:: SUBLEMMA semantic presentation

REAL is V45() V46() V47() V51() V63() V64() V66() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V45() V46() V47() V48() V49() V50() V51() V52() V61() V63() cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
COMPLEX is V45() V51() set
RAT is V45() V46() V47() V48() V51() set
INT is V45() V46() V47() V48() V49() V51() set
omega is non empty epsilon-transitive epsilon-connected ordinal V45() V46() V47() V48() V49() V50() V51() V52() V61() V63() cardinal limit_cardinal set
bool omega is non empty V52() set
bool NAT is non empty V52() set
[:COMPLEX,COMPLEX:] is Relation-like set
bool [:COMPLEX,COMPLEX:] is non empty set
[:COMPLEX,REAL:] is Relation-like set
bool [:COMPLEX,REAL:] is non empty set
K370() is set
{} is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional ext-real non positive non negative epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V45() V46() V47() V48() V49() V50() V51() V52() V63() V64() V65() V66() cardinal {} -element Function-yielding V82() set
the empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional ext-real non positive non negative epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V45() V46() V47() V48() V49() V50() V51() V52() V63() V64() V65() V66() cardinal {} -element Function-yielding V82() set is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional ext-real non positive non negative epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V45() V46() V47() V48() V49() V50() V51() V52() V63() V64() V65() V66() cardinal {} -element Function-yielding V82() set
1 is non empty ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V61() V62() V63() V64() V65() cardinal Element of NAT
TRUE is Element of K370()
0 is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional ext-real non positive non negative epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V51() V52() V63() V64() V65() V66() cardinal {} -element Function-yielding V82() Element of NAT
[0,0] is V1() set
{0,0} is non empty functional V45() V46() V47() V48() V49() V50() V61() V63() set
{0} is non empty trivial functional V45() V46() V47() V48() V49() V50() V61() V63() 1 -element set
{{0,0},{0}} is non empty set
<*[0,0]*> is Relation-like Function-like set
[:NAT,NAT:] is non empty Relation-like V52() set
[:NAT,[:NAT,NAT:]:] is non empty Relation-like V52() set
bool [:NAT,[:NAT,NAT:]:] is non empty V52() set
[0,0] is V1() Element of [:NAT,NAT:]
<*[0,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like FinSequence-like FinSequence of [:NAT,NAT:]
[1,0] is V1() Element of [:NAT,NAT:]
{1,0} is non empty V45() V46() V47() V48() V49() V50() V61() V63() set
{1} is non empty trivial V45() V46() V47() V48() V49() V50() V61() V63() 1 -element set
{{1,0},{1}} is non empty set
<*[1,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like FinSequence-like FinSequence of [:NAT,NAT:]
2 is non empty ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V61() V62() V63() V64() V65() cardinal Element of NAT
[2,0] is V1() Element of [:NAT,NAT:]
{2,0} is non empty V45() V46() V47() V48() V49() V50() V61() V63() set
{2} is non empty trivial V45() V46() V47() V48() V49() V50() V61() V63() 1 -element set
{{2,0},{2}} is non empty set
<*[2,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like FinSequence-like FinSequence of [:NAT,NAT:]
3 is non empty ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V61() V62() V63() V64() V65() cardinal Element of NAT
[3,0] is V1() Element of [:NAT,NAT:]
{3,0} is non empty V45() V46() V47() V48() V49() V50() V61() V63() set
{3} is non empty trivial V45() V46() V47() V48() V49() V50() V61() V63() 1 -element set
{{3,0},{3}} is non empty set
<*[3,0]*> is Relation-like NAT -defined [:NAT,NAT:] -valued Function-like FinSequence-like FinSequence of [:NAT,NAT:]
xSQ is Relation-like Function-like set
proj1 xSQ is set
J is Relation-like Function-like set
proj1 J is set
S is Relation-like Function-like set
proj1 S is set
Al is Relation-like Function-like set
A is Relation-like Function-like set
Al +* A is Relation-like Function-like set
(Al +* A) +* J is Relation-like Function-like set
Al +* xSQ is Relation-like Function-like set
A +* S is Relation-like Function-like set
(Al +* xSQ) +* (A +* S) is Relation-like Function-like set
((Al +* xSQ) +* (A +* S)) +* J is Relation-like Function-like set
proj1 (Al +* xSQ) is set
proj1 Al is set
(proj1 Al) \/ (proj1 xSQ) is set
proj1 (A +* S) is set
proj1 A is set
(proj1 A) \/ (proj1 S) is set
proj1 ((Al +* xSQ) +* (A +* S)) is set
((proj1 Al) \/ (proj1 xSQ)) \/ ((proj1 A) \/ (proj1 S)) is set
proj1 (((Al +* xSQ) +* (A +* S)) +* J) is set
(((proj1 Al) \/ (proj1 xSQ)) \/ ((proj1 A) \/ (proj1 S))) \/ (proj1 J) is set
((proj1 A) \/ (proj1 S)) \/ (proj1 J) is set
((proj1 Al) \/ (proj1 xSQ)) \/ (((proj1 A) \/ (proj1 S)) \/ (proj1 J)) is set
(proj1 S) \/ (proj1 J) is set
(proj1 A) \/ ((proj1 S) \/ (proj1 J)) is set
