is non empty cup-closed diff-closed preBoolean set
f is set
proj1 (A .--> p) is finite set
proj1 (q +* (A .--> p)) is set
h is set
(q +* (A .--> p)) . h is set
proj1 q is set
q . h is set
f is set
proj1 (q +* (A .--> p)) is set
h is set
(q +* (A .--> p)) . h is set
proj1 (A .--> p) is finite set
(A .--> p) . h is set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-pred_symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
r is Element of q -ary_QC-pred_symbols A
f is Relation-like NAT -defined QC-variables A -valued Function-like finite V80(q) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r ! f is Element of QC-WFF A
len f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
fixed_QC-variables A is non empty Element of bool (QC-variables A)
{ (f . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len f & f . b₁ in fixed_QC-variables A ) } is set
free_QC-variables A is non empty Element of bool (QC-variables A)
{ (f . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len f & f . b₁ in free_QC-variables A ) } is set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of QC-WFF A
'not' q is Element of QC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of QC-WFF A
r is Element of QC-WFF A
q '&' r is Element of QC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-variables 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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of bound_QC-variables A
r is Element of QC-WFF A
All (q,r) is Element of QC-WFF A
A is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like set
proj2 A is finite set
len A is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
{ (A . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len A ) } is set
p is set
dom A is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() Element of bool NAT
q is set
A . q is set
r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p is set
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A . q is set
dom A is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() Element of bool NAT
F₂() is non empty set
F₁() is non empty Relation-like QC-alphabet
QC-WFF F₁() is non empty set
[:(QC-WFF F₁()),F₂():] is non empty Relation-like set
bool [:(QC-WFF F₁()),F₂():] is non empty cup-closed diff-closed preBoolean set
VERUM F₁() is Element of CQC-WFF F₁()
CQC-WFF F₁() is non empty Element of bool (QC-WFF F₁())
bool (QC-WFF F₁()) is non empty cup-closed diff-closed preBoolean set
F₃() is Element of F₂()
A is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A + 1 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
p is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
q is Element of QC-WFF F₁()
@ q is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p . q is Element of F₂()
F₄(q) is Element of F₂()
the_argument_of q is Element of QC-WFF F₁()
p . (the_argument_of q) is Element of F₂()
F₅((p . (the_argument_of q)),q) is Element of F₂()
the_left_argument_of q is Element of QC-WFF F₁()
p . (the_left_argument_of q) is Element of F₂()
the_right_argument_of q is Element of QC-WFF F₁()
p . (the_right_argument_of q) is Element of F₂()
F₆((p . (the_left_argument_of q)),(p . (the_right_argument_of q)),q) is Element of F₂()
the_scope_of q is Element of QC-WFF F₁()
p . (the_scope_of q) is Element of F₂()
F₇((p . (the_scope_of q)),q) is Element of F₂()
r is Element of F₂()
r is Element of F₂()
r is Element of F₂()
r is Element of F₂()
r is Element of F₂()
r is Element of F₂()
r is Element of F₂()
f is Element of F₂()
h is Element of F₂()
u is Element of F₂()
K is Element of F₂()
f is Element of F₂()
q is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
r is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
f is Element of QC-WFF F₁()
@ f is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r . f is Element of F₂()
F₄(f) is Element of F₂()
the_argument_of f is Element of QC-WFF F₁()
r . (the_argument_of f) is Element of F₂()
F₅((r . (the_argument_of f)),f) is Element of F₂()
the_left_argument_of f is Element of QC-WFF F₁()
r . (the_left_argument_of f) is Element of F₂()
the_right_argument_of f is Element of QC-WFF F₁()
r . (the_right_argument_of f) is Element of F₂()
F₆((r . (the_left_argument_of f)),(r . (the_right_argument_of f)),f) is Element of F₂()
the_scope_of f is Element of QC-WFF F₁()
r . (the_scope_of f) is Element of F₂()
F₇((r . (the_scope_of f)),f) is Element of F₂()
p . f is Element of F₂()
p . f is Element of F₂()
@ (the_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p . (the_argument_of f) is Element of F₂()
p . f is Element of F₂()
@ (the_right_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_right_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p . (the_right_argument_of f) is Element of F₂()
@ (the_left_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_left_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p . (the_left_argument_of f) is Element of F₂()
p . f is Element of F₂()
@ (the_scope_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_scope_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p . (the_scope_of f) is Element of F₂()
p . f is Element of F₂()
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V42() V43() V44() V45() V46() V53() V54() V55() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of NAT
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
p is Element of QC-WFF F₁()
@ p is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . p is Element of F₂()
F₄(p) is Element of F₂()
the_argument_of p is Element of QC-WFF F₁()
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_argument_of p) is Element of F₂()
F₅(( the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_argument_of p)),p) is Element of F₂()
the_left_argument_of p is Element of QC-WFF F₁()
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_left_argument_of p) is Element of F₂()
the_right_argument_of p is Element of QC-WFF F₁()
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_right_argument_of p) is Element of F₂()
F₆(( the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_left_argument_of p)),( the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_right_argument_of p)),p) is Element of F₂()
the_scope_of p is Element of QC-WFF F₁()
the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_scope_of p) is Element of F₂()
F₇(( the non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():] . (the_scope_of p)),p) is Element of F₂()
A is set
p is Element of QC-WFF F₁()
@ p is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
q . A is set
r is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
r . p is Element of F₂()
f is Element of QC-WFF F₁()
@ f is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . f is Element of F₂()
r . f is Element of F₂()
F₄(f) is Element of F₂()
@ (VERUM F₁()) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (VERUM F₁())) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . (VERUM F₁()) is Element of F₂()
r . (VERUM F₁()) is Element of F₂()
the_argument_of f is Element of QC-WFF F₁()
@ (the_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . (the_argument_of f) is Element of F₂()
r . (the_argument_of f) is Element of F₂()
F₅((r . (the_argument_of f)),f) is Element of F₂()
the_left_argument_of f is Element of QC-WFF F₁()
@ (the_left_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_left_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . (the_left_argument_of f) is Element of F₂()
r . (the_left_argument_of f) is Element of F₂()
the_right_argument_of f is Element of QC-WFF F₁()
@ (the_right_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_right_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . (the_right_argument_of f) is Element of F₂()
r . (the_right_argument_of f) is Element of F₂()
F₆((r . (the_left_argument_of f)),(r . (the_right_argument_of f)),f) is Element of F₂()
the_scope_of f is Element of QC-WFF F₁()
@ (the_scope_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_scope_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . (the_scope_of f) is Element of F₂()
r . (the_scope_of f) is Element of F₂()
F₇((r . (the_scope_of f)),f) is Element of F₂()
A is Relation-like Function-like set
proj1 A is set
proj2 A is set
p is set
q is set
A . q is set
r is Element of QC-WFF F₁()
@ r is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ r) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
f . r is Element of F₂()
p is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
p . (VERUM F₁()) is Element of F₂()
q is Element of QC-WFF F₁()
@ q is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
QC-symbols F₁() is non empty set
[:NAT,(QC-symbols F₁()):] is non empty non trivial Relation-like non finite set
len (@ q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
r . (VERUM F₁()) is Element of F₂()
f is Element of QC-WFF F₁()
p . f is Element of F₂()
F₄(f) is Element of F₂()
the_argument_of f is Element of QC-WFF F₁()
p . (the_argument_of f) is Element of F₂()
F₅((p . (the_argument_of f)),f) is Element of F₂()
the_left_argument_of f is Element of QC-WFF F₁()
p . (the_left_argument_of f) is Element of F₂()
the_right_argument_of f is Element of QC-WFF F₁()
p . (the_right_argument_of f) is Element of F₂()
F₆((p . (the_left_argument_of f)),(p . (the_right_argument_of f)),f) is Element of F₂()
the_scope_of f is Element of QC-WFF F₁()
p . (the_scope_of f) is Element of F₂()
F₇((p . (the_scope_of f)),f) is Element of F₂()
h is Element of QC-WFF F₁()
@ h is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ h) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u is non empty Relation-like QC-WFF F₁() -defined F₂() -valued Function-like total quasi_total Element of bool [:(QC-WFF F₁()),F₂():]
u . f is Element of F₂()
@ f is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 is Element of QC-WFF F₁()
@ r9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ r9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . r9 is Element of F₂()
F₄(r9) is Element of F₂()
the_argument_of r9 is Element of QC-WFF F₁()
u . (the_argument_of r9) is Element of F₂()
F₅((u . (the_argument_of r9)),r9) is Element of F₂()
the_left_argument_of r9 is Element of QC-WFF F₁()
u . (the_left_argument_of r9) is Element of F₂()
the_right_argument_of r9 is Element of QC-WFF F₁()
u . (the_right_argument_of r9) is Element of F₂()
F₆((u . (the_left_argument_of r9)),(u . (the_right_argument_of r9)),r9) is Element of F₂()
the_scope_of r9 is Element of QC-WFF F₁()
u . (the_scope_of r9) is Element of F₂()
F₇((u . (the_scope_of r9)),r9) is Element of F₂()
@ (the_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
s9 is Element of QC-WFF F₁()
@ s9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ s9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . s9 is Element of F₂()
F₄(s9) is Element of F₂()
the_argument_of s9 is Element of QC-WFF F₁()
u . (the_argument_of s9) is Element of F₂()
F₅((u . (the_argument_of s9)),s9) is Element of F₂()
the_left_argument_of s9 is Element of QC-WFF F₁()
u . (the_left_argument_of s9) is Element of F₂()
the_right_argument_of s9 is Element of QC-WFF F₁()
u . (the_right_argument_of s9) is Element of F₂()
F₆((u . (the_left_argument_of s9)),(u . (the_right_argument_of s9)),s9) is Element of F₂()
the_scope_of s9 is Element of QC-WFF F₁()
u . (the_scope_of s9) is Element of F₂()
F₇((u . (the_scope_of s9)),s9) is Element of F₂()
u . (the_argument_of f) is Element of F₂()
s9 is Element of QC-WFF F₁()
@ s9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ s9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
@ (the_left_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_left_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
@ (the_right_argument_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_right_argument_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u is Element of QC-WFF F₁()
@ u is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . u is Element of F₂()
F₄(u) is Element of F₂()
the_argument_of u is Element of QC-WFF F₁()
u . (the_argument_of u) is Element of F₂()
F₅((u . (the_argument_of u)),u) is Element of F₂()
the_left_argument_of u is Element of QC-WFF F₁()
u . (the_left_argument_of u) is Element of F₂()
the_right_argument_of u is Element of QC-WFF F₁()
u . (the_right_argument_of u) is Element of F₂()
F₆((u . (the_left_argument_of u)),(u . (the_right_argument_of u)),u) is Element of F₂()
the_scope_of u is Element of QC-WFF F₁()
u . (the_scope_of u) is Element of F₂()
F₇((u . (the_scope_of u)),u) is Element of F₂()
u is Element of QC-WFF F₁()
@ u is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . u is Element of F₂()
F₄(u) is Element of F₂()
the_argument_of u is Element of QC-WFF F₁()
u . (the_argument_of u) is Element of F₂()
F₅((u . (the_argument_of u)),u) is Element of F₂()
the_left_argument_of u is Element of QC-WFF F₁()
u . (the_left_argument_of u) is Element of F₂()
the_right_argument_of u is Element of QC-WFF F₁()
u . (the_right_argument_of u) is Element of F₂()
F₆((u . (the_left_argument_of u)),(u . (the_right_argument_of u)),u) is Element of F₂()
the_scope_of u is Element of QC-WFF F₁()
u . (the_scope_of u) is Element of F₂()
F₇((u . (the_scope_of u)),u) is Element of F₂()
u . (the_right_argument_of f) is Element of F₂()
u is Element of QC-WFF F₁()
@ u is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . (the_left_argument_of f) is Element of F₂()
u is Element of QC-WFF F₁()
@ u is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
@ (the_scope_of f) is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ (the_scope_of f)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 is Element of QC-WFF F₁()
@ r9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ r9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . r9 is Element of F₂()
F₄(r9) is Element of F₂()
the_argument_of r9 is Element of QC-WFF F₁()
u . (the_argument_of r9) is Element of F₂()
F₅((u . (the_argument_of r9)),r9) is Element of F₂()
the_left_argument_of r9 is Element of QC-WFF F₁()
u . (the_left_argument_of r9) is Element of F₂()
the_right_argument_of r9 is Element of QC-WFF F₁()
u . (the_right_argument_of r9) is Element of F₂()
F₆((u . (the_left_argument_of r9)),(u . (the_right_argument_of r9)),r9) is Element of F₂()
the_scope_of r9 is Element of QC-WFF F₁()
u . (the_scope_of r9) is Element of F₂()
F₇((u . (the_scope_of r9)),r9) is Element of F₂()
u . (the_scope_of f) is Element of F₂()
r9 is Element of QC-WFF F₁()
@ r9 is Relation-like NAT -defined [:NAT,(QC-symbols F₁()):] -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of [:NAT,(QC-symbols F₁()):]
len (@ r9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
F₂() is non empty set
F₃() is non empty set
Funcs (F₂(),F₃()) is non empty functional FUNCTION_DOMAIN of F₂(),F₃()
F₁() is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
[:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty Relation-like set
bool [:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty cup-closed diff-closed preBoolean set
VERUM F₁() is Element of CQC-WFF F₁()
F₄() is Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of Funcs (F₂(),F₃())
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
QC-variables F₁() is non empty set
bool (QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols F₁() is non empty set
[:(QC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty Relation-like set
bool [:(QC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty cup-closed diff-closed preBoolean set
A is non empty Relation-like QC-WFF F₁() -defined Funcs (F₂(),F₃()) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(QC-WFF F₁()),(Funcs (F₂(),F₃())):]
A . (VERUM F₁()) is Relation-like Function-like Element of Funcs (F₂(),F₃())
A | (CQC-WFF F₁()) is Relation-like CQC-WFF F₁() -defined QC-WFF F₁() -defined Funcs (F₂(),F₃()) -valued Function-like Function-yielding V93() Element of bool [:(QC-WFF F₁()),(Funcs (F₂(),F₃())):]
p is non empty Relation-like CQC-WFF F₁() -defined Funcs (F₂(),F₃()) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):]
p . (VERUM F₁()) is Relation-like Function-like Element of Funcs (F₂(),F₃())
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty cup-closed diff-closed preBoolean set
r is Relation-like NAT -defined bound_QC-variables F₁() -valued QC-variables F₁() -valued Function-like finite V80(q) FinSequence-like FinSubsequence-like FinSequence of QC-variables F₁()
f is Element of q -ary_QC-pred_symbols F₁()
f ! r is Element of CQC-WFF F₁()
p . (f ! r) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₅(q,f,r) is Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of Funcs (F₂(),F₃())
the_arity_of f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
the_arguments_of (f ! r) is Relation-like NAT -defined QC-variables F₁() -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of QC-variables F₁()
the_pred_symbol_of (f ! r) is Element of QC-pred_symbols F₁()
A . (f ! r) is Relation-like Function-like Element of Funcs (F₂(),F₃())
q is Element of CQC-WFF F₁()
'not' q is Element of CQC-WFF F₁()
p . ('not' q) is Relation-like Function-like Element of Funcs (F₂(),F₃())
p . q is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₆((p . q),q) is Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of Funcs (F₂(),F₃())
r is Element of CQC-WFF F₁()
q '&' r is Element of CQC-WFF F₁()
p . (q '&' r) is Relation-like Function-like Element of Funcs (F₂(),F₃())
p . r is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₇((p . q),(p . r),q,r) is Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of Funcs (F₂(),F₃())
f is Element of bound_QC-variables F₁()
All (f,q) is Element of CQC-WFF F₁()
p . (All (f,q)) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₈(f,(p . q),q) is Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of Funcs (F₂(),F₃())
A . q is Relation-like Function-like Element of Funcs (F₂(),F₃())
the_argument_of ('not' q) is Element of QC-WFF F₁()
A . ('not' q) is Relation-like Function-like Element of Funcs (F₂(),F₃())
A . r is Relation-like Function-like Element of Funcs (F₂(),F₃())
the_left_argument_of (q '&' r) is Element of QC-WFF F₁()
the_right_argument_of (q '&' r) is Element of QC-WFF F₁()
A . (q '&' r) is Relation-like Function-like Element of Funcs (F₂(),F₃())
bound_in (All (f,q)) is Element of bound_QC-variables F₁()
the_scope_of (All (f,q)) is Element of QC-WFF F₁()
A . (All (f,q)) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₁() is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
F₂() is non empty set
F₃() is non empty set
Funcs (F₂(),F₃()) is non empty functional FUNCTION_DOMAIN of F₂(),F₃()
[:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty Relation-like set
bool [:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):] is non empty cup-closed diff-closed preBoolean set
[:F₂(),F₃():] is non empty Relation-like set
bool [:F₂(),F₃():] is non empty cup-closed diff-closed preBoolean set
F₄() is non empty Relation-like CQC-WFF F₁() -defined Funcs (F₂(),F₃()) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):]
VERUM F₁() is Element of CQC-WFF F₁()
F₄() . (VERUM F₁()) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₆() is non empty Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of bool [:F₂(),F₃():]
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
QC-variables F₁() is non empty set
bool (QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols F₁() is non empty set
F₅() is non empty Relation-like CQC-WFF F₁() -defined Funcs (F₂(),F₃()) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF F₁()),(Funcs (F₂(),F₃())):]
F₅() . (VERUM F₁()) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . (VERUM F₁()) is Relation-like Function-like set
F₅() . (VERUM F₁()) is Relation-like Function-like set
A is Element of CQC-WFF F₁()
F₄() . A is Relation-like Function-like set
F₅() . A is Relation-like Function-like set
'not' A is Element of CQC-WFF F₁()
F₄() . ('not' A) is Relation-like Function-like set
F₅() . ('not' A) is Relation-like Function-like set
p is Element of CQC-WFF F₁()
F₄() . p is Relation-like Function-like set
F₅() . p is Relation-like Function-like set
A '&' p is Element of CQC-WFF F₁()
F₄() . (A '&' p) is Relation-like Function-like set
F₅() . (A '&' p) is Relation-like Function-like set
q is Element of bound_QC-variables F₁()
All (q,A) is Element of CQC-WFF F₁()
F₄() . (All (q,A)) is Relation-like Function-like set
F₅() . (All (q,A)) is Relation-like Function-like set
r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r -ary_QC-pred_symbols F₁() is non empty Element of bool (QC-pred_symbols F₁())
bool (QC-pred_symbols F₁()) is non empty cup-closed diff-closed preBoolean set
f is Relation-like NAT -defined bound_QC-variables F₁() -valued QC-variables F₁() -valued Function-like finite V80(r) FinSequence-like FinSubsequence-like FinSequence of QC-variables F₁()
h is Element of r -ary_QC-pred_symbols F₁()
h ! f is Element of CQC-WFF F₁()
F₄() . (h ! f) is Relation-like Function-like set
F₅() . (h ! f) is Relation-like Function-like set
F₄() . (h ! f) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₇(r,h,f) is non empty Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of bool [:F₂(),F₃():]
F₅() . (h ! f) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . ('not' A) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . A is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₈((F₄() . A),A) is non empty Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of bool [:F₂(),F₃():]
F₅() . A is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₅() . ('not' A) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . (A '&' p) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . p is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₉((F₄() . A),(F₄() . p),A,p) is non empty Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of bool [:F₂(),F₃():]
F₅() . p is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₅() . (A '&' p) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₄() . (All (q,A)) is Relation-like Function-like Element of Funcs (F₂(),F₃())
F₁₀(q,(F₄() . A),A) is non empty Relation-like F₂() -defined F₃() -valued Function-like total quasi_total Element of bool [:F₂(),F₃():]
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
'not' p is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of CQC-WFF A