((proj1 Al) \/ (proj1 xSQ)) \/ ((proj1 A) \/ ((proj1 S) \/ (proj1 J))) is set
(proj1 A) \/ (proj1 J) is set
((proj1 Al) \/ (proj1 xSQ)) \/ ((proj1 A) \/ (proj1 J)) is set
((proj1 Al) \/ (proj1 xSQ)) \/ (proj1 J) is set
(((proj1 Al) \/ (proj1 xSQ)) \/ (proj1 J)) \/ (proj1 A) is set
(proj1 xSQ) \/ (proj1 J) is set
(proj1 Al) \/ ((proj1 xSQ) \/ (proj1 J)) is set
((proj1 Al) \/ ((proj1 xSQ) \/ (proj1 J))) \/ (proj1 A) is set
(proj1 Al) \/ (proj1 J) is set
((proj1 Al) \/ (proj1 J)) \/ (proj1 A) is set
proj1 ((Al +* A) +* J) is set
xSQ is set
((Al +* A) +* J) . xSQ is set
(((Al +* xSQ) +* (A +* S)) +* J) . xSQ is set
((Al +* xSQ) +* (A +* S)) . xSQ is set
(Al +* A) . xSQ is set
(A +* S) . xSQ is set
A . xSQ is set
(Al +* xSQ) . xSQ is set
Al . xSQ is set
J . xSQ is set
proj1 (Al +* A) is set
(proj1 Al) \/ (proj1 A) is set
((proj1 Al) \/ (proj1 A)) \/ (proj1 J) is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of bound_QC-variables Al
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Relation-like Function-like set
proj1 J is set
(proj1 J) \ {A} is Element of bool (proj1 J)
bool (proj1 J) is non empty set
J | ((proj1 J) \ {A}) is Relation-like Function-like set
J . A is set
A .--> (J . A) is trivial Relation-like bound_QC-variables Al -defined {A} -defined Function-like one-to-one constant set
{A} is non empty trivial 1 -element set
{A} --> (J . A) is non empty Relation-like {A} -defined {(J . A)} -valued Function-like constant total quasi_total Element of bool [:{A},{(J . A)}:]
{(J . A)} is non empty trivial 1 -element set
[:{A},{(J . A)}:] is non empty Relation-like set
bool [:{A},{(J . A)}:] is non empty set
(J | ((proj1 J) \ {A})) +* (A .--> (J . A)) is Relation-like Function-like set
((proj1 J) \ {A}) \/ {A} is non empty set
(proj1 J) \/ {A} is non empty set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
J is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
J +* xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like set
Funcs ((bound_QC-variables Al),A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J +* xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom (J +* xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom xSQ is Element of bool (bound_QC-variables Al)
(bound_QC-variables Al) \/ (dom xSQ) is non empty set
S is Relation-like Function-like set
proj1 S is set
proj2 S is set
rng (J +* xSQ) is Element of bool A
bool A is non empty set
rng J is Element of bool A
rng xSQ is Element of bool A
(rng J) \/ (rng xSQ) is Element of bool A
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
A `1 is set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of QC-Sub-WFF Al : b<sub>1</sub> `1 is Element of CQC-WFF Al } is set
J is Element of QC-Sub-WFF Al
J `1 is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
A is Element of CQC-Sub-WFF Al
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ (A `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(@ (A `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
VERUM Al is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
CQC_Sub A is Element of CQC-WFF Al
[:(QC-Sub-WFF Al),(QC-WFF Al):] is non empty Relation-like set
bool [:(QC-Sub-WFF Al),(QC-WFF Al):] is non empty set
J is Relation-like QC-Sub-WFF Al -defined QC-WFF Al -valued Function-like quasi_total Element of bool [:(QC-Sub-WFF Al),(QC-WFF Al):]
J . A is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
QC-pred_symbols Al is non empty set
K367(J) is set
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
xSQ is Element of CQC-Sub-WFF Al
CQC_Sub xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
S is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,xSQ,A,S) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
xSQ `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (xSQ `2)) * S is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,S,(Al,xSQ,A,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
VERUM Al is Element of CQC-WFF Al
(Al,xSQ) is Element of CQC-WFF Al
xSQ is Relation-like Function-like Element of vSUB Al
[(VERUM Al),xSQ] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(VERUM Al),xSQ} is non empty set
{(VERUM Al)} is non empty trivial 1 -element set
{{(VERUM Al),xSQ},{(VERUM Al)}} is non empty set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
J is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
dom xSQ is V45() V46() V47() V48() V49() V50() V63() A -element Element of bool NAT
xSQ . J is set
rng xSQ is Element of bool (QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
CQC_Sub A is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
(Al,A) is Element of CQC-WFF Al
the_pred_symbol_of (Al,A) is Element of QC-pred_symbols Al
QC-pred_symbols Al is non empty set
Sub_the_arguments_of A is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
QC-variables Al is non empty set
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
CQC_Subst ((Sub_the_arguments_of A),(A `2)) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
(the_pred_symbol_of (Al,A)) ! (CQC_Subst ((Sub_the_arguments_of A),(A `2))) is Element of QC-WFF Al
[:(QC-Sub-WFF Al),(QC-WFF Al):] is non empty Relation-like set
bool [:(QC-Sub-WFF Al),(QC-WFF Al):] is non empty set
VERUM Al is Element of CQC-WFF Al
J is Relation-like QC-Sub-WFF Al -defined QC-WFF Al -valued Function-like quasi_total Element of bool [:(QC-Sub-WFF Al),(QC-WFF Al):]
J . A is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is Element of A -ary_QC-pred_symbols Al
xSQ is Element of A -ary_QC-pred_symbols Al
S is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
v is Relation-like Function-like Element of vSUB Al
Sub_P (J,S,v) is Sub_atomic Element of QC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
Sub_the_arguments_of (Sub_P (J,S,v)) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
S1 is Relation-like Function-like Element of vSUB Al
Sub_P (xSQ,xSQ,S1) is Sub_atomic Element of QC-Sub-WFF Al
Sub_the_arguments_of (Sub_P (xSQ,xSQ,S1)) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
z is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
z -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
p is Relation-like NAT -defined QC-variables Al -valued Function-like z -element FinSequence-like FinSequence of QC-variables Al
q is Element of z -ary_QC-pred_symbols Al
a is Relation-like Function-like Element of vSUB Al
Sub_P (q,p,a) is Sub_atomic Element of QC-Sub-WFF Al
J ! S is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
<*J*> is Relation-like NAT -defined A -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of A -ary_QC-pred_symbols Al
<*J*> ^ S is Relation-like Function-like FinSequence-like set
q ! p is Element of QC-WFF Al
<*q*> is Relation-like NAT -defined z -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of z -ary_QC-pred_symbols Al
<*q*> ^ p is Relation-like Function-like FinSequence-like set
[(J ! S),v] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(J ! S),v} is non empty set
{(J ! S)} is non empty trivial 1 -element set
{{(J ! S),v},{(J ! S)}} is non empty set
[(q ! p),a] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(q ! p),a} is non empty set
{(q ! p)} is non empty trivial 1 -element set
{{(q ! p),a},{(q ! p)}} is non empty set
(<*q*> ^ p) . 1 is set
(<*J*> ^ S) . 1 is set
x is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
x -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
x is Relation-like NAT -defined QC-variables Al -valued Function-like x -element FinSequence-like FinSequence of QC-variables Al
b is Element of x -ary_QC-pred_symbols Al
e2 is Relation-like Function-like Element of vSUB Al
Sub_P (b,x,e2) is Sub_atomic Element of QC-Sub-WFF Al
xSQ ! xSQ is Element of CQC-WFF Al
<*xSQ*> is Relation-like NAT -defined A -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of A -ary_QC-pred_symbols Al
<*xSQ*> ^ xSQ is Relation-like Function-like FinSequence-like set
b ! x is Element of QC-WFF Al
<*b*> is Relation-like NAT -defined x -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of x -ary_QC-pred_symbols Al
<*b*> ^ x is Relation-like Function-like FinSequence-like set
[(xSQ ! xSQ),S1] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
{(xSQ ! xSQ),S1} is non empty set
{(xSQ ! xSQ)} is non empty trivial 1 -element set
{{(xSQ ! xSQ),S1},{(xSQ ! xSQ)}} is non empty set
[(b ! x),e2] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
{(b ! x),e2} is non empty set
{(b ! x)} is non empty trivial 1 -element set
{{(b ! x),e2},{(b ! x)}} is non empty set
(<*b*> ^ x) . 1 is set
(<*xSQ*> ^ xSQ) . 1 is set
A is non empty Relation-like QC-alphabet
QC-pred_symbols A is non empty set
Al is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Al -ary_QC-pred_symbols A is non empty Element of bool (QC-pred_symbols A)
bool (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 set
vSUB A is non empty functional set
J is Element of Al -ary_QC-pred_symbols A
xSQ is Relation-like NAT -defined bound_QC-variables A -valued QC-variables A -valued Function-like Al -element FinSequence-like FinSequence of QC-variables A
S is Relation-like Function-like Element of vSUB A
Sub_P (J,xSQ,S) is Sub_atomic Element of QC-Sub-WFF A
QC-Sub-WFF A is non empty A -Sub-closed set
CQC-Sub-WFF A is non empty Element of bool (QC-Sub-WFF A)
bool (QC-Sub-WFF A) is non empty set
QC-WFF A is non empty set
CQC-WFF A is non empty Element of bool (QC-WFF A)
bool (QC-WFF A) is non empty set
{ b₁ where b₁ is Element of QC-Sub-WFF A : b₁ `1 is Element of CQC-WFF A } is set
v is Element of QC-Sub-WFF A
v `1 is Element of QC-WFF A
J ! xSQ is Element of CQC-WFF A
[(J ! xSQ),S] is V1() Element of [:(CQC-WFF A),(vSUB A):]
[:(CQC-WFF A),(vSUB A):] is non empty Relation-like set
{(J ! xSQ),S} is non empty set
{(J ! xSQ)} is non empty trivial 1 -element set