p '&' q is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-variables 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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of bound_QC-variables A
All (q,p) is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
len q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q . r is set
dom q is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V80(p) Element of bool NAT
proj2 q is finite set
p is non empty set
A is non empty Relation-like QC-alphabet
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
[:p,(CQC-WFF A):] is non empty Relation-like set
bool [:p,(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
Funcs (p,(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of p, CQC-WFF A
q is non empty Relation-like p -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:p,(CQC-WFF A):]
r is Element of p
q . r is set
q . r is Element of CQC-WFF A
f is Element of CQC-WFF A
'not' f is Element of CQC-WFF A
h is Element of CQC-WFF A
'not' h is Element of CQC-WFF A
r is non empty Relation-like p -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:p,(CQC-WFF A):]
r is Relation-like p -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs (p,(CQC-WFF A))
f is Relation-like p -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs (p,(CQC-WFF A))
h is Element of p
r . h is Element of CQC-WFF A
f . h is Element of CQC-WFF A
q . h is Element of CQC-WFF A
u is Element of CQC-WFF A
'not' u is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
p is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
q is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is Element of QC-symbols A
f + r is Element of QC-symbols A
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[f,h] is V18() set
{f,h} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,h},{f}} is non empty finite V67() set
p . [f,h] is set
[(f + r),h] is V18() set
{(f + r),h} is non empty finite set
{(f + r)} is non empty trivial finite V80(1) set
{{(f + r),h},{(f + r)}} is non empty finite V67() set
q . [(f + r),h] is set
[f,h] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
p . [f,h] is Element of CQC-WFF A
[(f + r),h] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
q . [(f + r),h] is Element of CQC-WFF A
u is Element of CQC-WFF A
K is Element of CQC-WFF A
u '&' K is Element of CQC-WFF A
f is Element of CQC-WFF A
r9 is Element of CQC-WFF A
f '&' r9 is Element of CQC-WFF A
f is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
h is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
u is Element of QC-symbols A
u + r is Element of QC-symbols A
K is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
p . (u,K) is Element of CQC-WFF A
[u,K] is V18() set
{u,K} is non empty finite set
{u} is non empty trivial finite V80(1) set
{{u,K},{u}} is non empty finite V67() set
p . [u,K] is set
q . ((u + r),K) is Element of CQC-WFF A
[(u + r),K] is V18() set
{(u + r),K} is non empty finite set
{(u + r)} is non empty trivial finite V80(1) set
{{(u + r),K},{(u + r)}} is non empty finite V67() set
q . [(u + r),K] is set
h . (u,K) is Element of CQC-WFF A
h . [u,K] is set
f is Element of CQC-WFF A
r9 is Element of CQC-WFF A
f '&' r9 is Element of CQC-WFF A
f is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
u is Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
f . u is Element of CQC-WFF A
h . u is Element of CQC-WFF A
K is Element of QC-symbols A
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[K,f] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{K,f} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,f},{K}} is non empty finite V67() set
K + r is Element of QC-symbols A
q . ((K + r),f) is Element of CQC-WFF A
[(K + r),f] is V18() set
{(K + r),f} is non empty finite set
{(K + r)} is non empty trivial finite V80(1) set
{{(K + r),f},{(K + r)}} is non empty finite V67() set
q . [(K + r),f] is set
p . (K,f) is Element of CQC-WFF A
[K,f] is V18() set
p . [K,f] is set
f . (K,f) is Element of CQC-WFF A
f . [K,f] is set
s9 is Element of CQC-WFF A
r9 is Element of CQC-WFF A
s9 '&' r9 is Element of CQC-WFF A
h . (K,f) is Element of CQC-WFF A
h . [K,f] is set
A is non empty Relation-like QC-alphabet
QC-symbols A is non empty set
QC-variables 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 cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty Relation-like set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
x. p is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,p] is V18() set
{4,p} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,p},{4}} is non empty finite V67() set
q is Element of bound_QC-variables A
q .--> (x. p) is Relation-like bound_QC-variables A -defined {q} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{q} is non empty trivial finite V80(1) set
{q} --> (x. p) is non empty Relation-like {q} -defined bound_QC-variables A -valued {(x. p)} -valued Function-like constant total quasi_total finite Element of bool [:{q},{(x. p)}:]
{(x. p)} is non empty trivial finite V80(1) set
[:{q},{(x. p)}:] is non empty Relation-like finite set
bool [:{q},{(x. p)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
r is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
r +* (q .--> (x. p)) is Relation-like Function-like set
proj2 (r +* (q .--> (x. p))) is set
proj2 r is set
proj2 (q .--> (x. p)) is finite set
(proj2 r) \/ (proj2 (q .--> (x. p))) is set
proj1 (r +* (q .--> (x. p))) is set
proj1 r is set
{q} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{q} --> (x. p) is non empty Relation-like {q} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{q},(bound_QC-variables A):]
[:{q},(bound_QC-variables A):] is non empty Relation-like set
bool [:{q},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
[:{q},{(x. p)}:] is non empty Relation-like finite set
proj1 ({q} --> (x. p)) is non empty finite set
(proj1 r) \/ (proj1 ({q} --> (x. p))) is non empty set
(proj1 r) \/ {q} is non empty set
(bound_QC-variables A) \/ {q} is non empty set
A is non empty Relation-like QC-alphabet
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
p is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
q is Element of bound_QC-variables A
{q} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
r is Element of QC-symbols A
r ++ is Element of QC-symbols A
x. r is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,r] is V18() set
{4,r} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,r},{4}} is non empty finite V67() set
{q} --> (x. r) is non empty Relation-like {q} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{q},(bound_QC-variables A):]
[:{q},(bound_QC-variables A):] is non empty Relation-like set
bool [:{q},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{(x. r)} is non empty trivial finite V80(1) set
[:{q},{(x. r)}:] is non empty Relation-like finite set
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
f +* ({q} --> (x. r)) is Relation-like Function-like set
[(r ++),(f +* ({q} --> (x. r)))] is V18() set
{(r ++),(f +* ({q} --> (x. r)))} is non empty finite set
{(r ++)} is non empty trivial finite V80(1) set
{{(r ++),(f +* ({q} --> (x. r)))},{(r ++)}} is non empty finite V67() set
p . [(r ++),(f +* ({q} --> (x. r)))] is set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty Relation-like set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
q .--> (x. r) is Relation-like bound_QC-variables A -defined {q} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{q} is non empty trivial finite V80(1) set
{q} --> (x. r) is non empty Relation-like {q} -defined bound_QC-variables A -valued {(x. r)} -valued Function-like constant total quasi_total finite Element of bool [:{q},{(x. r)}:]
[:{q},{(x. r)}:] is non empty Relation-like finite set
bool [:{q},{(x. r)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
f +* (q .--> (x. r)) is Relation-like Function-like set
h is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(r ++),u] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(r ++),u} is non empty finite set
{{(r ++),u},{(r ++)}} is non empty finite V67() set
p . [(r ++),u] is Element of CQC-WFF A
K is Element of CQC-WFF A
All ((x. r),K) is Element of CQC-WFF A
f is Element of CQC-WFF A
All ((x. r),f) is Element of CQC-WFF A
r is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
f is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Element of QC-symbols A
h ++ is Element of QC-symbols A
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
q .--> (x. h) is Relation-like bound_QC-variables A -defined {q} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{q} is non empty trivial finite V80(1) set
{q} --> (x. h) is non empty Relation-like {q} -defined bound_QC-variables A -valued {(x. h)} -valued Function-like constant total quasi_total finite Element of bool [:{q},{(x. h)}:]
{(x. h)} is non empty trivial finite V80(1) set
[:{q},{(x. h)}:] is non empty Relation-like finite set
bool [:{q},{(x. h)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
u +* (q .--> (x. h)) is Relation-like Function-like set
p . ((h ++),(u +* (q .--> (x. h)))) is set
[(h ++),(u +* (q .--> (x. h)))] is V18() set
{(h ++),(u +* (q .--> (x. h)))} is non empty finite set
{(h ++)} is non empty trivial finite V80(1) set
{{(h ++),(u +* (q .--> (x. h)))},{(h ++)}} is non empty finite V67() set
p . [(h ++),(u +* (q .--> (x. h)))] is set
f . (h,u) is Element of CQC-WFF A
[h,u] is V18() set
{h,u} is non empty finite set
{h} is non empty trivial finite V80(1) set
{{h,u},{h}} is non empty finite V67() set
f . [h,u] is set
K is Element of CQC-WFF A
All ((x. h),K) is Element of CQC-WFF A
r is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
f is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
r . h is Element of CQC-WFF A
f . h is Element of CQC-WFF A
u is Element of QC-symbols A
K is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[u,K] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{u,K} is non empty finite set
{u} is non empty trivial finite V80(1) set
{{u,K},{u}} is non empty finite V67() set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty Relation-like set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
x. u is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,u] is V18() set
{4,u} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,u},{4}} is non empty finite V67() set
q .--> (x. u) is Relation-like bound_QC-variables A -defined {q} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{q} is non empty trivial finite V80(1) set
{q} --> (x. u) is non empty Relation-like {q} -defined bound_QC-variables A -valued {(x. u)} -valued Function-like constant total quasi_total finite Element of bool [:{q},{(x. u)}:]
{(x. u)} is non empty trivial finite V80(1) set
[:{q},{(x. u)}:] is non empty Relation-like finite set
bool [:{q},{(x. u)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
K +* (q .--> (x. u)) is Relation-like Function-like set
f is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of bool [:(bound_QC-variables A),(bound_QC-variables A):]
u ++ is Element of QC-symbols A
r9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
p . ((u ++),r9) is Element of CQC-WFF A
[(u ++),r9] is V18() set
{(u ++),r9} is non empty finite set
{(u ++)} is non empty trivial finite V80(1) set
{{(u ++),r9},{(u ++)}} is non empty finite V67() set
p . [(u ++),r9] is set
r . (u,K) is Element of CQC-WFF A
[u,K] is V18() set
r . [u,K] is set
s9 is Element of CQC-WFF A
All ((x. u),s9) is Element of CQC-WFF A
f . (u,K) is Element of CQC-WFF A
f . [u,K] is set
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
proj2 q is finite set
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
q * r is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite set
f is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of bound_QC-variables A
r * f is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite Element of bool [:NAT,(bound_QC-variables A):]
[:NAT,(bound_QC-variables A):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bound_QC-variables A):] is non empty non trivial cup-closed diff-closed preBoolean non finite set
h is Relation-like NAT -defined bound_QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of bound_QC-variables A
len h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
len f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
QC-pred_symbols A is non empty set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
QC-symbols A is non empty set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
q is Element of p -ary_QC-pred_symbols A
r is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
f is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
f is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
u is Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
f . u is Element of CQC-WFF A
h . u is Element of CQC-WFF A
K is Element of QC-symbols A
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[K,f] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{K,f} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,f},{K}} is non empty finite V67() set
f . (K,f) is Element of CQC-WFF A
[K,f] is V18() set
f . [K,f] is set
(A,p,r,f) is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued bound_QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
q ! (A,p,r,f) is Element of CQC-WFF A
h . (K,f) is Element of CQC-WFF A
h . [K,f] is set
0 is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V42() V43() V44() V45() V46() V53() V54() V55() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of NAT
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
p is Element of CQC-WFF A
VERUM A is Element of CQC-WFF A
QC-variables 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 cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
A is non empty Relation-like QC-alphabet
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
p is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
q is Element of CQC-WFF A
p . q is Relation-like Function-like set
p . q is Relation-like Function-like Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
A is non empty Relation-like QC-alphabet
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
VERUM A is Element of CQC-WFF A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] --> (VERUM A) is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like constant total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
{(VERUM A)} is non empty trivial finite V80(1) set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],{(VERUM A)}:] is non empty Relation-like set
QC-pred_symbols A is non empty set
q is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
r is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
f is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
(A,f,(VERUM A)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
h -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
K is Element of h -ary_QC-pred_symbols A
u is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(h) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
K ! u is Element of CQC-WFF A
(A,f,(K ! u)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,h,K,u) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
f is Element of CQC-WFF A
'not' f is Element of CQC-WFF A
(A,f,('not' f)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,f) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(A,f,f)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
r9 is Element of CQC-WFF A
s9 is Element of CQC-WFF A
r9 '&' s9 is Element of CQC-WFF A
(A,f,(r9 '&' s9)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,r9) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,s9) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,r9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,(A,f,r9),(A,f,s9),(A,r9)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
u is Element of bound_QC-variables A
i is Element of CQC-WFF A
All (u,i) is Element of CQC-WFF A
(A,f,(All (u,i))) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,i) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,(A,f,i),u) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
r is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
(A,r,(VERUM A)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
f is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
(A,f,(VERUM A)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
q is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
q is Element of QC-symbols A
r is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[q,r] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{q,r} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,r},{q}} is non empty finite V67() set
(A,(A),p) . [q,r] is Element of CQC-WFF A
A is non empty Relation-like 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 cup-closed diff-closed preBoolean set
(A,(VERUM A)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
QC-variables 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 cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p is Element of CQC-WFF A
(A,p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
h is non empty Relation-like CQC-WFF A -defined NAT -valued Function-like total quasi_total V43() V44() V45() V46() Element of bool [:(CQC-WFF A),NAT:]
r is Element of CQC-WFF A
h . r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
h . (VERUM A) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,r) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r is Element of p -ary_QC-pred_symbols A
r ! q 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 cup-closed diff-closed preBoolean set
(A,(r ! q)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
VERUM A is Element of CQC-WFF A
h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is Element of CQC-WFF A
(A,f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is non empty Relation-like CQC-WFF A -defined NAT -valued Function-like total quasi_total V43() V44() V45() V46() Element of bool [:(CQC-WFF A),NAT:]
u is Element of CQC-WFF A
f . u is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f . (VERUM A) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
'not' p is Element of CQC-WFF A
(A,('not' p)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
VERUM A is Element of CQC-WFF A
QC-variables 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 cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is Element of CQC-WFF A
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u is non empty Relation-like CQC-WFF A -defined NAT -valued Function-like total quasi_total V43() V44() V45() V46() Element of bool [:(CQC-WFF A),NAT:]
f is Element of CQC-WFF A
u . f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u . (VERUM A) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is Element of CQC-WFF A
p '&' q is Element of CQC-WFF A
(A,(p '&' q)) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,p) + (A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
VERUM A is Element of CQC-WFF A
QC-variables 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 cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r is Element of CQC-WFF A
(A,r) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K is non empty Relation-like CQC-WFF A -defined NAT -valued Function-like total quasi_total V43() V44() V45() V46() Element of bool [:(CQC-WFF A),NAT:]
h is Element of CQC-WFF A
K . h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K . (VERUM A) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,h) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
H₅(p) + H₅(q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-variables 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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,p) + 1 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
q is Element of bound_QC-variables A
All (q,p) is Element of CQC-WFF A
(A,(All (q,p))) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
[:(CQC-WFF A),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V43() V44() V45() V46() non finite set
bool [:(CQC-WFF A),NAT:] is non empty non trivial cup-closed diff-closed preBoolean non finite set
VERUM A is Element of CQC-WFF A
QC-pred_symbols A is non empty set
f is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r is Element of CQC-WFF A
(A,r) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K is non empty Relation-like CQC-WFF A -defined NAT -valued Function-like total quasi_total V43() V44() V45() V46() Element of bool [:(CQC-WFF A),NAT:]
h is Element of CQC-WFF A
K . h is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K . (VERUM A) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,h) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
H₅(p) + 1 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
A is non empty Relation-like 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 cup-closed diff-closed preBoolean set
still_not-bound_in (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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-WFF A
still_not-bound_in p is Element of bool (bound_QC-variables A)
the_argument_of p is Element of QC-WFF A
still_not-bound_in (the_argument_of p) is Element of bool (bound_QC-variables A)
the_left_argument_of p is Element of QC-WFF A
still_not-bound_in (the_left_argument_of p) is Element of bool (bound_QC-variables A)
the_right_argument_of p is Element of QC-WFF A
still_not-bound_in (the_right_argument_of p) is Element of bool (bound_QC-variables A)
the_scope_of p is Element of QC-WFF A
still_not-bound_in (the_scope_of p) is Element of bool (bound_QC-variables A)
the_arguments_of p is Relation-like NAT -defined QC-variables A -valued Function-like finite FinSequence-like FinSubsequence-like FinSequence of QC-variables A
len (the_arguments_of p) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(the_arguments_of p) . q is set
{ H₅(b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : S₃[b₁] } is set
{ H₅(b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : S₂[b₁] } is set
still_not-bound_in (the_arguments_of p) is Element of bool (bound_QC-variables A)
variables_in ((the_arguments_of p),(bound_QC-variables A)) is Element of bool (bound_QC-variables A)
{ ((the_arguments_of p) . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arguments_of p) & (the_arguments_of p) . b₁ in bound_QC-variables A ) } is set
proj2 (the_arguments_of p) is finite set
(still_not-bound_in (the_left_argument_of p)) \/ (still_not-bound_in (the_right_argument_of p)) is Element of bool (bound_QC-variables A)