{{(J ! xSQ),S},{(J ! xSQ)}} is non empty set
(Sub_P (J,xSQ,S)) `1 is Element of QC-WFF A
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
S is Relation-like Function-like Element of vSUB Al
(A,Al,J,xSQ,S) is Sub_atomic Element of CQC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
CQC_Sub (A,Al,J,xSQ,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
CQC_Subst (xSQ,S) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
J ! (CQC_Subst (xSQ,S)) is Element of QC-WFF Al
J ! xSQ is Element of CQC-WFF Al
[(J ! xSQ),S] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(J ! xSQ),S} is non empty set
{(J ! xSQ)} is non empty trivial 1 -element set
{{(J ! xSQ),S},{(J ! xSQ)}} is non empty set
(A,Al,J,xSQ,S) `2 is Relation-like Function-like Element of vSUB Al
(Al,(A,Al,J,xSQ,S)) is Element of CQC-WFF Al
Sub_the_arguments_of (A,Al,J,xSQ,S) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
the_pred_symbol_of (Al,(A,Al,J,xSQ,S)) is Element of QC-pred_symbols Al
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
S is Relation-like Function-like Element of vSUB Al
CQC_Subst (xSQ,S) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
J ! (CQC_Subst (xSQ,S)) is Element of QC-WFF Al
(A,Al,J,xSQ,S) is Sub_atomic Element of CQC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
CQC_Sub (A,Al,J,xSQ,S) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
J is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ is Relation-like Function-like Element of vSUB Al
CQC_Subst (J,xSQ) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
S is Relation-like NAT -defined bound_QC-variables Al -valued Function-like FinSequence-like FinSequence of bound_QC-variables Al
CQC_Subst (S,xSQ) is Relation-like NAT -defined bound_QC-variables Al -valued Function-like FinSequence-like FinSequence of bound_QC-variables Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued Function-like FinSequence-like FinSequence of bound_QC-variables Al
@ S is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
CQC_Subst ((@ S),xSQ) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
len S is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
len (@ S) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
len xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
vSUB Al is non empty functional set
J is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ is Relation-like Function-like Element of vSUB Al
CQC_Subst (J,xSQ) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ . A is Element of J
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
proj1 (S `2) is set
(Al,S,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,S,J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,xSQ,(Al,S,J,xSQ)) . A is Element of J
dom (@ (S `2)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom ((@ (S `2)) * xSQ) is Element of bool (bound_QC-variables Al)
dom (Al,S,J,xSQ) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
proj1 (S `2) is set
(Al,S,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,S,J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,xSQ,(Al,S,J,xSQ)) . A is Element of J
(Al,S,J,xSQ) . A is set
dom (@ (S `2)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
rng (@ (S `2)) is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
dom (Al,S,J,xSQ) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
v is Relation-like Function-like Element of vSUB Al
(A,Al,S,xSQ,v) is Sub_atomic Element of CQC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
(Al,(A,Al,S,xSQ,v),J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(A,Al,S,xSQ,v) `2 is Relation-like Function-like Element of vSUB Al
@ ((A,Al,S,xSQ,v) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((A,Al,S,xSQ,v) `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
CQC_Subst (xSQ,v) is Relation-like NAT -defined QC-variables Al -valued bound_QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ *' (CQC_Subst (xSQ,v)) is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
len xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
QC-WFF Al is non empty set
bool (QC-WFF Al) is non empty set
S ! xSQ is Element of CQC-WFF Al
[(S ! xSQ),v] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(S ! xSQ),v} is non empty set
{(S ! xSQ)} is non empty trivial 1 -element set
{{(S ! xSQ),v},{(S ! xSQ)}} is non empty set
len ((Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) *' xSQ) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
dom ((Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) *' xSQ) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
Seg A is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
q is ext-real epsilon-transitive epsilon-connected ordinal natural V52() cardinal set
((Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) *' xSQ) . q is set
(xSQ *' (CQC_Subst (xSQ,v))) . q is set
p is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Seg (len xSQ) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
dom xSQ is V45() V46() V47() V48() V49() V50() V63() A -element Element of bool NAT
xSQ . p is set
proj1 v is set
(Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) . (xSQ . p) is set
a is Element of bound_QC-variables Al
(Al,(A,Al,S,xSQ,v),J,xSQ) . a is set
dom (@ ((A,Al,S,xSQ,v) `2)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
(@ ((A,Al,S,xSQ,v) `2)) . (xSQ . p) is set
xSQ . ((@ ((A,Al,S,xSQ,v) `2)) . (xSQ . p)) is set
((A,Al,S,xSQ,v) `2) . (xSQ . p) is set
xSQ . (((A,Al,S,xSQ,v) `2) . (xSQ . p)) is set
((Al,J,xSQ,(Al,(A,Al,S,xSQ,v),J,xSQ)) *' xSQ) . p is set
(CQC_Subst (xSQ,v)) . p is set
xSQ . ((CQC_Subst (xSQ,v)) . p) is set
xSQ . (xSQ . p) is set
xSQ . a is Element of J
(xSQ *' (CQC_Subst (xSQ,v))) . p is set
len (xSQ *' (CQC_Subst (xSQ,v))) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
J ! xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
S is Relation-like Function-like Element of vSUB Al
(A,Al,J,xSQ,S) is Sub_atomic Element of CQC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
(Al,(A,Al,J,xSQ,S)) is Element of CQC-WFF Al
[(J ! xSQ),S] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(J ! xSQ),S} is non empty set
{(J ! xSQ)} is non empty trivial 1 -element set
{{(J ! xSQ),S},{(J ! xSQ)}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
v is Relation-like Function-like Element of vSUB Al
(A,Al,S,xSQ,v) is Sub_atomic Element of CQC-Sub-WFF Al
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
CQC_Sub (A,Al,S,xSQ,v) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
CQC_Subst (xSQ,v) is Relation-like NAT -defined QC-variables Al -valued bound_QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
S ! (CQC_Subst (xSQ,v)) is Element of CQC-WFF Al
a is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,(A,Al,S,xSQ,v),J,a) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(A,Al,S,xSQ,v) `2 is Relation-like Function-like Element of vSUB Al
@ ((A,Al,S,xSQ,v) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((A,Al,S,xSQ,v) `2)) * a is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,a,(Al,(A,Al,S,xSQ,v),J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
q is Element of CQC-WFF Al
Valid (q,xSQ) is Relation-like Valuations_in (Al,J) -defined K370() -valued Function-like quasi_total Element of Funcs ((Valuations_in (Al,J)),K370())
Funcs ((Valuations_in (Al,J)),K370()) is non empty FUNCTION_DOMAIN of Valuations_in (Al,J),K370()
(Valid (q,xSQ)) . a is Element of K370()
p is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
a *' p is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
xSQ . S is Element of K367(J)
(Al,J,a,(Al,(A,Al,S,xSQ,v),J,a)) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
S ! xSQ is Element of CQC-WFF Al
Valid ((S ! xSQ),xSQ) is Relation-like Valuations_in (Al,J) -defined K370() -valued Function-like quasi_total Element of Funcs ((Valuations_in (Al,J)),K370())
(Valid ((S ! xSQ),xSQ)) . (Al,J,a,(Al,(A,Al,S,xSQ,v),J,a)) is Element of K370()
(Al,(A,Al,S,xSQ,v)) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
Sub_not A is Sub_negative Element of QC-Sub-WFF Al
(Sub_not A) `1 is Element of QC-WFF Al
QC-WFF Al is non empty set
(Al,A) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
'not' (Al,A) is Element of CQC-WFF Al
(Sub_not A) `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
A `2 is Relation-like Function-like Element of vSUB Al
[('not' (Al,A)),(A `2)] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{('not' (Al,A)),(A `2)} is non empty set
{('not' (Al,A))} is non empty trivial 1 -element set
{{('not' (Al,A)),(A `2)},{('not' (Al,A))}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
Sub_not A is Sub_negative Element of QC-Sub-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
{ b<sub>1</sub> where b<sub>1</sub> is Element of QC-Sub-WFF Al : b<sub>1</sub> `1 is Element of CQC-WFF Al } is set
xSQ is Element of QC-Sub-WFF Al
xSQ `1 is Element of QC-WFF Al
(Al,A) is Element of CQC-WFF Al
'not' (Al,A) is Element of CQC-WFF Al
(Sub_not A) `1 is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
S is Element of CQC-Sub-WFF Al
(Al,S,A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
S `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,S,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,S) is Sub_negative Element of CQC-Sub-WFF Al
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
'not' (Al,S) is Element of CQC-WFF Al
(Al,(Al,S)) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is non empty set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A,J) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
xSQ `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (xSQ `2)) * J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,xSQ) is Sub_negative Element of CQC-Sub-WFF Al