bound_in p is Element of bound_QC-variables A
{(bound_in p)} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(still_not-bound_in (the_scope_of p)) \ {(bound_in p)} is Element of bool (bound_QC-variables A)
F₂() is set
F₁() is non empty set
A is finite set
p is set
q is set
r is set
p is set
q is set
p is set
q is Element of F₁()
r is Element of F₁()
A is set
id A is Relation-like A -defined A -valued Function-like one-to-one total set
Funcs (A,A) is non empty functional set
id A is Relation-like A -defined A -valued Function-like one-to-one total quasi_total Element of bool [:A,A:]
[:A,A:] is Relation-like set
bool [:A,A:] is non empty cup-closed diff-closed preBoolean set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols A is non empty set
p is Element of CQC-WFF A
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : S₁[b₁] } is set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is Element of bool (QC-symbols A)
QC-symbols A is non empty set
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
0 A is Element of QC-symbols A
r is Element of QC-symbols A
x. r is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,r] is V18() set
{4,r} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,r},{4}} is non empty finite V67() set
{ b₁ where b₁ is Element of QC-symbols A : S₁[b₁] } is set
r is set
f is Element of bound_QC-variables A
h is Element of QC-symbols A
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
u is set
K is Element of QC-symbols A
x. K is Element of bound_QC-variables A
[4,K] is V18() set
{4,K} is non empty finite set
{{4,K},{4}} is non empty finite V67() set
r is Relation-like Function-like set
proj1 r is set
proj2 r is set
[:(still_not-bound_in p),(QC-symbols A):] is Relation-like set
bool [:(still_not-bound_in p),(QC-symbols A):] is non empty cup-closed diff-closed preBoolean set
the Element of still_not-bound_in p is Element of still_not-bound_in p
u is Element of bound_QC-variables A
K is Element of QC-symbols A
x. K is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,K] is V18() set
{4,K} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,K},{4}} is non empty finite V67() set
{ b₁ where b₁ is Element of QC-symbols A : x. b₁ in still_not-bound_in p } is set
r9 is Element of QC-symbols A
f is Element of QC-symbols A
r9 is Element of QC-symbols A
f is Element of QC-symbols A
s9 is Element of QC-symbols A
{ H₅(b₁) where b₁ is Element of bound_QC-variables A : b₁ in still_not-bound_in p } is set
{ (A,b₁) where b₁ is Element of bound_QC-variables A : b₁ in still_not-bound_in p } is set
s9 is set
i is Element of bound_QC-variables A
(A,i) is Element of QC-symbols A
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
s9 is set
i is Element of QC-symbols A
x. i is Element of bound_QC-variables A
[4,i] is V18() set
{4,i} is non empty finite set
{{4,i},{4}} is non empty finite V67() set
(A,(x. i)) is Element of QC-symbols A
f is set
f is Element of QC-symbols A
f ++ is Element of QC-symbols A
r9 is Element of QC-symbols A
s9 is Element of QC-symbols A
x. s9 is Element of bound_QC-variables A
[4,s9] is V18() set
{4,s9} is non empty finite set
{{4,s9},{4}} is non empty finite V67() set
r9 is Element of QC-symbols A
r is Element of QC-symbols A
r is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is non empty Element of bool (QC-symbols A)
QC-symbols A is non empty set
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
0 A is Element of QC-symbols A
QC-symbols A is non empty set
p is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
q is Element of QC-symbols A
the Element of still_not-bound_in p is Element of still_not-bound_in p
f is Element of bound_QC-variables A
h is Element of QC-symbols A
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
q is Element of QC-symbols A
x. q is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,q] is V18() set
{4,q} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,q},{4}} is non empty finite V67() set
q is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
x. p is Element of bound_QC-variables A
QC-variables 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 cup-closed diff-closed preBoolean set
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,p] is V18() set
{4,p} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,p},{4}} is non empty finite V67() set
q is Element of CQC-WFF A
still_not-bound_in q is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
(A,q) is Element of QC-symbols A
(A,q) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in q ) } is set
min (A,q) is Element of QC-symbols A
r is Element of QC-symbols A
A is non empty Relation-like 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 cup-closed diff-closed preBoolean set
(A,(VERUM A)) is Element of QC-symbols A
QC-symbols A is non empty set
(A,(VERUM A)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (VERUM A) ) } is set
min (A,(VERUM A)) is Element of QC-symbols A
0 A is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
'not' p is Element of CQC-WFF A
(A,('not' p)) is Element of QC-symbols A
QC-symbols A is non empty set
(A,('not' p)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in ('not' p) 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in ('not' p) ) } is set
min (A,('not' p)) is Element of QC-symbols A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
still_not-bound_in p is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
q is Element of CQC-WFF A
p '&' q is Element of CQC-WFF A
(A,(p '&' q)) is Element of QC-symbols A
(A,(p '&' q)) is non empty Element of bool (QC-symbols A)
still_not-bound_in (p '&' q) is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (p '&' q) ) } is set
min (A,(p '&' q)) is Element of QC-symbols A
(A,q) is Element of QC-symbols A
(A,q) is non empty Element of bool (QC-symbols A)
still_not-bound_in q is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in q ) } is set
min (A,q) is Element of QC-symbols A
(still_not-bound_in p) \/ (still_not-bound_in q) is Element of bool (bound_QC-variables A)
r is set
f is Element of QC-symbols A
h is Element of QC-symbols A
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
r is set
f is Element of QC-symbols A
h is Element of QC-symbols A
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
A is non empty Relation-like 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 cup-closed diff-closed preBoolean set
(A,(VERUM A)) is Element of CQC-WFF A
(A,(VERUM A)) is Element of QC-symbols A
QC-symbols A is non empty set
(A,(VERUM A)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (VERUM A) ) } is set
min (A,(VERUM A)) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,(VERUM A),(A,(VERUM A)),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),(VERUM A)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,(VERUM A)),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,(VERUM A)),((bound_QC-variables A))} is non empty finite set
{(A,(VERUM A))} is non empty trivial finite V80(1) set
{{(A,(VERUM A)),((bound_QC-variables A))},{(A,(VERUM A))}} is non empty finite V67() set
(A,(A),(VERUM A)) . [(A,(VERUM A)),((bound_QC-variables A))] is Element of CQC-WFF A
0 A is Element of QC-symbols A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] --> (VERUM A) is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like constant total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
{(VERUM A)} is non empty trivial finite V80(1) set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],{(VERUM A)}:] is non empty Relation-like set
[(0 A),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(0 A),((bound_QC-variables A))} is non empty finite set
{(0 A)} is non empty trivial finite V80(1) set
{{(0 A),((bound_QC-variables A))},{(0 A)}} is non empty finite V67() set
([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] --> (VERUM A)) . [(0 A),((bound_QC-variables A))] is Element of CQC-WFF A
F₁() is non empty Relation-like QC-alphabet
VERUM F₁() is Element of CQC-WFF F₁()
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 cup-closed diff-closed preBoolean set
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
QC-variables F₁() is non empty set
bool (QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols F₁() is non empty set
A is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() 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 cup-closed diff-closed preBoolean set
q is Element of A -ary_QC-pred_symbols F₁()
p is Relation-like NAT -defined bound_QC-variables F₁() -valued QC-variables F₁() -valued Function-like finite V80(A) FinSequence-like FinSubsequence-like FinSequence of QC-variables F₁()
q ! p is Element of CQC-WFF F₁()
r is Element of CQC-WFF F₁()
'not' r is Element of CQC-WFF F₁()
f is Element of CQC-WFF F₁()
h is Element of CQC-WFF F₁()
f '&' h is Element of CQC-WFF F₁()
u is Element of CQC-WFF F₁()
K is Element of bound_QC-variables F₁()
All (K,u) is Element of CQC-WFF F₁()
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r is Element of p -ary_QC-pred_symbols A
r ! q 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 cup-closed diff-closed preBoolean set
(A,(r ! q)) is Element of CQC-WFF A
(A,(r ! q)) is Element of QC-symbols A
QC-symbols A is non empty set
(A,(r ! q)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (r ! q) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (r ! q) ) } is set
min (A,(r ! q)) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,(r ! q),(A,(r ! q)),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),(r ! q)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,(r ! q)),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,(r ! q)),((bound_QC-variables A))} is non empty finite set
{(A,(r ! q))} is non empty trivial finite V80(1) set
{{(A,(r ! q)),((bound_QC-variables A))},{(A,(r ! q))}} is non empty finite V67() set
(A,(A),(r ! q)) . [(A,(r ! q)),((bound_QC-variables A))] is Element of CQC-WFF A
dom q is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V80(p) Element of bool NAT
proj2 q is finite set
[:NAT,(bound_QC-variables A):] is non empty non trivial Relation-like non finite set
bool [:NAT,(bound_QC-variables A):] is non empty non trivial cup-closed diff-closed preBoolean non finite set
f is Relation-like NAT -defined bound_QC-variables A -valued Function-like Element of bool [:NAT,(bound_QC-variables A):]
f * ((bound_QC-variables A)) is Relation-like NAT -defined bound_QC-variables A -valued Function-like set
(A,p,r,q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,p,r,q) . ((A,(r ! q)),((bound_QC-variables A))) is Element of CQC-WFF A
[(A,(r ! q)),((bound_QC-variables A))] is V18() set
(A,p,r,q) . [(A,(r ! q)),((bound_QC-variables A))] is set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
QC-pred_symbols A is non empty set
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
q -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
r is Element of q -ary_QC-pred_symbols A
f is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(q) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r ! f is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
'not' p is Element of CQC-WFF A
(A,('not' p)) is Element of CQC-WFF A
(A,('not' p)) is Element of QC-symbols A
QC-symbols A is non empty set
(A,('not' p)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in ('not' p) 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in ('not' p) ) } is set
min (A,('not' p)) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,('not' p),(A,('not' p)),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),('not' p)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,('not' p)),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,('not' p)),((bound_QC-variables A))} is non empty finite set
{(A,('not' p))} is non empty trivial finite V80(1) set
{{(A,('not' p)),((bound_QC-variables A))},{(A,('not' p))}} is non empty finite V67() set
(A,(A),('not' p)) . [(A,('not' p)),((bound_QC-variables A))] is Element of CQC-WFF A
(A,p) is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
still_not-bound_in p is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
'not' (A,p) is Element of CQC-WFF A
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
q is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,('not' p)),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],q) . [(A,('not' p)),((bound_QC-variables A))] is Element of CQC-WFF A
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],q) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
the_argument_of p is Element of QC-WFF A
(A,p) is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
q is Element of CQC-WFF A
(A,q) is Element of CQC-WFF A
(A,q) is Element of QC-symbols A
(A,q) is non empty Element of bool (QC-symbols A)
still_not-bound_in q is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in q ) } is set
min (A,q) is Element of QC-symbols A
(A,q,(A,q),((bound_QC-variables A))) is Element of CQC-WFF A
(A,(A),q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,q),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,q),((bound_QC-variables A))} is non empty finite set
{(A,q)} is non empty trivial finite V80(1) set
{{(A,q),((bound_QC-variables A))},{(A,q)}} is non empty finite V67() set
(A,(A),q) . [(A,q),((bound_QC-variables A))] is Element of CQC-WFF A
'not' (A,q) is Element of CQC-WFF A
'not' q is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
{ b₁ where b₁ is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] : (A,p,b₁) } is set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean Element of bool (bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):])
bool (bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]) is non empty cup-closed diff-closed preBoolean set
f is set
h is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
f is Element of bool (bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):])
meet f is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
h is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[#] [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty non proper Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[p,(A,p),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[p,(A,p),({}. (bound_QC-variables A))] is V18() triple set
[p,(A,p)] is V18() set
{p,(A,p)} is non empty finite set
{p} is non empty trivial finite V80(1) set
{{p,(A,p)},{p}} is non empty finite V67() set
[[p,(A,p)],({}. (bound_QC-variables A))] is V18() set
{[p,(A,p)],({}. (bound_QC-variables A))} is non empty finite set
{[p,(A,p)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[p,(A,p)],({}. (bound_QC-variables A))},{[p,(A,p)]}} is non empty finite V67() set
[[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[p,(A,p),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[p,(A,p),({}. (bound_QC-variables A))]}} is non empty finite V67() set
K is Element of CQC-WFF A
'not' K is Element of CQC-WFF A
f is Element of QC-symbols A
r9 is finite Element of Fin (bound_QC-variables A)
s9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' K),f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' K),f,r9] is V18() triple set
[('not' K),f] is V18() set
{('not' K),f} is non empty finite set
{('not' K)} is non empty trivial finite V80(1) set
{{('not' K),f},{('not' K)}} is non empty finite V67() set
[[('not' K),f],r9] is V18() set
{[('not' K),f],r9} is non empty finite set
{[('not' K),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' K),f],r9},{[('not' K),f]}} is non empty finite V67() set
[[('not' K),f,r9],s9] is V18() set
{[('not' K),f,r9],s9} is non empty finite set
{[('not' K),f,r9]} is non empty trivial finite V80(1) set
{{[('not' K),f,r9],s9},{[('not' K),f,r9]}} is non empty finite V67() set
[K,f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,f,r9] is V18() triple set
[K,f] is V18() set
{K,f} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,f},{K}} is non empty finite V67() set
[[K,f],r9] is V18() set
{[K,f],r9} is non empty finite set
{[K,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,f],r9},{[K,f]}} is non empty finite V67() set
[[K,f,r9],s9] is V18() set
{[K,f,r9],s9} is non empty finite set
{[K,f,r9]} is non empty trivial finite V80(1) set
{{[K,f,r9],s9},{[K,f,r9]}} is non empty finite V67() set
K is Element of CQC-WFF A
f is Element of CQC-WFF A
K '&' f is Element of CQC-WFF A
r9 is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(K '&' f),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(K '&' f),r9,s9] is V18() triple set
[(K '&' f),r9] is V18() set
{(K '&' f),r9} is non empty finite set
{(K '&' f)} is non empty trivial finite V80(1) set
{{(K '&' f),r9},{(K '&' f)}} is non empty finite V67() set
[[(K '&' f),r9],s9] is V18() set
{[(K '&' f),r9],s9} is non empty finite set
{[(K '&' f),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(K '&' f),r9],s9},{[(K '&' f),r9]}} is non empty finite V67() set
[[(K '&' f),r9,s9],i] is V18() set
{[(K '&' f),r9,s9],i} is non empty finite set
{[(K '&' f),r9,s9]} is non empty trivial finite V80(1) set
{{[(K '&' f),r9,s9],i},{[(K '&' f),r9,s9]}} is non empty finite V67() set
[K,r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,r9,s9] is V18() triple set
[K,r9] is V18() set
{K,r9} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,r9},{K}} is non empty finite V67() set
[[K,r9],s9] is V18() set
{[K,r9],s9} is non empty finite set
{[K,r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,r9],s9},{[K,r9]}} is non empty finite V67() set
[[K,r9,s9],i] is V18() set
{[K,r9,s9],i} is non empty finite set
{[K,r9,s9]} is non empty trivial finite V80(1) set
{{[K,r9,s9],i},{[K,r9,s9]}} is non empty finite V67() set
(A,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 + (A,K) is Element of QC-symbols A
[f,(r9 + (A,K)),s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[f,(r9 + (A,K)),s9] is V18() triple set
[f,(r9 + (A,K))] is V18() set
{f,(r9 + (A,K))} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,(r9 + (A,K))},{f}} is non empty finite V67() set
[[f,(r9 + (A,K))],s9] is V18() set
{[f,(r9 + (A,K))],s9} is non empty finite set
{[f,(r9 + (A,K))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[f,(r9 + (A,K))],s9},{[f,(r9 + (A,K))]}} is non empty finite V67() set
[[f,(r9 + (A,K)),s9],i] is V18() set
{[f,(r9 + (A,K)),s9],i} is non empty finite set
{[f,(r9 + (A,K)),s9]} is non empty trivial finite V80(1) set
{{[f,(r9 + (A,K)),s9],i},{[f,(r9 + (A,K)),s9]}} is non empty finite V67() set
K is Element of CQC-WFF A
f is Element of bound_QC-variables A
All (f,K) is Element of CQC-WFF A
{f} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
r9 is Element of QC-symbols A
r9 ++ is Element of QC-symbols A
x. r9 is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,r9] is V18() set
{4,r9} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,r9},{4}} is non empty finite V67() set
f .--> (x. r9) is Relation-like bound_QC-variables A -defined {f} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{f} is non empty trivial finite V80(1) set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued {(x. r9)} -valued Function-like constant total quasi_total finite Element of bool [:{f},{(x. r9)}:]
{(x. r9)} is non empty trivial finite V80(1) set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
bool [:{f},{(x. r9)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
s9 is finite Element of Fin (bound_QC-variables A)
s9 \/ {f} is non empty finite set
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (f,K)),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,K)),r9,s9] is V18() triple set
[(All (f,K)),r9] is V18() set
{(All (f,K)),r9} is non empty finite set
{(All (f,K))} is non empty trivial finite V80(1) set
{{(All (f,K)),r9},{(All (f,K))}} is non empty finite V67() set
[[(All (f,K)),r9],s9] is V18() set
{[(All (f,K)),r9],s9} is non empty finite set
{[(All (f,K)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,K)),r9],s9},{[(All (f,K)),r9]}} is non empty finite V67() set
[[(All (f,K)),r9,s9],i] is V18() set
{[(All (f,K)),r9,s9],i} is non empty finite set
{[(All (f,K)),r9,s9]} is non empty trivial finite V80(1) set
{{[(All (f,K)),r9,s9],i},{[(All (f,K)),r9,s9]}} is non empty finite V67() set
i +* (f .--> (x. r9)) is Relation-like Function-like set
[K,(r9 ++),(s9 \/ {f}),(i +* (f .--> (x. r9)))] is V18() triple quadruple set
[K,(r9 ++),(s9 \/ {f})] is V18() triple set
[K,(r9 ++)] is V18() set
{K,(r9 ++)} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,(r9 ++)},{K}} is non empty finite V67() set
[[K,(r9 ++)],(s9 \/ {f})] is V18() set
{[K,(r9 ++)],(s9 \/ {f})} is non empty finite set
{[K,(r9 ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,(r9 ++)],(s9 \/ {f})},{[K,(r9 ++)]}} is non empty finite V67() set
[[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))] is V18() set
{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))} is non empty finite set
{[K,(r9 ++),(s9 \/ {f})]} is non empty trivial finite V80(1) set
{{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))},{[K,(r9 ++),(s9 \/ {f})]}} is non empty finite V67() set
proj2 (i +* (f .--> (x. r9))) is set
proj2 i is set
proj2 (f .--> (x. r9)) is finite set
(proj2 i) \/ (proj2 (f .--> (x. r9))) is set
{(x. r9)} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(bound_QC-variables A) \/ {(x. r9)} is non empty set
proj1 (i +* (f .--> (x. r9))) is set
proj1 i is set
proj1 (f .--> (x. r9)) is finite set
(proj1 i) \/ (proj1 (f .--> (x. r9))) is set
(bound_QC-variables A) \/ (proj1 (f .--> (x. r9))) is non empty set
(bound_QC-variables A) \/ {f} is non empty set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty Relation-like set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{.f.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
s9 \/ {.f.} is non empty finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[K,(r9 ++),(s9 \/ {.f.}),u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,(r9 ++),(s9 \/ {.f.})] is V18() triple set
[[K,(r9 ++)],(s9 \/ {.f.})] is V18() set
{[K,(r9 ++)],(s9 \/ {.f.})} is non empty finite set
{{[K,(r9 ++)],(s9 \/ {.f.})},{[K,(r9 ++)]}} is non empty finite V67() set
[[K,(r9 ++),(s9 \/ {.f.})],u] is V18() set
{[K,(r9 ++),(s9 \/ {.f.})],u} is non empty finite set
{[K,(r9 ++),(s9 \/ {.f.})]} is non empty trivial finite V80(1) set