(Al,(Al,xSQ),A,J) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,xSQ) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,xSQ) `2)) * J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
QC-WFF Al is non empty set
bool (QC-WFF Al) is non empty set
(Al,xSQ) is Element of CQC-WFF Al
'not' (Al,xSQ) is Element of CQC-WFF Al
[('not' (Al,xSQ)),(xSQ `2)] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{('not' (Al,xSQ)),(xSQ `2)} is non empty set
{('not' (Al,xSQ))} is non empty trivial 1 -element set
{{('not' (Al,xSQ)),(xSQ `2)},{('not' (Al,xSQ))}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
xSQ is Element of CQC-Sub-WFF Al
CQC_Sub xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
(Al,xSQ) is Sub_negative Element of CQC-Sub-WFF Al
CQC_Sub (Al,xSQ) is Element of CQC-WFF Al
S is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,xSQ),A,S) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
(Al,xSQ) `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ ((Al,xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((Al,xSQ) `2)) * S is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,S,(Al,(Al,xSQ),A,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
'not' (CQC_Sub xSQ) is Element of CQC-WFF Al
(Al,xSQ,A,S) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
xSQ `2 is Relation-like Function-like Element of vSUB Al
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (xSQ `2)) * S is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,S,(Al,xSQ,A,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
J is Element of CQC-Sub-WFF Al
J `2 is Relation-like Function-like Element of vSUB Al
Sub_& (A,J) is Element of QC-Sub-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
{ b₁ where b₁ is Element of QC-Sub-WFF Al : b₁ `1 is Element of CQC-WFF Al } is set
S is Element of QC-Sub-WFF Al
S `1 is Element of QC-WFF Al
(Al,A) is Element of CQC-WFF Al
(Al,J) is Element of CQC-WFF Al
(Al,A) '&' (Al,J) is Element of CQC-WFF Al
[((Al,A) '&' (Al,J)),(A `2)] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{((Al,A) '&' (Al,J)),(A `2)} is non empty set
{((Al,A) '&' (Al,J))} is non empty trivial 1 -element set
{{((Al,A) '&' (Al,J)),(A `2)},{((Al,A) '&' (Al,J))}} is non empty set
(Sub_& (A,J)) `1 is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
(Al,A) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
J is Element of CQC-Sub-WFF Al
J `2 is Relation-like Function-like Element of vSUB Al
(Al,A,J) is Element of CQC-Sub-WFF Al
(Al,(Al,A,J)) is Element of CQC-WFF Al
(Al,J) is Element of CQC-WFF Al
(Al,A) '&' (Al,J) is Element of CQC-WFF Al
(Al,A,J) `2 is Relation-like Function-like Element of vSUB Al
Sub_& (A,J) is Element of QC-Sub-WFF Al
[((Al,A) '&' (Al,J)),(A `2)] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{((Al,A) '&' (Al,J)),(A `2)} is non empty set
{((Al,A) '&' (Al,J))} is non empty trivial 1 -element set
{{((Al,A) '&' (Al,J)),(A `2)},{((Al,A) '&' (Al,J))}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
J is Element of CQC-Sub-WFF Al
J `2 is Relation-like Function-like Element of vSUB Al
(Al,A,J) is Element of CQC-Sub-WFF Al
(Al,A,J) `2 is Relation-like Function-like Element of vSUB Al
Sub_& (A,J) is Element of QC-Sub-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
QC-WFF Al is non empty set
bool (QC-WFF Al) is non empty set
(Al,A) is Element of CQC-WFF Al
(Al,J) is Element of CQC-WFF Al
(Al,A) '&' (Al,J) is Element of CQC-WFF Al
[((Al,A) '&' (Al,J)),(A `2)] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{((Al,A) '&' (Al,J)),(A `2)} is non empty set
{((Al,A) '&' (Al,J))} is non empty trivial 1 -element set
{{((Al,A) '&' (Al,J)),(A `2)},{((Al,A) '&' (Al,J))}} is non empty set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
xSQ is Element of CQC-Sub-WFF Al
xSQ `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
J is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,xSQ,A,J) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (xSQ `2)) * J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,xSQ,S) is Element of CQC-Sub-WFF Al
(Al,(Al,xSQ,S),A,J) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,xSQ,S) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,xSQ,S) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,xSQ,S) `2)) * J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,S,A,J) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
A `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
CQC_Sub A is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
J is Element of CQC-Sub-WFF Al
J `2 is Relation-like Function-like Element of vSUB Al
(Al,A,J) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,A,J) is Element of CQC-WFF Al
CQC_Sub J is Element of CQC-WFF Al
(CQC_Sub A) '&' (CQC_Sub J) is Element of CQC-WFF Al
Sub_& (A,J) is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
(Al,S,A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,S,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