{{[K,(r9 ++),(s9 \/ {.f.})],u},{[K,(r9 ++),(s9 \/ {.f.})]}} is non empty finite V67() set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[p,(A,p),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[p,(A,p),({}. (bound_QC-variables A))] is V18() triple set
[p,(A,p)] is V18() set
{p,(A,p)} is non empty finite set
{p} is non empty trivial finite V80(1) set
{{p,(A,p)},{p}} is non empty finite V67() set
[[p,(A,p)],({}. (bound_QC-variables A))] is V18() set
{[p,(A,p)],({}. (bound_QC-variables A))} is non empty finite set
{[p,(A,p)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[p,(A,p)],({}. (bound_QC-variables A))},{[p,(A,p)]}} is non empty finite V67() set
[[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[p,(A,p),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[p,(A,p),({}. (bound_QC-variables A))]}} is non empty finite V67() set
K is set
f is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
K is Element of CQC-WFF A
'not' K is Element of CQC-WFF A
f is Element of QC-symbols A
r9 is finite Element of Fin (bound_QC-variables A)
s9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' K),f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' K),f,r9] is V18() triple set
[('not' K),f] is V18() set
{('not' K),f} is non empty finite set
{('not' K)} is non empty trivial finite V80(1) set
{{('not' K),f},{('not' K)}} is non empty finite V67() set
[[('not' K),f],r9] is V18() set
{[('not' K),f],r9} is non empty finite set
{[('not' K),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' K),f],r9},{[('not' K),f]}} is non empty finite V67() set
[[('not' K),f,r9],s9] is V18() set
{[('not' K),f,r9],s9} is non empty finite set
{[('not' K),f,r9]} is non empty trivial finite V80(1) set
{{[('not' K),f,r9],s9},{[('not' K),f,r9]}} is non empty finite V67() set
[K,f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,f,r9] is V18() triple set
[K,f] is V18() set
{K,f} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,f},{K}} is non empty finite V67() set
[[K,f],r9] is V18() set
{[K,f],r9} is non empty finite set
{[K,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,f],r9},{[K,f]}} is non empty finite V67() set
[[K,f,r9],s9] is V18() set
{[K,f,r9],s9} is non empty finite set
{[K,f,r9]} is non empty trivial finite V80(1) set
{{[K,f,r9],s9},{[K,f,r9]}} is non empty finite V67() set
i is set
u is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
K is Element of CQC-WFF A
(A,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is Element of CQC-WFF A
K '&' f is Element of CQC-WFF A
r9 is Element of QC-symbols A
r9 + (A,K) is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(K '&' f),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(K '&' f),r9,s9] is V18() triple set
[(K '&' f),r9] is V18() set
{(K '&' f),r9} is non empty finite set
{(K '&' f)} is non empty trivial finite V80(1) set
{{(K '&' f),r9},{(K '&' f)}} is non empty finite V67() set
[[(K '&' f),r9],s9] is V18() set
{[(K '&' f),r9],s9} is non empty finite set
{[(K '&' f),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(K '&' f),r9],s9},{[(K '&' f),r9]}} is non empty finite V67() set
[[(K '&' f),r9,s9],i] is V18() set
{[(K '&' f),r9,s9],i} is non empty finite set
{[(K '&' f),r9,s9]} is non empty trivial finite V80(1) set
{{[(K '&' f),r9,s9],i},{[(K '&' f),r9,s9]}} is non empty finite V67() set
[K,r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,r9,s9] is V18() triple set
[K,r9] is V18() set
{K,r9} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,r9},{K}} is non empty finite V67() set
[[K,r9],s9] is V18() set
{[K,r9],s9} is non empty finite set
{[K,r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,r9],s9},{[K,r9]}} is non empty finite V67() set
[[K,r9,s9],i] is V18() set
{[K,r9,s9],i} is non empty finite set
{[K,r9,s9]} is non empty trivial finite V80(1) set
{{[K,r9,s9],i},{[K,r9,s9]}} is non empty finite V67() set
[f,(r9 + (A,K)),s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[f,(r9 + (A,K)),s9] is V18() triple set
[f,(r9 + (A,K))] is V18() set
{f,(r9 + (A,K))} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,(r9 + (A,K))},{f}} is non empty finite V67() set
[[f,(r9 + (A,K))],s9] is V18() set
{[f,(r9 + (A,K))],s9} is non empty finite set
{[f,(r9 + (A,K))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[f,(r9 + (A,K))],s9},{[f,(r9 + (A,K))]}} is non empty finite V67() set
[[f,(r9 + (A,K)),s9],i] is V18() set
{[f,(r9 + (A,K)),s9],i} is non empty finite set
{[f,(r9 + (A,K)),s9]} is non empty trivial finite V80(1) set
{{[f,(r9 + (A,K)),s9],i},{[f,(r9 + (A,K)),s9]}} is non empty finite V67() set
u is set
c₁₄ is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
u is set
c₁₄ is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
K is Element of CQC-WFF A
f is Element of bound_QC-variables A
All (f,K) is Element of CQC-WFF A
{f} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
r9 is Element of QC-symbols A
r9 ++ is Element of QC-symbols A
x. r9 is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,r9] is V18() set
{4,r9} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,r9},{4}} is non empty finite V67() set
f .--> (x. r9) is Relation-like bound_QC-variables A -defined {f} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{f} is non empty trivial finite V80(1) set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued {(x. r9)} -valued Function-like constant total quasi_total finite Element of bool [:{f},{(x. r9)}:]
{(x. r9)} is non empty trivial finite V80(1) set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
bool [:{f},{(x. r9)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
s9 is finite Element of Fin (bound_QC-variables A)
s9 \/ {f} is non empty finite set
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (f,K)),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,K)),r9,s9] is V18() triple set
[(All (f,K)),r9] is V18() set
{(All (f,K)),r9} is non empty finite set
{(All (f,K))} is non empty trivial finite V80(1) set
{{(All (f,K)),r9},{(All (f,K))}} is non empty finite V67() set
[[(All (f,K)),r9],s9] is V18() set
{[(All (f,K)),r9],s9} is non empty finite set
{[(All (f,K)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,K)),r9],s9},{[(All (f,K)),r9]}} is non empty finite V67() set
[[(All (f,K)),r9,s9],i] is V18() set
{[(All (f,K)),r9,s9],i} is non empty finite set
{[(All (f,K)),r9,s9]} is non empty trivial finite V80(1) set
{{[(All (f,K)),r9,s9],i},{[(All (f,K)),r9,s9]}} is non empty finite V67() set
i +* (f .--> (x. r9)) is Relation-like Function-like set
[K,(r9 ++),(s9 \/ {f}),(i +* (f .--> (x. r9)))] is V18() triple quadruple set
[K,(r9 ++),(s9 \/ {f})] is V18() triple set
[K,(r9 ++)] is V18() set
{K,(r9 ++)} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,(r9 ++)},{K}} is non empty finite V67() set
[[K,(r9 ++)],(s9 \/ {f})] is V18() set
{[K,(r9 ++)],(s9 \/ {f})} is non empty finite set
{[K,(r9 ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,(r9 ++)],(s9 \/ {f})},{[K,(r9 ++)]}} is non empty finite V67() set
[[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))] is V18() set
{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))} is non empty finite set
{[K,(r9 ++),(s9 \/ {f})]} is non empty trivial finite V80(1) set
{{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))},{[K,(r9 ++),(s9 \/ {f})]}} is non empty finite V67() set
u is set
c₁₄ is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
K is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
q is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
r is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
p is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
[p,(A,p),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[p,(A,p),({}. (bound_QC-variables A))] is V18() triple set
[p,(A,p)] is V18() set
{p,(A,p)} is non empty finite set
{p} is non empty trivial finite V80(1) set
{{p,(A,p)},{p}} is non empty finite V67() set
[[p,(A,p)],({}. (bound_QC-variables A))] is V18() set
{[p,(A,p)],({}. (bound_QC-variables A))} is non empty finite set
{[p,(A,p)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[p,(A,p)],({}. (bound_QC-variables A))},{[p,(A,p)]}} is non empty finite V67() set
[[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[p,(A,p),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[p,(A,p),({}. (bound_QC-variables A))]}} is non empty finite V67() set
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
p is Element of CQC-WFF A
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
q is Element of CQC-WFF A
'not' q is Element of CQC-WFF A
r is Element of QC-symbols A
f is finite Element of Fin (bound_QC-variables A)
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' q),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),r,f] is V18() triple set
[('not' q),r] is V18() set
{('not' q),r} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),r},{('not' q)}} is non empty finite V67() set
[[('not' q),r],f] is V18() set
{[('not' q),r],f} is non empty finite set
{[('not' q),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),r],f},{[('not' q),r]}} is non empty finite V67() set
[[('not' q),r,f],h] is V18() set
{[('not' q),r,f],h} is non empty finite set
{[('not' q),r,f]} is non empty trivial finite V80(1) set
{{[('not' q),r,f],h},{[('not' q),r,f]}} is non empty finite V67() set
[q,r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,r,f] is V18() triple set
[q,r] is V18() set
{q,r} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,r},{q}} is non empty finite V67() set
[[q,r],f] is V18() set
{[q,r],f} is non empty finite set
{[q,r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,r],f},{[q,r]}} is non empty finite V67() set
[[q,r,f],h] is V18() set
{[q,r,f],h} is non empty finite set
{[q,r,f]} is non empty trivial finite V80(1) set
{{[q,r,f],h},{[q,r,f]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
p is Element of CQC-WFF A
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
q is Element of CQC-WFF A
r is Element of CQC-WFF A
q '&' r is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(q '&' r),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' r),f,h] is V18() triple set
[(q '&' r),f] is V18() set
{(q '&' r),f} is non empty finite set
{(q '&' r)} is non empty trivial finite V80(1) set
{{(q '&' r),f},{(q '&' r)}} is non empty finite V67() set
[[(q '&' r),f],h] is V18() set
{[(q '&' r),f],h} is non empty finite set
{[(q '&' r),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' r),f],h},{[(q '&' r),f]}} is non empty finite V67() set
[[(q '&' r),f,h],u] is V18() set
{[(q '&' r),f,h],u} is non empty finite set
{[(q '&' r),f,h]} is non empty trivial finite V80(1) set
{{[(q '&' r),f,h],u},{[(q '&' r),f,h]}} is non empty finite V67() set
[q,f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,f,h] is V18() triple set
[q,f] is V18() set
{q,f} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,f},{q}} is non empty finite V67() set
[[q,f],h] is V18() set
{[q,f],h} is non empty finite set
{[q,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,f],h},{[q,f]}} is non empty finite V67() set
[[q,f,h],u] is V18() set
{[q,f,h],u} is non empty finite set
{[q,f,h]} is non empty trivial finite V80(1) set
{{[q,f,h],u},{[q,f,h]}} is non empty finite V67() set
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f + (A,q) is Element of QC-symbols A
[r,(f + (A,q)),h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[r,(f + (A,q)),h] is V18() triple set
[r,(f + (A,q))] is V18() set
{r,(f + (A,q))} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,(f + (A,q))},{r}} is non empty finite V67() set
[[r,(f + (A,q))],h] is V18() set
{[r,(f + (A,q))],h} is non empty finite set
{[r,(f + (A,q))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,(f + (A,q))],h},{[r,(f + (A,q))]}} is non empty finite V67() set
[[r,(f + (A,q)),h],u] is V18() set
{[r,(f + (A,q)),h],u} is non empty finite set
{[r,(f + (A,q)),h]} is non empty trivial finite V80(1) set
{{[r,(f + (A,q)),h],u},{[r,(f + (A,q)),h]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-variables 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 cup-closed diff-closed preBoolean set
QC-symbols A is non empty set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
p is Element of CQC-WFF A
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
r is Element of bound_QC-variables A
q is Element of CQC-WFF A
All (r,q) is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (r,q)),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r,q)),f,h] is V18() triple set
[(All (r,q)),f] is V18() set
{(All (r,q)),f} is non empty finite set
{(All (r,q))} is non empty trivial finite V80(1) set
{{(All (r,q)),f},{(All (r,q))}} is non empty finite V67() set
[[(All (r,q)),f],h] is V18() set
{[(All (r,q)),f],h} is non empty finite set
{[(All (r,q)),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r,q)),f],h},{[(All (r,q)),f]}} is non empty finite V67() set
[[(All (r,q)),f,h],u] is V18() set
{[(All (r,q)),f,h],u} is non empty finite set
{[(All (r,q)),f,h]} is non empty trivial finite V80(1) set
{{[(All (r,q)),f,h],u},{[(All (r,q)),f,h]}} is non empty finite V67() set
f ++ is Element of QC-symbols A
{r} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
h \/ {r} is non empty finite set
x. f is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,f] is V18() set
{4,f} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,f},{4}} is non empty finite V67() set
r .--> (x. f) is Relation-like bound_QC-variables A -defined {r} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{r} is non empty trivial finite V80(1) set
{r} --> (x. f) is non empty Relation-like {r} -defined bound_QC-variables A -valued {(x. f)} -valued Function-like constant total quasi_total finite Element of bool [:{r},{(x. f)}:]
{(x. f)} is non empty trivial finite V80(1) set
[:{r},{(x. f)}:] is non empty Relation-like finite set
bool [:{r},{(x. f)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
u +* (r .--> (x. f)) is Relation-like Function-like set
[q,(f ++),(h \/ {r}),(u +* (r .--> (x. f)))] is V18() triple quadruple set
[q,(f ++),(h \/ {r})] is V18() triple set
[q,(f ++)] is V18() set
{q,(f ++)} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,(f ++)},{q}} is non empty finite V67() set
[[q,(f ++)],(h \/ {r})] is V18() set
{[q,(f ++)],(h \/ {r})} is non empty finite set
{[q,(f ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,(f ++)],(h \/ {r})},{[q,(f ++)]}} is non empty finite V67() set
[[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))] is V18() set
{[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))} is non empty finite set
{[q,(f ++),(h \/ {r})]} is non empty trivial finite V80(1) set
{{[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))},{[q,(f ++),(h \/ {r})]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
p is Element of QC-symbols A
q is Element of CQC-WFF A
'not' q is Element of CQC-WFF A
r is Element of CQC-WFF A
(A,r) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
(A,r) is Element of QC-symbols A
(A,r) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in r is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in r ) } is set
min (A,r) is Element of QC-symbols A
[r,(A,r),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[r,(A,r),({}. (bound_QC-variables A))] is V18() triple set
[r,(A,r)] is V18() set
{r,(A,r)} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,(A,r)},{r}} is non empty finite V67() set
[[r,(A,r)],({}. (bound_QC-variables A))] is V18() set
{[r,(A,r)],({}. (bound_QC-variables A))} is non empty finite set
{[r,(A,r)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,(A,r)],({}. (bound_QC-variables A))},{[r,(A,r)]}} is non empty finite V67() set
[[r,(A,r),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[r,(A,r),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[r,(A,r),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[r,(A,r),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[r,(A,r),({}. (bound_QC-variables A))]}} is non empty finite V67() set
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
h is finite Element of Fin (bound_QC-variables A)
[q,p,h,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,p,h] is V18() triple set
[q,p] is V18() set
{q,p} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,p},{q}} is non empty finite V67() set
[[q,p],h] is V18() set
{[q,p],h} is non empty finite set
{[q,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,p],h},{[q,p]}} is non empty finite V67() set
[[q,p,h],f] is V18() set
{[q,p,h],f} is non empty finite set
{[q,p,h]} is non empty trivial finite V80(1) set
{{[q,p,h],f},{[q,p,h]}} is non empty finite V67() set
[('not' q),p,h,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),p,h] is V18() triple set
[('not' q),p] is V18() set
{('not' q),p} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),p},{('not' q)}} is non empty finite V67() set
[[('not' q),p],h] is V18() set
{[('not' q),p],h} is non empty finite set
{[('not' q),p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),p],h},{[('not' q),p]}} is non empty finite V67() set
[[('not' q),p,h],f] is V18() set
{[('not' q),p,h],f} is non empty finite set
{[('not' q),p,h]} is non empty trivial finite V80(1) set
{{[('not' q),p,h],f},{[('not' q),p,h]}} is non empty finite V67() set
bool h is non empty cup-closed diff-closed preBoolean finite V67() set
{[q,p,h,f]} is non empty trivial finite V80(1) Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
(A,r) \ {[q,p,h,f]} is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
u is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
K is Element of CQC-WFF A
'not' K is Element of CQC-WFF A
f is Element of QC-symbols A
r9 is finite Element of Fin (bound_QC-variables A)
s9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' K),f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' K),f,r9] is V18() triple set
[('not' K),f] is V18() set
{('not' K),f} is non empty finite set
{('not' K)} is non empty trivial finite V80(1) set
{{('not' K),f},{('not' K)}} is non empty finite V67() set
[[('not' K),f],r9] is V18() set
{[('not' K),f],r9} is non empty finite set
{[('not' K),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' K),f],r9},{[('not' K),f]}} is non empty finite V67() set
[[('not' K),f,r9],s9] is V18() set
{[('not' K),f,r9],s9} is non empty finite set
{[('not' K),f,r9]} is non empty trivial finite V80(1) set
{{[('not' K),f,r9],s9},{[('not' K),f,r9]}} is non empty finite V67() set
[K,f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,f,r9] is V18() triple set
[K,f] is V18() set
{K,f} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,f},{K}} is non empty finite V67() set
[[K,f],r9] is V18() set
{[K,f],r9} is non empty finite set
{[K,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,f],r9},{[K,f]}} is non empty finite V67() set
[[K,f,r9],s9] is V18() set
{[K,f,r9],s9} is non empty finite set
{[K,f,r9]} is non empty trivial finite V80(1) set
{{[K,f,r9],s9},{[K,f,r9]}} is non empty finite V67() set
K is Element of CQC-WFF A
(A,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is Element of CQC-WFF A
K '&' f is Element of CQC-WFF A
r9 is Element of QC-symbols A
r9 + (A,K) is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(K '&' f),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(K '&' f),r9,s9] is V18() triple set
[(K '&' f),r9] is V18() set
{(K '&' f),r9} is non empty finite set
{(K '&' f)} is non empty trivial finite V80(1) set
{{(K '&' f),r9},{(K '&' f)}} is non empty finite V67() set
[[(K '&' f),r9],s9] is V18() set
{[(K '&' f),r9],s9} is non empty finite set
{[(K '&' f),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(K '&' f),r9],s9},{[(K '&' f),r9]}} is non empty finite V67() set
[[(K '&' f),r9,s9],i] is V18() set
{[(K '&' f),r9,s9],i} is non empty finite set
{[(K '&' f),r9,s9]} is non empty trivial finite V80(1) set
{{[(K '&' f),r9,s9],i},{[(K '&' f),r9,s9]}} is non empty finite V67() set
[K,r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[K,r9,s9] is V18() triple set
[K,r9] is V18() set
{K,r9} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,r9},{K}} is non empty finite V67() set
[[K,r9],s9] is V18() set
{[K,r9],s9} is non empty finite set
{[K,r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,r9],s9},{[K,r9]}} is non empty finite V67() set
[[K,r9,s9],i] is V18() set
{[K,r9,s9],i} is non empty finite set
{[K,r9,s9]} is non empty trivial finite V80(1) set
{{[K,r9,s9],i},{[K,r9,s9]}} is non empty finite V67() set
[f,(r9 + (A,K)),s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[f,(r9 + (A,K)),s9] is V18() triple set
[f,(r9 + (A,K))] is V18() set
{f,(r9 + (A,K))} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,(r9 + (A,K))},{f}} is non empty finite V67() set
[[f,(r9 + (A,K))],s9] is V18() set
{[f,(r9 + (A,K))],s9} is non empty finite set
{[f,(r9 + (A,K))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[f,(r9 + (A,K))],s9},{[f,(r9 + (A,K))]}} is non empty finite V67() set
[[f,(r9 + (A,K)),s9],i] is V18() set
{[f,(r9 + (A,K)),s9],i} is non empty finite set
{[f,(r9 + (A,K)),s9]} is non empty trivial finite V80(1) set
{{[f,(r9 + (A,K)),s9],i},{[f,(r9 + (A,K)),s9]}} is non empty finite V67() set
K is Element of CQC-WFF A
f is Element of bound_QC-variables A
All (f,K) is Element of CQC-WFF A
{f} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
r9 is Element of QC-symbols A
r9 ++ is Element of QC-symbols A
x. r9 is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,r9] is V18() set
{4,r9} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,r9},{4}} is non empty finite V67() set
f .--> (x. r9) is Relation-like bound_QC-variables A -defined {f} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{f} is non empty trivial finite V80(1) set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued {(x. r9)} -valued Function-like constant total quasi_total finite Element of bool [:{f},{(x. r9)}:]
{(x. r9)} is non empty trivial finite V80(1) set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
bool [:{f},{(x. r9)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
s9 is finite Element of Fin (bound_QC-variables A)
s9 \/ {f} is non empty finite set
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (f,K)),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,K)),r9,s9] is V18() triple set
[(All (f,K)),r9] is V18() set
{(All (f,K)),r9} is non empty finite set
{(All (f,K))} is non empty trivial finite V80(1) set
{{(All (f,K)),r9},{(All (f,K))}} is non empty finite V67() set
[[(All (f,K)),r9],s9] is V18() set
{[(All (f,K)),r9],s9} is non empty finite set
{[(All (f,K)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,K)),r9],s9},{[(All (f,K)),r9]}} is non empty finite V67() set
[[(All (f,K)),r9,s9],i] is V18() set
{[(All (f,K)),r9,s9],i} is non empty finite set
{[(All (f,K)),r9,s9]} is non empty trivial finite V80(1) set
{{[(All (f,K)),r9,s9],i},{[(All (f,K)),r9,s9]}} is non empty finite V67() set
i +* (f .--> (x. r9)) is Relation-like Function-like set
[K,(r9 ++),(s9 \/ {f}),(i +* (f .--> (x. r9)))] is V18() triple quadruple set
[K,(r9 ++),(s9 \/ {f})] is V18() triple set
[K,(r9 ++)] is V18() set
{K,(r9 ++)} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,(r9 ++)},{K}} is non empty finite V67() set
[[K,(r9 ++)],(s9 \/ {f})] is V18() set
{[K,(r9 ++)],(s9 \/ {f})} is non empty finite set
{[K,(r9 ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,(r9 ++)],(s9 \/ {f})},{[K,(r9 ++)]}} is non empty finite V67() set
[[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))] is V18() set
{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))} is non empty finite set
{[K,(r9 ++),(s9 \/ {f})]} is non empty trivial finite V80(1) set
{{[K,(r9 ++),(s9 \/ {f})],(i +* (f .--> (x. r9)))},{[K,(r9 ++),(s9 \/ {f})]}} is non empty finite V67() set
All (f,q) is Element of CQC-WFF A
[(All (f,q)),r9,h,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,q)),r9,h] is V18() triple set
[(All (f,q)),r9] is V18() set
{(All (f,q)),r9} is non empty finite set
{(All (f,q))} is non empty trivial finite V80(1) set
{{(All (f,q)),r9},{(All (f,q))}} is non empty finite V67() set
[[(All (f,q)),r9],h] is V18() set
{[(All (f,q)),r9],h} is non empty finite set
{[(All (f,q)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,q)),r9],h},{[(All (f,q)),r9]}} is non empty finite V67() set
[[(All (f,q)),r9,h],i] is V18() set
{[(All (f,q)),r9,h],i} is non empty finite set
{[(All (f,q)),r9,h]} is non empty trivial finite V80(1) set
{{[(All (f,q)),r9,h],i},{[(All (f,q)),r9,h]}} is non empty finite V67() set
h \ {f} is finite Element of bool h
[(All (f,q)),r9,(h \ {f}),i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(bool h),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(bool h),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[(All (f,q)),r9,(h \ {f})] is V18() triple set
[[(All (f,q)),r9],(h \ {f})] is V18() set
{[(All (f,q)),r9],(h \ {f})} is non empty finite set
{{[(All (f,q)),r9],(h \ {f})},{[(All (f,q)),r9]}} is non empty finite V67() set
[[(All (f,q)),r9,(h \ {f})],i] is V18() set
{[(All (f,q)),r9,(h \ {f})],i} is non empty finite set
{[(All (f,q)),r9,(h \ {f})]} is non empty trivial finite V80(1) set
{{[(All (f,q)),r9,(h \ {f})],i},{[(All (f,q)),r9,(h \ {f})]}} is non empty finite V67() set
s9 \ {f} is finite Element of bool s9
bool s9 is non empty cup-closed diff-closed preBoolean finite V67() set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{f},(bound_QC-variables A):]
[:{f},(bound_QC-variables A):] is non empty Relation-like set
bool [:{f},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
i +* ({f} --> (x. r9)) is Relation-like Function-like set
F₁() is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
F₂() is Element of CQC-WFF F₁()
(F₁(),F₂()) is Element of QC-symbols F₁()
QC-symbols F₁() is non empty set
(F₁(),F₂()) is non empty Element of bool (QC-symbols F₁())
bool (QC-symbols F₁()) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in F₂() is Element of bool (bound_QC-variables F₁())
bound_QC-variables F₁() is non empty Element of bool (QC-variables F₁())
QC-variables F₁() is non empty set
bool (QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols F₁() : for b₂ being Element of QC-symbols F₁() holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in F₂() ) } is set
min (F₁(),F₂()) is Element of QC-symbols F₁()
{}. (bound_QC-variables F₁()) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables F₁())
Fin (bound_QC-variables F₁()) is non empty cup-closed diff-closed preBoolean set
((bound_QC-variables F₁())) is non empty Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is non empty functional set
Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) is non empty functional FUNCTION_DOMAIN of bound_QC-variables F₁(), bound_QC-variables F₁()
(F₁(),F₂()) is Element of bool [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):] is non empty set
bool [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):] is non empty cup-closed diff-closed preBoolean set
{ [b₁,b₃,b₂,b₄] where b₁ is Element of CQC-WFF F₁(), b₂ is finite Element of Fin (bound_QC-variables F₁()), b₃ is Element of QC-symbols F₁(), b₄ is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) : P₁[b₁,b₃,b₂,b₄] } is set
(F₁(),F₂()) /\ { [b₁,b₃,b₂,b₄] where b₁ is Element of CQC-WFF F₁(), b₂ is finite Element of Fin (bound_QC-variables F₁()), b₃ is Element of QC-symbols F₁(), b₄ is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁())) : P₁[b₁,b₃,b₂,b₄] } is Element of bool [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
p is Element of bool [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁())),((bound_QC-variables F₁()))] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):] is non empty set
[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))] is V18() triple set
[F₂(),(F₁(),F₂())] is V18() set
{F₂(),(F₁(),F₂())} is non empty finite set
{F₂()} is non empty trivial finite V80(1) set
{{F₂(),(F₁(),F₂())},{F₂()}} is non empty finite V67() set
[[F₂(),(F₁(),F₂())],({}. (bound_QC-variables F₁()))] is V18() set
{[F₂(),(F₁(),F₂())],({}. (bound_QC-variables F₁()))} is non empty finite set
{[F₂(),(F₁(),F₂())]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[F₂(),(F₁(),F₂())],({}. (bound_QC-variables F₁()))},{[F₂(),(F₁(),F₂())]}} is non empty finite V67() set
[[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))],((bound_QC-variables F₁()))] is V18() set
{[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))],((bound_QC-variables F₁()))} is non empty finite set
{[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))]} is non empty trivial finite V80(1) set
{{[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))],((bound_QC-variables F₁()))},{[F₂(),(F₁(),F₂()),({}. (bound_QC-variables F₁()))]}} is non empty finite V67() set
q is Element of CQC-WFF F₁()
'not' q is Element of CQC-WFF F₁()
r is Element of QC-symbols F₁()
f is finite Element of Fin (bound_QC-variables F₁())
h is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[('not' q),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[('not' q),r,f] is V18() triple set
[('not' q),r] is V18() set
{('not' q),r} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),r},{('not' q)}} is non empty finite V67() set
[[('not' q),r],f] is V18() set
{[('not' q),r],f} is non empty finite set
{[('not' q),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),r],f},{[('not' q),r]}} is non empty finite V67() set
[[('not' q),r,f],h] is V18() set
{[('not' q),r,f],h} is non empty finite set
{[('not' q),r,f]} is non empty trivial finite V80(1) set
{{[('not' q),r,f],h},{[('not' q),r,f]}} is non empty finite V67() set
[q,r,f,h] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[q,r,f] is V18() triple set
[q,r] is V18() set
{q,r} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,r},{q}} is non empty finite V67() set
[[q,r],f] is V18() set
{[q,r],f} is non empty finite set
{[q,r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,r],f},{[q,r]}} is non empty finite V67() set
[[q,r,f],h] is V18() set
{[q,r,f],h} is non empty finite set
{[q,r,f]} is non empty trivial finite V80(1) set
{{[q,r,f],h},{[q,r,f]}} is non empty finite V67() set
u is Element of CQC-WFF F₁()
f is Element of QC-symbols F₁()
K is finite Element of Fin (bound_QC-variables F₁())
r9 is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[u,f,K,r9] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[u,f,K] is V18() triple set
[u,f] is V18() set
{u,f} is non empty finite set
{u} is non empty trivial finite V80(1) set
{{u,f},{u}} is non empty finite V67() set
[[u,f],K] is V18() set
{[u,f],K} is non empty finite set
{[u,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[u,f],K},{[u,f]}} is non empty finite V67() set
[[u,f,K],r9] is V18() set
{[u,f,K],r9} is non empty finite set
{[u,f,K]} is non empty trivial finite V80(1) set
{{[u,f,K],r9},{[u,f,K]}} is non empty finite V67() set
q is Element of CQC-WFF F₁()
r is Element of CQC-WFF F₁()
q '&' r is Element of CQC-WFF F₁()
(F₁(),q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f is Element of QC-symbols F₁()
f + (F₁(),q) is Element of QC-symbols F₁()
h is finite Element of Fin (bound_QC-variables F₁())
u is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[(q '&' r),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[(q '&' r),f,h] is V18() triple set
[(q '&' r),f] is V18() set
{(q '&' r),f} is non empty finite set
{(q '&' r)} is non empty trivial finite V80(1) set
{{(q '&' r),f},{(q '&' r)}} is non empty finite V67() set
[[(q '&' r),f],h] is V18() set
{[(q '&' r),f],h} is non empty finite set
{[(q '&' r),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' r),f],h},{[(q '&' r),f]}} is non empty finite V67() set
[[(q '&' r),f,h],u] is V18() set
{[(q '&' r),f,h],u} is non empty finite set
{[(q '&' r),f,h]} is non empty trivial finite V80(1) set
{{[(q '&' r),f,h],u},{[(q '&' r),f,h]}} is non empty finite V67() set
[q,f,h,u] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[q,f,h] is V18() triple set
[q,f] is V18() set
{q,f} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,f},{q}} is non empty finite V67() set
[[q,f],h] is V18() set
{[q,f],h} is non empty finite set
{[q,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,f],h},{[q,f]}} is non empty finite V67() set
[[q,f,h],u] is V18() set
{[q,f,h],u} is non empty finite set
{[q,f,h]} is non empty trivial finite V80(1) set
{{[q,f,h],u},{[q,f,h]}} is non empty finite V67() set
[r,(f + (F₁(),q)),h,u] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[r,(f + (F₁(),q)),h] is V18() triple set
[r,(f + (F₁(),q))] is V18() set
{r,(f + (F₁(),q))} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,(f + (F₁(),q))},{r}} is non empty finite V67() set
[[r,(f + (F₁(),q))],h] is V18() set
{[r,(f + (F₁(),q))],h} is non empty finite set
{[r,(f + (F₁(),q))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,(f + (F₁(),q))],h},{[r,(f + (F₁(),q))]}} is non empty finite V67() set
[[r,(f + (F₁(),q)),h],u] is V18() set
{[r,(f + (F₁(),q)),h],u} is non empty finite set
{[r,(f + (F₁(),q)),h]} is non empty trivial finite V80(1) set
{{[r,(f + (F₁(),q)),h],u},{[r,(f + (F₁(),q)),h]}} is non empty finite V67() set
K is Element of CQC-WFF F₁()
r9 is Element of QC-symbols F₁()
f is finite Element of Fin (bound_QC-variables F₁())
s9 is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[K,r9,f,s9] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[K,r9,f] is V18() triple set
[K,r9] is V18() set
{K,r9} is non empty finite set
{K} is non empty trivial finite V80(1) set
{{K,r9},{K}} is non empty finite V67() set
[[K,r9],f] is V18() set
{[K,r9],f} is non empty finite set
{[K,r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[K,r9],f},{[K,r9]}} is non empty finite V67() set
[[K,r9,f],s9] is V18() set
{[K,r9,f],s9} is non empty finite set
{[K,r9,f]} is non empty trivial finite V80(1) set
{{[K,r9,f],s9},{[K,r9,f]}} is non empty finite V67() set
q is Element of CQC-WFF F₁()
r is Element of bound_QC-variables F₁()
All (r,q) is Element of CQC-WFF F₁()
{r} is non empty trivial finite V80(1) Element of bool (bound_QC-variables F₁())
f is Element of QC-symbols F₁()
f ++ is Element of QC-symbols F₁()
x. f is Element of bound_QC-variables F₁()
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,f] is V18() set
{4,f} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,f},{4}} is non empty finite V67() set
r .--> (x. f) is Relation-like bound_QC-variables F₁() -defined {r} -defined bound_QC-variables F₁() -valued Function-like one-to-one finite set
{r} is non empty trivial finite V80(1) set
{r} --> (x. f) is non empty Relation-like {r} -defined bound_QC-variables F₁() -valued {(x. f)} -valued Function-like constant total quasi_total finite Element of bool [:{r},{(x. f)}:]
{(x. f)} is non empty trivial finite V80(1) set
[:{r},{(x. f)}:] is non empty Relation-like finite set
bool [:{r},{(x. f)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
h is finite Element of Fin (bound_QC-variables F₁())
h \/ {r} is non empty finite set
u is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[(All (r,q)),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[(All (r,q)),f,h] is V18() triple set
[(All (r,q)),f] is V18() set
{(All (r,q)),f} is non empty finite set
{(All (r,q))} is non empty trivial finite V80(1) set
{{(All (r,q)),f},{(All (r,q))}} is non empty finite V67() set
[[(All (r,q)),f],h] is V18() set
{[(All (r,q)),f],h} is non empty finite set
{[(All (r,q)),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r,q)),f],h},{[(All (r,q)),f]}} is non empty finite V67() set
[[(All (r,q)),f,h],u] is V18() set
{[(All (r,q)),f,h],u} is non empty finite set
{[(All (r,q)),f,h]} is non empty trivial finite V80(1) set
{{[(All (r,q)),f,h],u},{[(All (r,q)),f,h]}} is non empty finite V67() set
u +* (r .--> (x. f)) is Relation-like Function-like set
[q,(f ++),(h \/ {r}),(u +* (r .--> (x. f)))] is V18() triple quadruple set
[q,(f ++),(h \/ {r})] is V18() triple set
[q,(f ++)] is V18() set
{q,(f ++)} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,(f ++)},{q}} is non empty finite V67() set
[[q,(f ++)],(h \/ {r})] is V18() set
{[q,(f ++)],(h \/ {r})} is non empty finite set
{[q,(f ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,(f ++)],(h \/ {r})},{[q,(f ++)]}} is non empty finite V67() set
[[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))] is V18() set
{[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))} is non empty finite set
{[q,(f ++),(h \/ {r})]} is non empty trivial finite V80(1) set
{{[q,(f ++),(h \/ {r})],(u +* (r .--> (x. f)))},{[q,(f ++),(h \/ {r})]}} is non empty finite V67() set
[:(bound_QC-variables F₁()),(bound_QC-variables F₁()):] is non empty Relation-like set
bool [:(bound_QC-variables F₁()),(bound_QC-variables F₁()):] is non empty cup-closed diff-closed preBoolean set
f is Element of CQC-WFF F₁()
s9 is Element of QC-symbols F₁()
r9 is finite Element of Fin (bound_QC-variables F₁())
i is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[f,s9,r9,i] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[f,s9,r9] is V18() triple set
[f,s9] is V18() set
{f,s9} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,s9},{f}} is non empty finite V67() set
[[f,s9],r9] is V18() set
{[f,s9],r9} is non empty finite set
{[f,s9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[f,s9],r9},{[f,s9]}} is non empty finite V67() set
[[f,s9,r9],i] is V18() set
{[f,s9,r9],i} is non empty finite set
{[f,s9,r9]} is non empty trivial finite V80(1) set
{{[f,s9,r9],i},{[f,s9,r9]}} is non empty finite V67() set
K is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
{.r.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables F₁())
h \/ {.r.} is non empty finite Element of Fin (bound_QC-variables F₁())
[q,(f ++),(h \/ {.r.}),(u +* (r .--> (x. f)))] is V18() triple quadruple set
[q,(f ++),(h \/ {.r.})] is V18() triple set
[[q,(f ++)],(h \/ {.r.})] is V18() set
{[q,(f ++)],(h \/ {.r.})} is non empty finite set
{{[q,(f ++)],(h \/ {.r.})},{[q,(f ++)]}} is non empty finite V67() set
[[q,(f ++),(h \/ {.r.})],(u +* (r .--> (x. f)))] is V18() set
{[q,(f ++),(h \/ {.r.})],(u +* (r .--> (x. f)))} is non empty finite set
{[q,(f ++),(h \/ {.r.})]} is non empty trivial finite V80(1) set
{{[q,(f ++),(h \/ {.r.})],(u +* (r .--> (x. f)))},{[q,(f ++),(h \/ {.r.})]}} is non empty finite V67() set
q is Element of CQC-WFF F₁()
r is Element of QC-symbols F₁()
f is finite Element of Fin (bound_QC-variables F₁())
h is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[q,r,f,h] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[q,r,f] is V18() triple set
[q,r] is V18() set
{q,r} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,r},{q}} is non empty finite V67() set
[[q,r],f] is V18() set
{[q,r],f} is non empty finite set
{[q,r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,r],f},{[q,r]}} is non empty finite V67() set
[[q,r,f],h] is V18() set
{[q,r,f],h} is non empty finite set
{[q,r,f]} is non empty trivial finite V80(1) set
{{[q,r,f],h},{[q,r,f]}} is non empty finite V67() set
u is Element of CQC-WFF F₁()
f is Element of QC-symbols F₁()
K is finite Element of Fin (bound_QC-variables F₁())
r9 is Relation-like bound_QC-variables F₁() -defined bound_QC-variables F₁() -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))
[u,f,K,r9] is V18() triple quadruple Element of [:(CQC-WFF F₁()),(QC-symbols F₁()),(Fin (bound_QC-variables F₁())),(Funcs ((bound_QC-variables F₁()),(bound_QC-variables F₁()))):]
[u,f,K] is V18() triple set
[u,f] is V18() set
{u,f} is non empty finite set
{u} is non empty trivial finite V80(1) set
{{u,f},{u}} is non empty finite V67() set
[[u,f],K] is V18() set
{[u,f],K} is non empty finite set
{[u,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[u,f],K},{[u,f]}} is non empty finite V67() set
[[u,f,K],r9] is V18() set
{[u,f,K],r9} is non empty finite set
{[u,f,K]} is non empty trivial finite V80(1) set
{{[u,f,K],r9},{[u,f,K]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
p is Element of CQC-WFF A
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
q is Element of CQC-WFF A
'not' q is Element of CQC-WFF A
r is Element of QC-symbols A
f is finite Element of Fin (bound_QC-variables A)
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' q),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),r,f] is V18() triple set
[('not' q),r] is V18() set
{('not' q),r} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),r},{('not' q)}} is non empty finite V67() set
[[('not' q),r],f] is V18() set
{[('not' q),r],f} is non empty finite set
{[('not' q),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),r],f},{[('not' q),r]}} is non empty finite V67() set
[[('not' q),r,f],h] is V18() set
{[('not' q),r,f],h} is non empty finite set
{[('not' q),r,f]} is non empty trivial finite V80(1) set
{{[('not' q),r,f],h},{[('not' q),r,f]}} is non empty finite V67() set
r is Element of bound_QC-variables A
q is Element of CQC-WFF A
All (r,q) is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (r,q)),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r,q)),f,h] is V18() triple set
[(All (r,q)),f] is V18() set
{(All (r,q)),f} is non empty finite set
{(All (r,q))} is non empty trivial finite V80(1) set
{{(All (r,q)),f},{(All (r,q))}} is non empty finite V67() set
[[(All (r,q)),f],h] is V18() set
{[(All (r,q)),f],h} is non empty finite set
{[(All (r,q)),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r,q)),f],h},{[(All (r,q)),f]}} is non empty finite V67() set
[[(All (r,q)),f,h],u] is V18() set
{[(All (r,q)),f,h],u} is non empty finite set
{[(All (r,q)),f,h]} is non empty trivial finite V80(1) set
{{[(All (r,q)),f,h],u},{[(All (r,q)),f,h]}} is non empty finite V67() set
f ++ is Element of QC-symbols A
{r} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
h \/ {r} is non empty finite set
x. f is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,f] is V18() set
{4,f} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,f},{4}} is non empty finite V67() set
r .--> (x. f) is Relation-like bound_QC-variables A -defined {r} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{r} is non empty trivial finite V80(1) set
{r} --> (x. f) is non empty Relation-like {r} -defined bound_QC-variables A -valued {(x. f)} -valued Function-like constant total quasi_total finite Element of bool [:{r},{(x. f)}:]
{(x. f)} is non empty trivial finite V80(1) set
[:{r},{(x. f)}:] is non empty Relation-like finite set
bool [:{r},{(x. f)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
u +* (r .--> (x. f)) is Relation-like Function-like set
q is Element of CQC-WFF A
r is Element of CQC-WFF A
q '&' r is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(q '&' r),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' r),f,h] is V18() triple set
[(q '&' r),f] is V18() set
{(q '&' r),f} is non empty finite set
{(q '&' r)} is non empty trivial finite V80(1) set
{{(q '&' r),f},{(q '&' r)}} is non empty finite V67() set
[[(q '&' r),f],h] is V18() set
{[(q '&' r),f],h} is non empty finite set
{[(q '&' r),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' r),f],h},{[(q '&' r),f]}} is non empty finite V67() set
[[(q '&' r),f,h],u] is V18() set
{[(q '&' r),f,h],u} is non empty finite set
{[(q '&' r),f,h]} is non empty trivial finite V80(1) set
{{[(q '&' r),f,h],u},{[(q '&' r),f,h]}} is non empty finite V67() set
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f + (A,q) is Element of QC-symbols A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
A is non empty Relation-like 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 cup-closed diff-closed preBoolean set
(A,(VERUM A)) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
0 A is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(VERUM A),(0 A),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(VERUM A),(0 A),({}. (bound_QC-variables A))] is V18() triple set
[(VERUM A),(0 A)] is V18() set
{(VERUM A),(0 A)} is non empty finite set
{(VERUM A)} is non empty trivial finite V80(1) set
{{(VERUM A),(0 A)},{(VERUM A)}} is non empty finite V67() set
[[(VERUM A),(0 A)],({}. (bound_QC-variables A))] is V18() set
{[(VERUM A),(0 A)],({}. (bound_QC-variables A))} is non empty finite set
{[(VERUM A),(0 A)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(VERUM A),(0 A)],({}. (bound_QC-variables A))},{[(VERUM A),(0 A)]}} is non empty finite V67() set
[[(VERUM A),(0 A),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[(VERUM A),(0 A),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[(VERUM A),(0 A),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[(VERUM A),(0 A),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[(VERUM A),(0 A),({}. (bound_QC-variables A))]}} is non empty finite V67() set
{[(VERUM A),(0 A),({}. (bound_QC-variables A)),((bound_QC-variables A))]} is non empty trivial finite V80(1) Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
p is set
q is Element of CQC-WFF A
r is Element of QC-symbols A