xSQ is Element of CQC-Sub-WFF Al
xSQ `2 is Relation-like Function-like Element of vSUB Al
(Al,xSQ,A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (xSQ `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,xSQ,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,S,xSQ) is Element of CQC-Sub-WFF Al
(Al,(Al,S,xSQ),A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,S,xSQ) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,S,xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,S,xSQ) `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,(Al,S,xSQ),A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
(Al,xSQ) is Element of CQC-WFF Al
(Al,S) '&' (Al,xSQ) is Element of CQC-WFF Al
(Al,(Al,S,xSQ)) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
xSQ is Element of CQC-Sub-WFF Al
xSQ `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
CQC_Sub xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
CQC_Sub S is Element of CQC-WFF Al
(Al,xSQ,S) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,xSQ,S) is Element of CQC-WFF Al
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,xSQ,S),A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
(Al,xSQ,S) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,xSQ,S) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((Al,xSQ,S) `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,(Al,xSQ,S),A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,xSQ,A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (xSQ `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,xSQ,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,S,A,xSQ) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,S,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(CQC_Sub xSQ) '&' (CQC_Sub S) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
A `2 is Element of bound_QC-variables Al
A `1 is Element of QC-Sub-WFF Al
(A `1) `1 is Element of QC-WFF Al
QC-WFF Al is non empty set
All ((A `2),((A `1) `1)) is Element of QC-WFF Al
J is Relation-like Function-like second_Q_comp of A
Sub_All (A,J) is Element of QC-Sub-WFF Al
(Sub_All (A,J)) `1 is Element of QC-WFF Al
(Sub_All (A,J)) `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
[(All ((A `2),((A `1) `1))),J] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(All ((A `2),((A `1) `1))),J} is non empty set
{(All ((A `2),((A `1) `1)))} is non empty trivial 1 -element set
{{(All ((A `2),((A `1) `1))),J},{(All ((A `2),((A `1) `1)))}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
vSUB Al is non empty functional set
the Relation-like Function-like Element of vSUB Al is Relation-like Function-like Element of vSUB Al
the Element of bound_QC-variables Al is Element of bound_QC-variables Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
QC-WFF Al is non empty set
bool (QC-WFF Al) is non empty set
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
VERUM Al is Element of CQC-WFF Al
[(VERUM Al), the Relation-like Function-like Element of vSUB Al] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
{(VERUM Al), the Relation-like Function-like Element of vSUB Al} is non empty set
{(VERUM Al)} is non empty trivial 1 -element set
{{(VERUM Al), the Relation-like Function-like Element of vSUB Al},{(VERUM Al)}} is non empty set
[[(VERUM Al), the Relation-like Function-like Element of vSUB Al], the Element of bound_QC-variables Al] is V1() Element of [:[:(CQC-WFF Al),(vSUB Al):],(bound_QC-variables Al):]
[:[:(CQC-WFF Al),(vSUB Al):],(bound_QC-variables Al):] is non empty Relation-like set
{[(VERUM Al), the Relation-like Function-like Element of vSUB Al], the Element of bound_QC-variables Al} is non empty set
{[(VERUM Al), the Relation-like Function-like Element of vSUB Al]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[(VERUM Al), the Relation-like Function-like Element of vSUB Al], the Element of bound_QC-variables Al},{[(VERUM Al), the Relation-like Function-like Element of vSUB Al]}} is non empty set
[<*[0,0]*>, the Relation-like Function-like Element of vSUB Al] is V1() Element of [:(bool [:NAT,[:NAT,NAT:]:]),(vSUB Al):]
[:(bool [:NAT,[:NAT,NAT:]:]),(vSUB Al):] is non empty Relation-like V52() set
{<*[0,0]*>, the Relation-like Function-like Element of vSUB Al} is non empty functional set
{<*[0,0]*>} is non empty trivial functional 1 -element set
{{<*[0,0]*>, the Relation-like Function-like Element of vSUB Al},{<*[0,0]*>}} is non empty set
xSQ is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
{ b<sub>1</sub> where b<sub>1</sub> is Element of QC-Sub-WFF Al : b<sub>1</sub> `1 is Element of CQC-WFF Al } is set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
S is Element of QC-Sub-WFF Al
S `1 is Element of QC-WFF Al
xSQ `1 is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-Sub-WFF Al
J is Element of bound_QC-variables Al
[A,J] is V1() set
{A,J} is non empty set