f is finite Element of Fin (bound_QC-variables A)
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[q,r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,r,f] is V18() triple set
[q,r] is V18() set
{q,r} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,r},{q}} is non empty finite V67() set
[[q,r],f] is V18() set
{[q,r],f} is non empty finite set
{[q,r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,r],f},{[q,r]}} is non empty finite V67() set
[[q,r,f],h] is V18() set
{[q,r,f],h} is non empty finite set
{[q,r,f]} is non empty trivial finite V80(1) set
{{[q,r,f],h},{[q,r,f]}} is non empty finite V67() set
K is Element of QC-symbols A
K ++ is Element of QC-symbols A
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
u is Element of bound_QC-variables A
{u} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
x. K is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,K] is V18() set
{4,K} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,K},{4}} is non empty finite V67() set
{u} --> (x. K) is non empty Relation-like {u} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{u},(bound_QC-variables A):]
[:{u},(bound_QC-variables A):] is non empty Relation-like set
bool [:{u},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{(x. K)} is non empty trivial finite V80(1) set
[:{u},{(x. K)}:] is non empty Relation-like finite set
f +* ({u} --> (x. K)) is Relation-like Function-like set
All (u,q) is Element of CQC-WFF A
[(All (u,q)),K,f,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (u,q)),K,f] is V18() triple set
[(All (u,q)),K] is V18() set
{(All (u,q)),K} is non empty finite set
{(All (u,q))} is non empty trivial finite V80(1) set
{{(All (u,q)),K},{(All (u,q))}} is non empty finite V67() set
[[(All (u,q)),K],f] is V18() set
{[(All (u,q)),K],f} is non empty finite set
{[(All (u,q)),K]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (u,q)),K],f},{[(All (u,q)),K]}} is non empty finite V67() set
[[(All (u,q)),K,f],f] is V18() set
{[(All (u,q)),K,f],f} is non empty finite set
{[(All (u,q)),K,f]} is non empty trivial finite V80(1) set
{{[(All (u,q)),K,f],f},{[(All (u,q)),K,f]}} is non empty finite V67() set
{.u.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
f \ {.u.} is finite Element of Fin (bound_QC-variables A)
[(All (u,q)),K,(f \ {.u.}),f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (u,q)),K,(f \ {.u.})] is V18() triple set
[[(All (u,q)),K],(f \ {.u.})] is V18() set
{[(All (u,q)),K],(f \ {.u.})} is non empty finite set
{{[(All (u,q)),K],(f \ {.u.})},{[(All (u,q)),K]}} is non empty finite V67() set
[[(All (u,q)),K,(f \ {.u.})],f] is V18() set
{[(All (u,q)),K,(f \ {.u.})],f} is non empty finite set
{[(All (u,q)),K,(f \ {.u.})]} is non empty trivial finite V80(1) set
{{[(All (u,q)),K,(f \ {.u.})],f},{[(All (u,q)),K,(f \ {.u.})]}} is non empty finite V67() set
K is Element of QC-symbols A
u is Element of CQC-WFF A
(A,u) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
K + (A,u) is Element of QC-symbols A
u '&' q is Element of CQC-WFF A
[(u '&' q),K,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(u '&' q),K,f] is V18() triple set
[(u '&' q),K] is V18() set
{(u '&' q),K} is non empty finite set
{(u '&' q)} is non empty trivial finite V80(1) set
{{(u '&' q),K},{(u '&' q)}} is non empty finite V67() set
[[(u '&' q),K],f] is V18() set
{[(u '&' q),K],f} is non empty finite set
{[(u '&' q),K]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(u '&' q),K],f},{[(u '&' q),K]}} is non empty finite V67() set
[[(u '&' q),K,f],h] is V18() set
{[(u '&' q),K,f],h} is non empty finite set
{[(u '&' q),K,f]} is non empty trivial finite V80(1) set
{{[(u '&' q),K,f],h},{[(u '&' q),K,f]}} is non empty finite V67() set
u is Element of CQC-WFF A
q '&' u is Element of CQC-WFF A
[(q '&' u),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' u),r,f] is V18() triple set
[(q '&' u),r] is V18() set
{(q '&' u),r} is non empty finite set
{(q '&' u)} is non empty trivial finite V80(1) set
{{(q '&' u),r},{(q '&' u)}} is non empty finite V67() set
[[(q '&' u),r],f] is V18() set
{[(q '&' u),r],f} is non empty finite set
{[(q '&' u),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' u),r],f},{[(q '&' u),r]}} is non empty finite V67() set
[[(q '&' u),r,f],h] is V18() set
{[(q '&' u),r,f],h} is non empty finite set
{[(q '&' u),r,f]} is non empty trivial finite V80(1) set
{{[(q '&' u),r,f],h},{[(q '&' u),r,f]}} is non empty finite V67() set
'not' q is Element of CQC-WFF A
[('not' q),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),r,f] is V18() triple set
[('not' q),r] is V18() set
{('not' q),r} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),r},{('not' q)}} is non empty finite V67() set
[[('not' q),r],f] is V18() set
{[('not' q),r],f} is non empty finite set
{[('not' q),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),r],f},{[('not' q),r]}} is non empty finite V67() set
[[('not' q),r,f],h] is V18() set
{[('not' q),r,f],h} is non empty finite set
{[('not' q),r,f]} is non empty trivial finite V80(1) set
{{[('not' q),r,f],h},{[('not' q),r,f]}} is non empty finite V67() set
(A,(VERUM A)) is Element of QC-symbols A
(A,(VERUM A)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (VERUM A) is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (VERUM A) ) } is set
min (A,(VERUM A)) is Element of QC-symbols A
[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))] is V18() triple set
[(VERUM A),(A,(VERUM A))] is V18() set
{(VERUM A),(A,(VERUM A))} is non empty finite set
{{(VERUM A),(A,(VERUM A))},{(VERUM A)}} is non empty finite V67() set
[[(VERUM A),(A,(VERUM A))],({}. (bound_QC-variables A))] is V18() set
{[(VERUM A),(A,(VERUM A))],({}. (bound_QC-variables A))} is non empty finite set
{[(VERUM A),(A,(VERUM A))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(VERUM A),(A,(VERUM A))],({}. (bound_QC-variables A))},{[(VERUM A),(A,(VERUM A))]}} is non empty finite V67() set
[[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[(VERUM A),(A,(VERUM A)),({}. (bound_QC-variables A))]}} is non empty finite V67() set
bool f is non empty cup-closed diff-closed preBoolean finite V67() set
K is Element of CQC-WFF A
q '&' K is Element of CQC-WFF A
[(q '&' K),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' K),r,f] is V18() triple set
[(q '&' K),r] is V18() set
{(q '&' K),r} is non empty finite set
{(q '&' K)} is non empty trivial finite V80(1) set
{{(q '&' K),r},{(q '&' K)}} is non empty finite V67() set
[[(q '&' K),r],f] is V18() set
{[(q '&' K),r],f} is non empty finite set
{[(q '&' K),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' K),r],f},{[(q '&' K),r]}} is non empty finite V67() set
[[(q '&' K),r,f],h] is V18() set
{[(q '&' K),r,f],h} is non empty finite set
{[(q '&' K),r,f]} is non empty trivial finite V80(1) set
{{[(q '&' K),r,f],h},{[(q '&' K),r,f]}} is non empty finite V67() set
r9 is Element of QC-symbols A
f is Element of CQC-WFF A
(A,f) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 + (A,f) is Element of QC-symbols A
f '&' q is Element of CQC-WFF A
[(f '&' q),r9,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(f '&' q),r9,f] is V18() triple set
[(f '&' q),r9] is V18() set
{(f '&' q),r9} is non empty finite set
{(f '&' q)} is non empty trivial finite V80(1) set
{{(f '&' q),r9},{(f '&' q)}} is non empty finite V67() set
[[(f '&' q),r9],f] is V18() set
{[(f '&' q),r9],f} is non empty finite set
{[(f '&' q),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(f '&' q),r9],f},{[(f '&' q),r9]}} is non empty finite V67() set
[[(f '&' q),r9,f],h] is V18() set
{[(f '&' q),r9,f],h} is non empty finite set
{[(f '&' q),r9,f]} is non empty trivial finite V80(1) set
{{[(f '&' q),r9,f],h},{[(f '&' q),r9,f]}} is non empty finite V67() set
i is Element of QC-symbols A
i ++ is Element of QC-symbols A
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
s9 is Element of bound_QC-variables A
{s9} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
x. i is Element of bound_QC-variables A
[4,i] is V18() set
{4,i} is non empty finite set
{{4,i},{4}} is non empty finite V67() set
{s9} --> (x. i) is non empty Relation-like {s9} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{s9},(bound_QC-variables A):]
[:{s9},(bound_QC-variables A):] is non empty Relation-like set
bool [:{s9},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{(x. i)} is non empty trivial finite V80(1) set
[:{s9},{(x. i)}:] is non empty Relation-like finite set
u +* ({s9} --> (x. i)) is Relation-like Function-like set
All (s9,q) is Element of CQC-WFF A
[(All (s9,q)),i,f,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (s9,q)),i,f] is V18() triple set
[(All (s9,q)),i] is V18() set
{(All (s9,q)),i} is non empty finite set
{(All (s9,q))} is non empty trivial finite V80(1) set
{{(All (s9,q)),i},{(All (s9,q))}} is non empty finite V67() set
[[(All (s9,q)),i],f] is V18() set
{[(All (s9,q)),i],f} is non empty finite set
{[(All (s9,q)),i]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (s9,q)),i],f},{[(All (s9,q)),i]}} is non empty finite V67() set
[[(All (s9,q)),i,f],u] is V18() set
{[(All (s9,q)),i,f],u} is non empty finite set
{[(All (s9,q)),i,f]} is non empty trivial finite V80(1) set
{{[(All (s9,q)),i,f],u},{[(All (s9,q)),i,f]}} is non empty finite V67() set
f \ {s9} is finite Element of bool f
[(All (s9,q)),i,(f \ {s9}),u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(bool f),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(bool f),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[(All (s9,q)),i,(f \ {s9})] is V18() triple set
[[(All (s9,q)),i],(f \ {s9})] is V18() set
{[(All (s9,q)),i],(f \ {s9})} is non empty finite set
{{[(All (s9,q)),i],(f \ {s9})},{[(All (s9,q)),i]}} is non empty finite V67() set
[[(All (s9,q)),i,(f \ {s9})],u] is V18() set
{[(All (s9,q)),i,(f \ {s9})],u} is non empty finite set
{[(All (s9,q)),i,(f \ {s9})]} is non empty trivial finite V80(1) set
{{[(All (s9,q)),i,(f \ {s9})],u},{[(All (s9,q)),i,(f \ {s9})]}} is non empty finite V67() set
(A,(VERUM A)) is Element of QC-symbols A
(A,(VERUM A)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (VERUM A) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (VERUM A) ) } is set
min (A,(VERUM A)) is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
QC-pred_symbols A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
QC-WFF A is non empty set
bool (QC-WFF A) is non empty cup-closed diff-closed preBoolean set
QC-symbols A is non empty set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
p is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
p -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
q is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(p) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
r is Element of p -ary_QC-pred_symbols A
r ! q is Element of CQC-WFF A
(A,(r ! q)) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
(A,(r ! q)) is Element of QC-symbols A
(A,(r ! q)) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in (r ! q) is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (r ! q) ) } is set
min (A,(r ! q)) is Element of QC-symbols A
[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))] is V18() triple set
[(r ! q),(A,(r ! q))] is V18() set
{(r ! q),(A,(r ! q))} is non empty finite set
{(r ! q)} is non empty trivial finite V80(1) set
{{(r ! q),(A,(r ! q))},{(r ! q)}} is non empty finite V67() set
[[(r ! q),(A,(r ! q))],({}. (bound_QC-variables A))] is V18() set
{[(r ! q),(A,(r ! q))],({}. (bound_QC-variables A))} is non empty finite set
{[(r ! q),(A,(r ! q))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(r ! q),(A,(r ! q))],({}. (bound_QC-variables A))},{[(r ! q),(A,(r ! q))]}} is non empty finite V67() set
[[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A))]}} is non empty finite V67() set
{[(r ! q),(A,(r ! q)),({}. (bound_QC-variables A)),((bound_QC-variables A))]} is non empty trivial finite V80(1) Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
f is set
h is Element of CQC-WFF A
u is Element of QC-symbols A
K is finite Element of Fin (bound_QC-variables A)
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[h,u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[h,u,K] is V18() triple set
[h,u] is V18() set
{h,u} is non empty finite set
{h} is non empty trivial finite V80(1) set
{{h,u},{h}} is non empty finite V67() set
[[h,u],K] is V18() set
{[h,u],K} is non empty finite set
{[h,u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[h,u],K},{[h,u]}} is non empty finite V67() set
[[h,u,K],f] is V18() set
{[h,u,K],f} is non empty finite set
{[h,u,K]} is non empty trivial finite V80(1) set
{{[h,u,K],f},{[h,u,K]}} is non empty finite V67() set
s9 is Element of QC-symbols A
s9 ++ is Element of QC-symbols A
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
r9 is Element of bound_QC-variables A
{r9} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
x. s9 is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,s9] is V18() set
{4,s9} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,s9},{4}} is non empty finite V67() set
{r9} --> (x. s9) is non empty Relation-like {r9} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{r9},(bound_QC-variables A):]
[:{r9},(bound_QC-variables A):] is non empty Relation-like set
bool [:{r9},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{(x. s9)} is non empty trivial finite V80(1) set
[:{r9},{(x. s9)}:] is non empty Relation-like finite set
i +* ({r9} --> (x. s9)) is Relation-like Function-like set
All (r9,h) is Element of CQC-WFF A
[(All (r9,h)),s9,K,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r9,h)),s9,K] is V18() triple set
[(All (r9,h)),s9] is V18() set
{(All (r9,h)),s9} is non empty finite set
{(All (r9,h))} is non empty trivial finite V80(1) set
{{(All (r9,h)),s9},{(All (r9,h))}} is non empty finite V67() set
[[(All (r9,h)),s9],K] is V18() set
{[(All (r9,h)),s9],K} is non empty finite set
{[(All (r9,h)),s9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r9,h)),s9],K},{[(All (r9,h)),s9]}} is non empty finite V67() set
[[(All (r9,h)),s9,K],i] is V18() set
{[(All (r9,h)),s9,K],i} is non empty finite set
{[(All (r9,h)),s9,K]} is non empty trivial finite V80(1) set
{{[(All (r9,h)),s9,K],i},{[(All (r9,h)),s9,K]}} is non empty finite V67() set
{.r9.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
K \ {.r9.} is finite Element of Fin (bound_QC-variables A)
[(All (r9,h)),s9,(K \ {.r9.}),i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r9,h)),s9,(K \ {.r9.})] is V18() triple set
[[(All (r9,h)),s9],(K \ {.r9.})] is V18() set
{[(All (r9,h)),s9],(K \ {.r9.})} is non empty finite set
{{[(All (r9,h)),s9],(K \ {.r9.})},{[(All (r9,h)),s9]}} is non empty finite V67() set
[[(All (r9,h)),s9,(K \ {.r9.})],i] is V18() set
{[(All (r9,h)),s9,(K \ {.r9.})],i} is non empty finite set
{[(All (r9,h)),s9,(K \ {.r9.})]} is non empty trivial finite V80(1) set
{{[(All (r9,h)),s9,(K \ {.r9.})],i},{[(All (r9,h)),s9,(K \ {.r9.})]}} is non empty finite V67() set
s9 is Element of QC-symbols A
r9 is Element of CQC-WFF A
(A,r9) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
s9 + (A,r9) is Element of QC-symbols A
r9 '&' h is Element of CQC-WFF A
[(r9 '&' h),s9,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(r9 '&' h),s9,K] is V18() triple set
[(r9 '&' h),s9] is V18() set
{(r9 '&' h),s9} is non empty finite set
{(r9 '&' h)} is non empty trivial finite V80(1) set
{{(r9 '&' h),s9},{(r9 '&' h)}} is non empty finite V67() set
[[(r9 '&' h),s9],K] is V18() set
{[(r9 '&' h),s9],K} is non empty finite set
{[(r9 '&' h),s9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(r9 '&' h),s9],K},{[(r9 '&' h),s9]}} is non empty finite V67() set
[[(r9 '&' h),s9,K],f] is V18() set
{[(r9 '&' h),s9,K],f} is non empty finite set
{[(r9 '&' h),s9,K]} is non empty trivial finite V80(1) set
{{[(r9 '&' h),s9,K],f},{[(r9 '&' h),s9,K]}} is non empty finite V67() set
r9 is Element of CQC-WFF A
h '&' r9 is Element of CQC-WFF A
[(h '&' r9),u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(h '&' r9),u,K] is V18() triple set
[(h '&' r9),u] is V18() set
{(h '&' r9),u} is non empty finite set
{(h '&' r9)} is non empty trivial finite V80(1) set
{{(h '&' r9),u},{(h '&' r9)}} is non empty finite V67() set
[[(h '&' r9),u],K] is V18() set
{[(h '&' r9),u],K} is non empty finite set
{[(h '&' r9),u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(h '&' r9),u],K},{[(h '&' r9),u]}} is non empty finite V67() set
[[(h '&' r9),u,K],f] is V18() set
{[(h '&' r9),u,K],f} is non empty finite set
{[(h '&' r9),u,K]} is non empty trivial finite V80(1) set
{{[(h '&' r9),u,K],f},{[(h '&' r9),u,K]}} is non empty finite V67() set
'not' h is Element of CQC-WFF A
[('not' h),u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' h),u,K] is V18() triple set
[('not' h),u] is V18() set
{('not' h),u} is non empty finite set
{('not' h)} is non empty trivial finite V80(1) set
{{('not' h),u},{('not' h)}} is non empty finite V67() set
[[('not' h),u],K] is V18() set
{[('not' h),u],K} is non empty finite set
{[('not' h),u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' h),u],K},{[('not' h),u]}} is non empty finite V67() set
[[('not' h),u,K],f] is V18() set
{[('not' h),u,K],f} is non empty finite set
{[('not' h),u,K]} is non empty trivial finite V80(1) set
{{[('not' h),u,K],f},{[('not' h),u,K]}} is non empty finite V67() set
bool K is non empty cup-closed diff-closed preBoolean finite V67() set
s9 is Element of CQC-WFF A
h '&' s9 is Element of CQC-WFF A
[(h '&' s9),u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(h '&' s9),u,K] is V18() triple set
[(h '&' s9),u] is V18() set
{(h '&' s9),u} is non empty finite set
{(h '&' s9)} is non empty trivial finite V80(1) set
{{(h '&' s9),u},{(h '&' s9)}} is non empty finite V67() set
[[(h '&' s9),u],K] is V18() set
{[(h '&' s9),u],K} is non empty finite set
{[(h '&' s9),u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(h '&' s9),u],K},{[(h '&' s9),u]}} is non empty finite V67() set
[[(h '&' s9),u,K],f] is V18() set
{[(h '&' s9),u,K],f} is non empty finite set
{[(h '&' s9),u,K]} is non empty trivial finite V80(1) set
{{[(h '&' s9),u,K],f},{[(h '&' s9),u,K]}} is non empty finite V67() set
u is Element of QC-symbols A
i is Element of CQC-WFF A
(A,i) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u + (A,i) is Element of QC-symbols A
i '&' h is Element of CQC-WFF A
[(i '&' h),u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(i '&' h),u,K] is V18() triple set
[(i '&' h),u] is V18() set
{(i '&' h),u} is non empty finite set
{(i '&' h)} is non empty trivial finite V80(1) set
{{(i '&' h),u},{(i '&' h)}} is non empty finite V67() set
[[(i '&' h),u],K] is V18() set
{[(i '&' h),u],K} is non empty finite set
{[(i '&' h),u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(i '&' h),u],K},{[(i '&' h),u]}} is non empty finite V67() set
[[(i '&' h),u,K],f] is V18() set
{[(i '&' h),u,K],f} is non empty finite set
{[(i '&' h),u,K]} is non empty trivial finite V80(1) set
{{[(i '&' h),u,K],f},{[(i '&' h),u,K]}} is non empty finite V67() set
c₁₅ is Element of QC-symbols A
c₁₅ ++ is Element of QC-symbols A
c₁₆ is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
c₁₄ is Element of bound_QC-variables A
{c₁₄} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
x. c₁₅ is Element of bound_QC-variables A
[4,c₁₅] is V18() set
{4,c₁₅} is non empty finite set
{{4,c₁₅},{4}} is non empty finite V67() set
{c₁₄} --> (x. c₁₅) is non empty Relation-like {c₁₄} -defined bound_QC-variables A -valued Function-like constant total quasi_total finite Element of bool [:{c₁₄},(bound_QC-variables A):]
[:{c₁₄},(bound_QC-variables A):] is non empty Relation-like set
bool [:{c₁₄},(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
{(x. c₁₅)} is non empty trivial finite V80(1) set
[:{c₁₄},{(x. c₁₅)}:] is non empty Relation-like finite set
c₁₆ +* ({c₁₄} --> (x. c₁₅)) is Relation-like Function-like set
All (c₁₄,h) is Element of CQC-WFF A
[(All (c₁₄,h)),c₁₅,K,c₁₆] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (c₁₄,h)),c₁₅,K] is V18() triple set
[(All (c₁₄,h)),c₁₅] is V18() set
{(All (c₁₄,h)),c₁₅} is non empty finite set
{(All (c₁₄,h))} is non empty trivial finite V80(1) set
{{(All (c₁₄,h)),c₁₅},{(All (c₁₄,h))}} is non empty finite V67() set
[[(All (c₁₄,h)),c₁₅],K] is V18() set
{[(All (c₁₄,h)),c₁₅],K} is non empty finite set
{[(All (c₁₄,h)),c₁₅]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (c₁₄,h)),c₁₅],K},{[(All (c₁₄,h)),c₁₅]}} is non empty finite V67() set
[[(All (c₁₄,h)),c₁₅,K],c₁₆] is V18() set
{[(All (c₁₄,h)),c₁₅,K],c₁₆} is non empty finite set
{[(All (c₁₄,h)),c₁₅,K]} is non empty trivial finite V80(1) set
{{[(All (c₁₄,h)),c₁₅,K],c₁₆},{[(All (c₁₄,h)),c₁₅,K]}} is non empty finite V67() set
K \ {c₁₄} is finite Element of bool K
[(All (c₁₄,h)),c₁₅,(K \ {c₁₄}),c₁₆] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(bool K),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(bool K),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})] is V18() triple set
[[(All (c₁₄,h)),c₁₅],(K \ {c₁₄})] is V18() set
{[(All (c₁₄,h)),c₁₅],(K \ {c₁₄})} is non empty finite set
{{[(All (c₁₄,h)),c₁₅],(K \ {c₁₄})},{[(All (c₁₄,h)),c₁₅]}} is non empty finite V67() set
[[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})],c₁₆] is V18() set
{[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})],c₁₆} is non empty finite set
{[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})]} is non empty trivial finite V80(1) set
{{[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})],c₁₆},{[(All (c₁₄,h)),c₁₅,(K \ {c₁₄})]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
QC-symbols 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
p is Element of CQC-WFF A
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
q is Element of CQC-WFF A
'not' q is Element of CQC-WFF A
r is Element of QC-symbols A
f is finite Element of Fin (bound_QC-variables A)
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' q),r,f,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),r,f] is V18() triple set
[('not' q),r] is V18() set
{('not' q),r} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),r},{('not' q)}} is non empty finite V67() set
[[('not' q),r],f] is V18() set
{[('not' q),r],f} is non empty finite set
{[('not' q),r]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),r],f},{[('not' q),r]}} is non empty finite V67() set
[[('not' q),r,f],h] is V18() set
{[('not' q),r,f],h} is non empty finite set
{[('not' q),r,f]} is non empty trivial finite V80(1) set
{{[('not' q),r,f],h},{[('not' q),r,f]}} is non empty finite V67() set
still_not-bound_in ('not' q) is Element of bool (bound_QC-variables A)
(still_not-bound_in p) \/ f is set
still_not-bound_in q is Element of bool (bound_QC-variables A)
q is Element of CQC-WFF A
r is Element of CQC-WFF A
q '&' r is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(q '&' r),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' r),f,h] is V18() triple set
[(q '&' r),f] is V18() set
{(q '&' r),f} is non empty finite set
{(q '&' r)} is non empty trivial finite V80(1) set
{{(q '&' r),f},{(q '&' r)}} is non empty finite V67() set
[[(q '&' r),f],h] is V18() set
{[(q '&' r),f],h} is non empty finite set
{[(q '&' r),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' r),f],h},{[(q '&' r),f]}} is non empty finite V67() set
[[(q '&' r),f,h],u] is V18() set
{[(q '&' r),f,h],u} is non empty finite set
{[(q '&' r),f,h]} is non empty trivial finite V80(1) set
{{[(q '&' r),f,h],u},{[(q '&' r),f,h]}} is non empty finite V67() set
still_not-bound_in (q '&' r) is Element of bool (bound_QC-variables A)
H₅(p) \/ h is set
still_not-bound_in q is Element of bool (bound_QC-variables A)
still_not-bound_in r is Element of bool (bound_QC-variables A)
(still_not-bound_in q) \/ (still_not-bound_in r) is Element of bool (bound_QC-variables A)
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
f + (A,q) is Element of QC-symbols A
r is Element of bound_QC-variables A
q is Element of CQC-WFF A
All (r,q) is Element of CQC-WFF A
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (r,q)),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r,q)),f,h] is V18() triple set
[(All (r,q)),f] is V18() set
{(All (r,q)),f} is non empty finite set
{(All (r,q))} is non empty trivial finite V80(1) set
{{(All (r,q)),f},{(All (r,q))}} is non empty finite V67() set
[[(All (r,q)),f],h] is V18() set
{[(All (r,q)),f],h} is non empty finite set
{[(All (r,q)),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r,q)),f],h},{[(All (r,q)),f]}} is non empty finite V67() set
[[(All (r,q)),f,h],u] is V18() set
{[(All (r,q)),f,h],u} is non empty finite set
{[(All (r,q)),f,h]} is non empty trivial finite V80(1) set
{{[(All (r,q)),f,h],u},{[(All (r,q)),f,h]}} is non empty finite V67() set
still_not-bound_in (All (r,q)) is Element of bool (bound_QC-variables A)
H₅(p) \/ h is set
still_not-bound_in q is Element of bool (bound_QC-variables A)
{r} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(still_not-bound_in q) \ {r} is Element of bool (bound_QC-variables A)
(still_not-bound_in p) \/ h is set
((still_not-bound_in p) \/ h) \/ {r} is non empty set
f ++ is Element of QC-symbols A
h \/ {r} is non empty finite set
x. f is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,f] is V18() set
{4,f} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,f},{4}} is non empty finite V67() set
r .--> (x. f) is Relation-like bound_QC-variables A -defined {r} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{r} is non empty trivial finite V80(1) set
{r} --> (x. f) is non empty Relation-like {r} -defined bound_QC-variables A -valued {(x. f)} -valued Function-like constant total quasi_total finite Element of bool [:{r},{(x. f)}:]
{(x. f)} is non empty trivial finite V80(1) set
[:{r},{(x. f)}:] is non empty Relation-like finite set
bool [:{r},{(x. f)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
u +* (r .--> (x. f)) is Relation-like Function-like set
H₅(p) \/ (h \/ {r}) is non empty set
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
H₅(p) \/ ({}. (bound_QC-variables A)) is set
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
q is Element of QC-symbols A
x. q is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,q] is V18() set
{4,q} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,q},{4}} is non empty finite V67() set
r is Element of CQC-WFF A
f is Element of CQC-WFF A
(A,f) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
u is finite Element of Fin (bound_QC-variables A)
[r,p,u,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[r,p,u] is V18() triple set
[r,p] is V18() set
{r,p} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,p},{r}} is non empty finite V67() set
[[r,p],u] is V18() set
{[r,p],u} is non empty finite set
{[r,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,p],u},{[r,p]}} is non empty finite V67() set
[[r,p,u],h] is V18() set
{[r,p,u],h} is non empty finite set
{[r,p,u]} is non empty trivial finite V80(1) set
{{[r,p,u],h},{[r,p,u]}} is non empty finite V67() set
h .: u is finite Element of Fin (bound_QC-variables A)
K is Element of CQC-WFF A
'not' K is Element of CQC-WFF A
f is Element of QC-symbols A
r9 is finite Element of Fin (bound_QC-variables A)
s9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' K),f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' K),f,r9] is V18() triple set
[('not' K),f] is V18() set
{('not' K),f} is non empty finite set
{('not' K)} is non empty trivial finite V80(1) set
{{('not' K),f},{('not' K)}} is non empty finite V67() set
[[('not' K),f],r9] is V18() set
{[('not' K),f],r9} is non empty finite set
{[('not' K),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' K),f],r9},{[('not' K),f]}} is non empty finite V67() set
[[('not' K),f,r9],s9] is V18() set
{[('not' K),f,r9],s9} is non empty finite set
{[('not' K),f,r9]} is non empty trivial finite V80(1) set
{{[('not' K),f,r9],s9},{[('not' K),f,r9]}} is non empty finite V67() set
s9 .: r9 is finite set
i is Element of QC-symbols A
x. i is Element of bound_QC-variables A
[4,i] is V18() set
{4,i} is non empty finite set
{{4,i},{4}} is non empty finite V67() set
K is Element of CQC-WFF A
f is Element of CQC-WFF A
K '&' f is Element of CQC-WFF A
r9 is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(K '&' f),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(K '&' f),r9,s9] is V18() triple set
[(K '&' f),r9] is V18() set
{(K '&' f),r9} is non empty finite set
{(K '&' f)} is non empty trivial finite V80(1) set
{{(K '&' f),r9},{(K '&' f)}} is non empty finite V67() set
[[(K '&' f),r9],s9] is V18() set
{[(K '&' f),r9],s9} is non empty finite set
{[(K '&' f),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(K '&' f),r9],s9},{[(K '&' f),r9]}} is non empty finite V67() set
[[(K '&' f),r9,s9],i] is V18() set
{[(K '&' f),r9,s9],i} is non empty finite set
{[(K '&' f),r9,s9]} is non empty trivial finite V80(1) set
{{[(K '&' f),r9,s9],i},{[(K '&' f),r9,s9]}} is non empty finite V67() set
i .: s9 is finite set
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
(A,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 + (A,K) is Element of QC-symbols A
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
i .: s9 is finite Element of Fin (bound_QC-variables A)
f is Element of bound_QC-variables A
K is Element of CQC-WFF A
All (f,K) is Element of CQC-WFF A
r9 is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (f,K)),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,K)),r9,s9] is V18() triple set
[(All (f,K)),r9] is V18() set
{(All (f,K)),r9} is non empty finite set
{(All (f,K))} is non empty trivial finite V80(1) set
{{(All (f,K)),r9},{(All (f,K))}} is non empty finite V67() set
[[(All (f,K)),r9],s9] is V18() set
{[(All (f,K)),r9],s9} is non empty finite set
{[(All (f,K)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,K)),r9],s9},{[(All (f,K)),r9]}} is non empty finite V67() set
[[(All (f,K)),r9,s9],i] is V18() set
{[(All (f,K)),r9,s9],i} is non empty finite set
{[(All (f,K)),r9,s9]} is non empty trivial finite V80(1) set
{{[(All (f,K)),r9,s9],i},{[(All (f,K)),r9,s9]}} is non empty finite V67() set
i .: s9 is finite set
r9 ++ is Element of QC-symbols A
{.f.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
s9 \/ {.f.} is non empty finite Element of Fin (bound_QC-variables A)
x. r9 is Element of bound_QC-variables A
[4,r9] is V18() set
{4,r9} is non empty finite set
{{4,r9},{4}} is non empty finite V67() set
f .--> (x. r9) is Relation-like bound_QC-variables A -defined {f} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{f} is non empty trivial finite V80(1) set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued {(x. r9)} -valued Function-like constant total quasi_total finite Element of bool [:{f},{(x. r9)}:]
{(x. r9)} is non empty trivial finite V80(1) set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
bool [:{f},{(x. r9)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
i +* (f .--> (x. r9)) is Relation-like Function-like set
(i +* (f .--> (x. r9))) .: (s9 \/ {.f.}) is finite set
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
{f} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
s9 \/ {f} is non empty finite set
(i +* (f .--> (x. r9))) .: (s9 \/ {f}) is finite set
(i +* (f .--> (x. r9))) .: s9 is finite set
(i +* (f .--> (x. r9))) .: {f} is finite set
((i +* (f .--> (x. r9))) .: s9) \/ ((i +* (f .--> (x. r9))) .: {f}) is finite set
Im ((i +* (f .--> (x. r9))),f) is set
(i +* (f .--> (x. r9))) .: {f} is finite set
i .: s9 is finite Element of Fin (bound_QC-variables A)
{(x. r9)} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(i .: s9) \/ {(x. r9)} is non empty finite set
(A,f) is Element of QC-symbols A
(A,f) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in f is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in f ) } is set
min (A,f) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
((bound_QC-variables A)) .: ({}. (bound_QC-variables A)) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() set
K is Element of QC-symbols A
x. K is Element of bound_QC-variables A
[4,K] is V18() set
{4,K} is non empty finite set
{{4,K},{4}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
x. p is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,p] is V18() set
{4,p} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,p},{4}} is non empty finite V67() set
q is Element of CQC-WFF A
r is Element of CQC-WFF A
(A,r) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
h is finite Element of Fin (bound_QC-variables A)
[q,p,h,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,p,h] is V18() triple set
[q,p] is V18() set
{q,p} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,p},{q}} is non empty finite V67() set
[[q,p],h] is V18() set
{[q,p],h} is non empty finite set
{[q,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,p],h},{[q,p]}} is non empty finite V67() set
[[q,p,h],f] is V18() set
{[q,p,h],f} is non empty finite set
{[q,p,h]} is non empty trivial finite V80(1) set
{{[q,p,h],f},{[q,p,h]}} is non empty finite V67() set
f .: h is finite Element of Fin (bound_QC-variables A)
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
q is Element of QC-symbols A
x. q is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,q] is V18() set
{4,q} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,q},{4}} is non empty finite V67() set
r is Element of CQC-WFF A
f is Element of CQC-WFF A
(A,f) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
still_not-bound_in f is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
h .: (still_not-bound_in f) is set
u is finite Element of Fin (bound_QC-variables A)
[r,p,u,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[r,p,u] is V18() triple set
[r,p] is V18() set
{r,p} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,p},{r}} is non empty finite V67() set
[[r,p],u] is V18() set
{[r,p],u} is non empty finite set
{[r,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,p],u},{[r,p]}} is non empty finite V67() set
[[r,p,u],h] is V18() set
{[r,p,u],h} is non empty finite set
{[r,p,u]} is non empty trivial finite V80(1) set
{{[r,p,u],h},{[r,p,u]}} is non empty finite V67() set
K is Element of CQC-WFF A
f is Element of CQC-WFF A
K '&' f is Element of CQC-WFF A
r9 is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(K '&' f),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(K '&' f),r9,s9] is V18() triple set
[(K '&' f),r9] is V18() set
{(K '&' f),r9} is non empty finite set
{(K '&' f)} is non empty trivial finite V80(1) set
{{(K '&' f),r9},{(K '&' f)}} is non empty finite V67() set
[[(K '&' f),r9],s9] is V18() set
{[(K '&' f),r9],s9} is non empty finite set
{[(K '&' f),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(K '&' f),r9],s9},{[(K '&' f),r9]}} is non empty finite V67() set
[[(K '&' f),r9,s9],i] is V18() set
{[(K '&' f),r9,s9],i} is non empty finite set
{[(K '&' f),r9,s9]} is non empty trivial finite V80(1) set
{{[(K '&' f),r9,s9],i},{[(K '&' f),r9,s9]}} is non empty finite V67() set
i .: (still_not-bound_in f) is set
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
(A,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r9 + (A,K) is Element of QC-symbols A
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
(A,f) is Element of QC-symbols A
(A,f) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in f ) } is set
min (A,f) is Element of QC-symbols A
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
((bound_QC-variables A)) .: (still_not-bound_in f) is set
K is Element of QC-symbols A
x. K is Element of bound_QC-variables A
[4,K] is V18() set
{4,K} is non empty finite set
{{4,K},{4}} is non empty finite V67() set
f is Element of bound_QC-variables A
K is Element of CQC-WFF A
All (f,K) is Element of CQC-WFF A
r9 is Element of QC-symbols A
s9 is finite Element of Fin (bound_QC-variables A)
i is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (f,K)),r9,s9,i] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (f,K)),r9,s9] is V18() triple set
[(All (f,K)),r9] is V18() set
{(All (f,K)),r9} is non empty finite set
{(All (f,K))} is non empty trivial finite V80(1) set
{{(All (f,K)),r9},{(All (f,K))}} is non empty finite V67() set
[[(All (f,K)),r9],s9] is V18() set
{[(All (f,K)),r9],s9} is non empty finite set
{[(All (f,K)),r9]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (f,K)),r9],s9},{[(All (f,K)),r9]}} is non empty finite V67() set
[[(All (f,K)),r9,s9],i] is V18() set
{[(All (f,K)),r9,s9],i} is non empty finite set
{[(All (f,K)),r9,s9]} is non empty trivial finite V80(1) set
{{[(All (f,K)),r9,s9],i},{[(All (f,K)),r9,s9]}} is non empty finite V67() set
i .: (still_not-bound_in f) is set
r9 ++ is Element of QC-symbols A
{.f.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
s9 \/ {.f.} is non empty finite Element of Fin (bound_QC-variables A)
x. r9 is Element of bound_QC-variables A
[4,r9] is V18() set
{4,r9} is non empty finite set
{{4,r9},{4}} is non empty finite V67() set
f .--> (x. r9) is Relation-like bound_QC-variables A -defined {f} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{f} is non empty trivial finite V80(1) set
{f} --> (x. r9) is non empty Relation-like {f} -defined bound_QC-variables A -valued {(x. r9)} -valued Function-like constant total quasi_total finite Element of bool [:{f},{(x. r9)}:]
{(x. r9)} is non empty trivial finite V80(1) set
[:{f},{(x. r9)}:] is non empty Relation-like finite set
bool [:{f},{(x. r9)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
i +* (f .--> (x. r9)) is Relation-like Function-like set
(i +* (f .--> (x. r9))) .: (still_not-bound_in f) is set
u is Element of QC-symbols A
x. u is Element of bound_QC-variables A
[4,u] is V18() set
{4,u} is non empty finite set
{{4,u},{4}} is non empty finite V67() set
{(x. r9)} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(i .: (still_not-bound_in f)) \/ {(x. r9)} is non empty set
K is Element of CQC-WFF A
'not' K is Element of CQC-WFF A
f is Element of QC-symbols A
r9 is finite Element of Fin (bound_QC-variables A)
s9 is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' K),f,r9,s9] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' K),f,r9] is V18() triple set
[('not' K),f] is V18() set
{('not' K),f} is non empty finite set
{('not' K)} is non empty trivial finite V80(1) set
{{('not' K),f},{('not' K)}} is non empty finite V67() set
[[('not' K),f],r9] is V18() set
{[('not' K),f],r9} is non empty finite set
{[('not' K),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' K),f],r9},{[('not' K),f]}} is non empty finite V67() set
[[('not' K),f,r9],s9] is V18() set
{[('not' K),f,r9],s9} is non empty finite set
{[('not' K),f,r9]} is non empty trivial finite V80(1) set
{{[('not' K),f,r9],s9},{[('not' K),f,r9]}} is non empty finite V67() set
s9 .: (still_not-bound_in f) is set
i is Element of QC-symbols A
x. i is Element of bound_QC-variables A
[4,i] is V18() set
{4,i} is non empty finite set
{{4,i},{4}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
q is Element of QC-symbols A
x. q is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,q] is V18() set
{4,q} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,q},{4}} is non empty finite V67() set
r is Element of CQC-WFF A
still_not-bound_in r is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
f is Element of CQC-WFF A
(A,f) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
h is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
h .: (still_not-bound_in r) is set
u is finite Element of Fin (bound_QC-variables A)
[r,p,u,h] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[r,p,u] is V18() triple set
[r,p] is V18() set
{r,p} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,p},{r}} is non empty finite V67() set
[[r,p],u] is V18() set
{[r,p],u} is non empty finite set
{[r,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,p],u},{[r,p]}} is non empty finite V67() set
[[r,p,u],h] is V18() set
{[r,p,u],h} is non empty finite set
{[r,p,u]} is non empty trivial finite V80(1) set
{{[r,p,u],h},{[r,p,u]}} is non empty finite V67() set
still_not-bound_in f is Element of bool (bound_QC-variables A)
(still_not-bound_in f) \/ u is set
h .: ((still_not-bound_in f) \/ u) is set
h .: (still_not-bound_in f) is set
h .: u is finite Element of Fin (bound_QC-variables A)
(h .: (still_not-bound_in f)) \/ (h .: u) is set
A is non empty Relation-like QC-alphabet
QC-symbols 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 cup-closed diff-closed preBoolean set
bound_QC-variables A is non empty Element of bool (QC-variables A)
QC-variables A is non empty set
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
p is Element of QC-symbols A
x. p is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,p] is V18() set
{4,p} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,p},{4}} is non empty finite V67() set
q is Element of CQC-WFF A
still_not-bound_in q is Element of bool (bound_QC-variables A)
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
r is Element of CQC-WFF A
(A,r) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
f .: (still_not-bound_in q) is set
h is finite Element of Fin (bound_QC-variables A)
[q,p,h,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,p,h] is V18() triple set
[q,p] is V18() set
{q,p} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,p},{q}} is non empty finite V67() set
[[q,p],h] is V18() set
{[q,p],h} is non empty finite set
{[q,p]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,p],h},{[q,p]}} is non empty finite V67() set
[[q,p,h],f] is V18() set
{[q,p,h],f} is non empty finite set
{[q,p,h]} is non empty trivial finite V80(1) set
{{[q,p,h],f},{[q,p,h]}} is non empty finite V67() set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
(A,p) is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
still_not-bound_in (A,p) is Element of bool (bound_QC-variables A)
Fin (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
(A,p) is Element of bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
bool [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty cup-closed diff-closed preBoolean set
{}. (bound_QC-variables A) is empty Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional ext-real non positive non negative V35() V36() V37() V39() V40() V41() V43() V44() V45() V46() V56() V57() V58() V59() V60() V61() V62() finite finite-yielding V67() V74() V75() V76() V77() V78() V80( {} ) FinSequence-like FinSubsequence-like FinSequence-membered Function-yielding V93() Element of Fin (bound_QC-variables A)
[p,(A,p),({}. (bound_QC-variables A)),((bound_QC-variables A))] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty set
[p,(A,p),({}. (bound_QC-variables A))] is V18() triple set
[p,(A,p)] is V18() set
{p,(A,p)} is non empty finite set
{p} is non empty trivial finite V80(1) set
{{p,(A,p)},{p}} is non empty finite V67() set
[[p,(A,p)],({}. (bound_QC-variables A))] is V18() set
{[p,(A,p)],({}. (bound_QC-variables A))} is non empty finite set
{[p,(A,p)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[p,(A,p)],({}. (bound_QC-variables A))},{[p,(A,p)]}} is non empty finite V67() set
[[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))] is V18() set
{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))} is non empty finite set
{[p,(A,p),({}. (bound_QC-variables A))]} is non empty trivial finite V80(1) set
{{[p,(A,p),({}. (bound_QC-variables A))],((bound_QC-variables A))},{[p,(A,p),({}. (bound_QC-variables A))]}} is non empty finite V67() set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty Relation-like set
bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):] is non empty cup-closed diff-closed preBoolean set
q is Element of CQC-WFF A
(A,(A),q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
still_not-bound_in q is Element of bool (bound_QC-variables A)
'not' q is Element of CQC-WFF A
(A,(A),('not' q)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
r is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
still_not-bound_in ('not' q) is Element of bool (bound_QC-variables A)
f is Element of QC-symbols A
h is finite Element of Fin (bound_QC-variables A)
u is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[('not' q),f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[('not' q),f,h] is V18() triple set
[('not' q),f] is V18() set
{('not' q),f} is non empty finite set
{('not' q)} is non empty trivial finite V80(1) set
{{('not' q),f},{('not' q)}} is non empty finite V67() set
[[('not' q),f],h] is V18() set
{[('not' q),f],h} is non empty finite set
{[('not' q),f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[('not' q),f],h},{[('not' q),f]}} is non empty finite V67() set
[[('not' q),f,h],u] is V18() set
{[('not' q),f,h],u} is non empty finite set
{[('not' q),f,h]} is non empty trivial finite V80(1) set
{{[('not' q),f,h],u},{[('not' q),f,h]}} is non empty finite V67() set
u .: (still_not-bound_in ('not' q)) is set
[f,u] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{f,u} is non empty finite set
{f} is non empty trivial finite V80(1) set
{{f,u},{f}} is non empty finite V67() set
(A,(A),('not' q)) . [f,u] is Element of CQC-WFF A
still_not-bound_in ((A,(A),('not' q)) . [f,u]) is Element of bool (bound_QC-variables A)
[q,f,h,u] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,f,h] is V18() triple set
[q,f] is V18() set
{q,f} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,f},{q}} is non empty finite V67() set
[[q,f],h] is V18() set
{[q,f],h} is non empty finite set
{[q,f]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,f],h},{[q,f]}} is non empty finite V67() set
[[q,f,h],u] is V18() set
{[q,f,h],u} is non empty finite set
{[q,f,h]} is non empty trivial finite V80(1) set
{{[q,f,h],u},{[q,f,h]}} is non empty finite V67() set
r . [f,u] is Element of CQC-WFF A
f is Element of CQC-WFF A
still_not-bound_in f is Element of bool (bound_QC-variables A)
'not' f is Element of CQC-WFF A
still_not-bound_in ('not' f) is Element of bool (bound_QC-variables A)
(A,[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],r) . [f,u] is Element of CQC-WFF A
q is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
QC-pred_symbols A is non empty set
q -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (QC-pred_symbols A) is non empty cup-closed diff-closed preBoolean set
f is Element of q -ary_QC-pred_symbols A
r is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like finite V80(q) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
f ! r is Element of CQC-WFF A
still_not-bound_in (f ! r) is Element of bool (bound_QC-variables A)
(A,(A),(f ! r)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Element of QC-symbols A
u is finite Element of Fin (bound_QC-variables A)
K is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(f ! r),h,u,K] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(f ! r),h,u] is V18() triple set
[(f ! r),h] is V18() set
{(f ! r),h} is non empty finite set
{(f ! r)} is non empty trivial finite V80(1) set
{{(f ! r),h},{(f ! r)}} is non empty finite V67() set
[[(f ! r),h],u] is V18() set
{[(f ! r),h],u} is non empty finite set
{[(f ! r),h]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(f ! r),h],u},{[(f ! r),h]}} is non empty finite V67() set
[[(f ! r),h,u],K] is V18() set
{[(f ! r),h,u],K} is non empty finite set
{[(f ! r),h,u]} is non empty trivial finite V80(1) set
{{[(f ! r),h,u],K},{[(f ! r),h,u]}} is non empty finite V67() set
K .: (still_not-bound_in (f ! r)) is set
[h,K] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{h,K} is non empty finite set
{h} is non empty trivial finite V80(1) set
{{h,K},{h}} is non empty finite V67() set
(A,(A),(f ! r)) . [h,K] is Element of CQC-WFF A
still_not-bound_in ((A,(A),(f ! r)) . [h,K]) is Element of bool (bound_QC-variables A)
(A,q,r,K) is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued bound_QC-variables A -valued Function-like finite V80(q) FinSequence-like FinSubsequence-like FinSequence of QC-variables A
len r is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
{ (r . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len r & r . b₁ in bound_QC-variables A ) } is set
K .: { (r . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len r & r . b₁ in bound_QC-variables A ) } is set
len (A,q,r,K) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
{ ((A,q,r,K) . b₁) where b₁ is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT : ( 1 <= b₁ & b₁ <= len (A,q,r,K) & (A,q,r,K) . b₁ in bound_QC-variables A ) } is set
r9 is set
proj1 K is set
s9 is set
K . s9 is set
i is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
r . i is set
dom r is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V80(q) Element of bool NAT
K . (r . i) is set
(A,q,r,K) . i is set
r9 is set
s9 is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
(A,q,r,K) . s9 is set
dom r is V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V80(q) Element of bool NAT
r . s9 is set
K . (r . s9) is set
proj1 K is set
still_not-bound_in r is Element of bool (bound_QC-variables A)
K .: (still_not-bound_in r) is set
variables_in (r,(bound_QC-variables A)) is Element of bool (bound_QC-variables A)
K .: (variables_in (r,(bound_QC-variables A))) is set
variables_in ((A,q,r,K),(bound_QC-variables A)) is Element of bool (bound_QC-variables A)
still_not-bound_in (A,q,r,K) is Element of bool (bound_QC-variables A)
f ! (A,q,r,K) is Element of CQC-WFF A
still_not-bound_in (f ! (A,q,r,K)) is Element of bool (bound_QC-variables A)
(A,q,f,r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,q,f,r) . (h,K) is Element of CQC-WFF A
[h,K] is V18() set
(A,q,f,r) . [h,K] is set
q is Element of CQC-WFF A
still_not-bound_in q is Element of bool (bound_QC-variables A)
(A,(A),q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
r is Element of bound_QC-variables A
All (r,q) is Element of CQC-WFF A
still_not-bound_in (All (r,q)) is Element of bool (bound_QC-variables A)
(A,(A),(All (r,q))) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
h is Element of QC-symbols A
u is finite Element of Fin (bound_QC-variables A)
K is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(All (r,q)),h,u,K] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(All (r,q)),h,u] is V18() triple set
[(All (r,q)),h] is V18() set
{(All (r,q)),h} is non empty finite set
{(All (r,q))} is non empty trivial finite V80(1) set
{{(All (r,q)),h},{(All (r,q))}} is non empty finite V67() set
[[(All (r,q)),h],u] is V18() set
{[(All (r,q)),h],u} is non empty finite set
{[(All (r,q)),h]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(All (r,q)),h],u},{[(All (r,q)),h]}} is non empty finite V67() set
[[(All (r,q)),h,u],K] is V18() set
{[(All (r,q)),h,u],K} is non empty finite set
{[(All (r,q)),h,u]} is non empty trivial finite V80(1) set
{{[(All (r,q)),h,u],K},{[(All (r,q)),h,u]}} is non empty finite V67() set
K .: (still_not-bound_in (All (r,q))) is set
[h,K] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{h,K} is non empty finite set
{h} is non empty trivial finite V80(1) set
{{h,K},{h}} is non empty finite V67() set
(A,(A),(All (r,q))) . [h,K] is Element of CQC-WFF A
still_not-bound_in ((A,(A),(All (r,q))) . [h,K]) is Element of bool (bound_QC-variables A)
h ++ is Element of QC-symbols A
{.r.} is non empty trivial finite V80(1) Element of Fin (bound_QC-variables A)
u \/ {.r.} is non empty finite Element of Fin (bound_QC-variables A)
x. h is Element of bound_QC-variables A
4 is non empty ext-real positive non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V72() V73() V74() V75() V76() V78() Element of NAT
[4,h] is V18() set
{4,h} is non empty finite set
{4} is non empty trivial V56() V57() V58() V59() V60() V61() finite V67() V72() V73() V74() V75() V76() V80(1) set
{{4,h},{4}} is non empty finite V67() set
r .--> (x. h) is Relation-like bound_QC-variables A -defined {r} -defined bound_QC-variables A -valued Function-like one-to-one finite set
{r} is non empty trivial finite V80(1) set
{r} --> (x. h) is non empty Relation-like {r} -defined bound_QC-variables A -valued {(x. h)} -valued Function-like constant total quasi_total finite Element of bool [:{r},{(x. h)}:]
{(x. h)} is non empty trivial finite V80(1) set
[:{r},{(x. h)}:] is non empty Relation-like finite set
bool [:{r},{(x. h)}:] is non empty cup-closed diff-closed preBoolean finite V67() set
K +* (r .--> (x. h)) is Relation-like Function-like set
[q,(h ++),(u \/ {.r.}),(K +* (r .--> (x. h)))] is V18() triple quadruple set
[q,(h ++),(u \/ {.r.})] is V18() triple set
[q,(h ++)] is V18() set
{q,(h ++)} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,(h ++)},{q}} is non empty finite V67() set
[[q,(h ++)],(u \/ {.r.})] is V18() set
{[q,(h ++)],(u \/ {.r.})} is non empty finite set
{[q,(h ++)]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,(h ++)],(u \/ {.r.})},{[q,(h ++)]}} is non empty finite V67() set
[[q,(h ++),(u \/ {.r.})],(K +* (r .--> (x. h)))] is V18() set
{[q,(h ++),(u \/ {.r.})],(K +* (r .--> (x. h)))} is non empty finite set
{[q,(h ++),(u \/ {.r.})]} is non empty trivial finite V80(1) set
{{[q,(h ++),(u \/ {.r.})],(K +* (r .--> (x. h)))},{[q,(h ++),(u \/ {.r.})]}} is non empty finite V67() set
[:(bound_QC-variables A),(bound_QC-variables A):] is non empty Relation-like set
bool [:(bound_QC-variables A),(bound_QC-variables A):] is non empty cup-closed diff-closed preBoolean set
f is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
f . ((h ++),f) is Element of CQC-WFF A
[(h ++),f] is V18() set
{(h ++),f} is non empty finite set
{(h ++)} is non empty trivial finite V80(1) set
{{(h ++),f},{(h ++)}} is non empty finite V67() set
f . [(h ++),f] is set
(A,f,r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,r) . (h,K) is Element of CQC-WFF A
[h,K] is V18() set
(A,f,r) . [h,K] is set
r9 is Element of CQC-WFF A
All ((x. h),r9) is Element of CQC-WFF A
{r} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(still_not-bound_in q) \ {r} is Element of bool (bound_QC-variables A)
K .: ((still_not-bound_in q) \ {r}) is set
f .: ((still_not-bound_in q) \ {r}) is set
f .: (still_not-bound_in q) is set
{(x. h)} is non empty trivial finite V80(1) Element of bool (bound_QC-variables A)
(f .: (still_not-bound_in q)) \ {(x. h)} is Element of bool (f .: (still_not-bound_in q))
bool (f .: (still_not-bound_in q)) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in r9 is Element of bool (bound_QC-variables A)
(still_not-bound_in r9) \ {(x. h)} is Element of bool (bound_QC-variables A)
still_not-bound_in (All ((x. h),r9)) is Element of bool (bound_QC-variables A)
q is Element of CQC-WFF A
still_not-bound_in q is Element of bool (bound_QC-variables A)
(A,(A),q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
r is Element of CQC-WFF A
still_not-bound_in r is Element of bool (bound_QC-variables A)
(A,(A),r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
q '&' r is Element of CQC-WFF A
still_not-bound_in (q '&' r) is Element of bool (bound_QC-variables A)
(A,(A),(q '&' r)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
u is Element of QC-symbols A
K is finite Element of Fin (bound_QC-variables A)
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(q '&' r),u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(q '&' r),u,K] is V18() triple set
[(q '&' r),u] is V18() set
{(q '&' r),u} is non empty finite set
{(q '&' r)} is non empty trivial finite V80(1) set
{{(q '&' r),u},{(q '&' r)}} is non empty finite V67() set
[[(q '&' r),u],K] is V18() set
{[(q '&' r),u],K} is non empty finite set
{[(q '&' r),u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(q '&' r),u],K},{[(q '&' r),u]}} is non empty finite V67() set
[[(q '&' r),u,K],f] is V18() set
{[(q '&' r),u,K],f} is non empty finite set
{[(q '&' r),u,K]} is non empty trivial finite V80(1) set
{{[(q '&' r),u,K],f},{[(q '&' r),u,K]}} is non empty finite V67() set
f .: (still_not-bound_in (q '&' r)) is set
[u,f] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{u,f} is non empty finite set
{u} is non empty trivial finite V80(1) set
{{u,f},{u}} is non empty finite V67() set
(A,(A),(q '&' r)) . [u,f] is Element of CQC-WFF A
still_not-bound_in ((A,(A),(q '&' r)) . [u,f]) is Element of bool (bound_QC-variables A)
f is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
f . (u,f) is Element of CQC-WFF A
[u,f] is V18() set
f . [u,f] is set
h is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
(A,q) is ext-real non negative V35() V36() V37() V41() V42() V53() V54() V55() V56() V57() V58() V59() V60() V61() finite V74() V75() V76() V78() Element of NAT
u + (A,q) is Element of QC-symbols A
h . ((u + (A,q)),f) is Element of CQC-WFF A
[(u + (A,q)),f] is V18() set
{(u + (A,q)),f} is non empty finite set
{(u + (A,q))} is non empty trivial finite V80(1) set
{{(u + (A,q)),f},{(u + (A,q))}} is non empty finite V67() set
h . [(u + (A,q)),f] is set
(A,f,h,(A,q)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
(A,f,h,(A,q)) . (u,f) is Element of CQC-WFF A
(A,f,h,(A,q)) . [u,f] is set
r9 is Element of CQC-WFF A
s9 is Element of CQC-WFF A
r9 '&' s9 is Element of CQC-WFF A
[q,u,K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[q,u,K] is V18() triple set
[q,u] is V18() set
{q,u} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,u},{q}} is non empty finite V67() set
[[q,u],K] is V18() set
{[q,u],K} is non empty finite set
{[q,u]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[q,u],K},{[q,u]}} is non empty finite V67() set
[[q,u,K],f] is V18() set
{[q,u,K],f} is non empty finite set
{[q,u,K]} is non empty trivial finite V80(1) set
{{[q,u,K],f},{[q,u,K]}} is non empty finite V67() set
f .: (still_not-bound_in q) is set
still_not-bound_in r9 is Element of bool (bound_QC-variables A)
[r,(u + (A,q)),K,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[r,(u + (A,q)),K] is V18() triple set
[r,(u + (A,q))] is V18() set
{r,(u + (A,q))} is non empty finite set
{r} is non empty trivial finite V80(1) set
{{r,(u + (A,q))},{r}} is non empty finite V67() set
[[r,(u + (A,q))],K] is V18() set
{[r,(u + (A,q))],K} is non empty finite set
{[r,(u + (A,q))]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[r,(u + (A,q))],K},{[r,(u + (A,q))]}} is non empty finite V67() set
[[r,(u + (A,q)),K],f] is V18() set
{[r,(u + (A,q)),K],f} is non empty finite set
{[r,(u + (A,q)),K]} is non empty trivial finite V80(1) set
{{[r,(u + (A,q)),K],f},{[r,(u + (A,q)),K]}} is non empty finite V67() set
f .: (still_not-bound_in r) is set
still_not-bound_in s9 is Element of bool (bound_QC-variables A)
(still_not-bound_in q) \/ (still_not-bound_in r) is Element of bool (bound_QC-variables A)
f .: ((still_not-bound_in q) \/ (still_not-bound_in r)) is set
(still_not-bound_in r9) \/ (still_not-bound_in s9) is Element of bool (bound_QC-variables A)
still_not-bound_in (r9 '&' s9) is Element of bool (bound_QC-variables A)
VERUM A is Element of CQC-WFF A
(A,(A),(VERUM A)) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] --> (VERUM A) is non empty Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like constant total quasi_total Element of bool [:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A):]
{(VERUM A)} is non empty trivial finite V80(1) set
[:[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],{(VERUM A)}:] is non empty Relation-like set
still_not-bound_in (VERUM A) is Element of bool (bound_QC-variables A)
q is Element of QC-symbols A
r is finite Element of Fin (bound_QC-variables A)
f is Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like total quasi_total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
[(VERUM A),q,r,f] is V18() triple quadruple Element of [:(CQC-WFF A),(QC-symbols A),(Fin (bound_QC-variables A)),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
[(VERUM A),q,r] is V18() triple set
[(VERUM A),q] is V18() set
{(VERUM A),q} is non empty finite set
{{(VERUM A),q},{(VERUM A)}} is non empty finite V67() set
[[(VERUM A),q],r] is V18() set
{[(VERUM A),q],r} is non empty finite set
{[(VERUM A),q]} is non empty trivial Relation-like Function-like constant finite V80(1) set
{{[(VERUM A),q],r},{[(VERUM A),q]}} is non empty finite V67() set
[[(VERUM A),q,r],f] is V18() set
{[(VERUM A),q,r],f} is non empty finite set
{[(VERUM A),q,r]} is non empty trivial finite V80(1) set
{{[(VERUM A),q,r],f},{[(VERUM A),q,r]}} is non empty finite V67() set
f .: (still_not-bound_in (VERUM A)) is set
[q,f] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{q,f} is non empty finite set
{q} is non empty trivial finite V80(1) set
{{q,f},{q}} is non empty finite V67() set
(A,(A),(VERUM A)) . [q,f] is Element of CQC-WFF A
still_not-bound_in ((A,(A),(VERUM A)) . [q,f]) is Element of bool (bound_QC-variables A)
((bound_QC-variables A)) .: (still_not-bound_in p) is set
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
QC-symbols A is non empty set
(A,p) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in p 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
(A,p) is Element of CQC-WFF A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A
(A,(A,p)) is Element of QC-symbols A
(A,(A,p)) is non empty Element of bool (QC-symbols A)
still_not-bound_in (A,p) is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in (A,p) ) } is set
min (A,(A,p)) is Element of QC-symbols A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
r is Element of CQC-WFF A
(A,r) is Element of CQC-WFF A
(A,r) is Element of QC-symbols A
QC-symbols A is non empty set
(A,r) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in r 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in r ) } is set
min (A,r) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,r,(A,r),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,r),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,r),((bound_QC-variables A))} is non empty finite set
{(A,r)} is non empty trivial finite V80(1) set
{{(A,r),((bound_QC-variables A))},{(A,r)}} is non empty finite V67() set
(A,(A),r) . [(A,r),((bound_QC-variables A))] is Element of CQC-WFF A
r is Element of CQC-WFF A
(A,r) is Element of CQC-WFF A
(A,r) is Element of QC-symbols A
QC-symbols A is non empty set
(A,r) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in r 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in r ) } is set
min (A,r) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,r,(A,r),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,r),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,r),((bound_QC-variables A))} is non empty finite set
{(A,r)} is non empty trivial finite V80(1) set
{{(A,r),((bound_QC-variables A))},{(A,r)}} is non empty finite V67() set
(A,(A),r) . [(A,r),((bound_QC-variables A))] is Element of CQC-WFF A
f is Element of CQC-WFF A
(A,f) is Element of CQC-WFF A
(A,f) is Element of QC-symbols A
(A,f) is non empty Element of bool (QC-symbols A)
still_not-bound_in f is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in f ) } is set
min (A,f) is Element of QC-symbols A
(A,f,(A,f),((bound_QC-variables A))) is Element of CQC-WFF A
(A,(A),f) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,f),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,f),((bound_QC-variables A))} is non empty finite set
{(A,f)} is non empty trivial finite V80(1) set
{{(A,f),((bound_QC-variables A))},{(A,f)}} is non empty finite V67() set
(A,(A),f) . [(A,f),((bound_QC-variables A))] is Element of CQC-WFF A
A is non empty Relation-like QC-alphabet
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 cup-closed diff-closed preBoolean set
p is Element of CQC-WFF A
q is Element of CQC-WFF A
r is Element of CQC-WFF A
(A,q) is Element of CQC-WFF A
(A,q) is Element of QC-symbols A
QC-symbols A is non empty set
(A,q) is non empty Element of bool (QC-symbols A)
bool (QC-symbols A) is non empty cup-closed diff-closed preBoolean set
still_not-bound_in q 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
bool (QC-variables A) is non empty cup-closed diff-closed preBoolean set
bool (bound_QC-variables A) is non empty cup-closed diff-closed preBoolean set
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in q ) } is set
min (A,q) is Element of QC-symbols A
((bound_QC-variables A)) is non empty Relation-like bound_QC-variables A -defined bound_QC-variables A -valued Function-like one-to-one total Element of Funcs ((bound_QC-variables A),(bound_QC-variables A))
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional set
(A,q,(A,q),((bound_QC-variables A))) is Element of CQC-WFF A
Funcs ((bound_QC-variables A),(bound_QC-variables A)) is non empty functional FUNCTION_DOMAIN of bound_QC-variables A, bound_QC-variables A
[:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] is non empty Relation-like set
(A) is non empty Relation-like CQC-WFF A -defined Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) -valued Function-like total quasi_total Function-yielding V93() Element of bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):]
Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A)) is non empty functional FUNCTION_DOMAIN of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):], CQC-WFF A
[:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty Relation-like set
bool [:(CQC-WFF A),(Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))):] is non empty cup-closed diff-closed preBoolean set
(A,(A),q) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,q),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,q),((bound_QC-variables A))} is non empty finite set
{(A,q)} is non empty trivial finite V80(1) set
{{(A,q),((bound_QC-variables A))},{(A,q)}} is non empty finite V67() set
(A,(A),q) . [(A,q),((bound_QC-variables A))] is Element of CQC-WFF A
(A,r) is Element of CQC-WFF A
(A,r) is Element of QC-symbols A
(A,r) is non empty Element of bool (QC-symbols A)
still_not-bound_in r is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in r ) } is set
min (A,r) is Element of QC-symbols A
(A,r,(A,r),((bound_QC-variables A))) is Element of CQC-WFF A
(A,(A),r) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,r),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,r),((bound_QC-variables A))} is non empty finite set
{(A,r)} is non empty trivial finite V80(1) set
{{(A,r),((bound_QC-variables A))},{(A,r)}} is non empty finite V67() set
(A,(A),r) . [(A,r),((bound_QC-variables A))] is Element of CQC-WFF A
(A,p) is Element of CQC-WFF A
(A,p) is Element of QC-symbols A
(A,p) is non empty Element of bool (QC-symbols A)
still_not-bound_in p is Element of bool (bound_QC-variables A)
{ b₁ where b₁ is Element of QC-symbols A : for b₂ being Element of QC-symbols A holds
( not b₁ <= b₂ or not x. b₂ in still_not-bound_in p ) } is set
min (A,p) is Element of QC-symbols A
(A,p,(A,p),((bound_QC-variables A))) is Element of CQC-WFF A
(A,(A),p) is Relation-like [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):] -defined CQC-WFF A -valued Function-like total quasi_total Element of Funcs ([:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):],(CQC-WFF A))
[(A,p),((bound_QC-variables A))] is V18() Element of [:(QC-symbols A),(Funcs ((bound_QC-variables A),(bound_QC-variables A))):]
{(A,p),((bound_QC-variables A))} is non empty finite set
{(A,p)} is non empty trivial finite V80(1) set
{{(A,p),((bound_QC-variables A))},{(A,p)}} is non empty finite V67() set
(A,(A),p) . [(A,p),((bound_QC-variables A))] is Element of CQC-WFF A