{A} is non empty trivial 1 -element set
{{A,J},{A}} is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
[A,J] is V1() Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[A,J] `1 is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
A `1 is set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
J is Relation-like Function-like second_Q_comp of A
Sub_All (A,J) is Element of QC-Sub-WFF Al
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
{ b₁ where b₁ is Element of QC-Sub-WFF Al : b₁ `1 is Element of CQC-WFF Al } is set
S is Element of QC-Sub-WFF Al
S `1 is Element of QC-WFF Al
A `2 is Element of bound_QC-variables Al
(Al,A) is Element of CQC-Sub-WFF Al
(Al,(Al,A)) is Element of CQC-WFF Al
All ((A `2),(Al,(Al,A))) is Element of CQC-WFF Al
(Sub_All (A,J)) `1 is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
J is Relation-like Function-like second_Q_comp of A
(Al,A,J) is Element of CQC-Sub-WFF Al
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
Sub_All (A,J) is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
Sub_the_scope_of A is Element of QC-Sub-WFF Al
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
J is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
xSQ is Relation-like Function-like second_Q_comp of J
Sub_All (J,xSQ) is Element of QC-Sub-WFF Al
J `1 is Element of QC-Sub-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
{ b₁ where b₁ is Element of QC-Sub-WFF Al : b₁ `1 is Element of CQC-WFF Al } is set
xSQ is Element of QC-Sub-WFF Al
xSQ `1 is Element of QC-WFF Al
(Al,A) is Element of CQC-WFF Al
J `2 is Element of bound_QC-variables Al
(J `1) `1 is Element of QC-WFF Al
All ((J `2),((J `1) `1)) is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
J is Element of CQC-WFF Al
(Al,A) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,A) is Element of CQC-WFF Al
Quant (A,J) is Element of QC-WFF Al
Sub_the_scope_of A is Element of QC-Sub-WFF Al
CQC_Sub A is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of CQC-Sub-WFF Al
CQC_Sub A is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
(Al,A) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,A) is Element of CQC-WFF Al
(Al,A,(CQC_Sub (Al,A))) is Element of CQC-WFF Al
Sub_the_scope_of A is Element of QC-Sub-WFF Al
CQC_Sub (Sub_the_scope_of A) is Element of QC-WFF Al
Quant (A,(CQC_Sub (Sub_the_scope_of A))) is Element of QC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
(Al,A) is Element of CQC-Sub-WFF Al
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
J is Relation-like Function-like second_Q_comp of A
(Al,A,J) is Element of CQC-Sub-WFF Al
(Al,(Al,A,J)) is Element of CQC-Sub-WFF Al
Sub_All (A,J) is Element of QC-Sub-WFF Al
Sub_the_scope_of (Sub_All (A,J)) is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
CQC_Sub J is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
(Al,(Al,(Al,J,A),xSQ),(CQC_Sub (Al,(Al,(Al,J,A),xSQ)))) is Element of CQC-WFF Al
(Al,(Al,(Al,J,A),xSQ),(CQC_Sub J)) is Element of CQC-WFF Al
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
CQC_Sub J is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ),(CQC_Sub J)) is Element of CQC-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
All ((S_Bound (@ (Al,(Al,J,A),xSQ))),(CQC_Sub J)) is Element of CQC-WFF Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
Quant ((Al,(Al,J,A),xSQ),(CQC_Sub (Al,(Al,(Al,J,A),xSQ)))) is Element of QC-WFF Al
All ((S_Bound (@ (Al,(Al,J,A),xSQ))),(CQC_Sub (Al,(Al,(Al,J,A),xSQ)))) is Element of CQC-WFF Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ),(CQC_Sub (Al,(Al,(Al,J,A),xSQ)))) is Element of CQC-WFF Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
S `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
proj1 (S `2) is set
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) . A is set
xSQ . ((@ (S `2)) . A) is set
(Al,S,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(@ (S `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,S,J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,xSQ,(Al,S,J,xSQ)) . A is Element of J
(Al,S,J,xSQ) . A is set
dom (@ (S `2)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
J `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ (J `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
dom (@ (J `2)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
(@ (J `2)) . A is set
rng (@ (J `2)) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
QSub Al is Relation-like Function-like set
proj1 (QSub Al) is set
A is set
J is set
xSQ is set
[J,xSQ] is V1() set
{J,xSQ} is non empty set
{J} is non empty trivial 1 -element set
{{J,xSQ},{J}} is non empty set
xSQ is Element of QC-WFF Al
S is Relation-like Function-like Element of vSUB Al
[xSQ,S] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
{xSQ,S} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,S},{xSQ}} is non empty set
[[xSQ,S],{}] is V1() set
{[xSQ,S],{}} is non empty set
{[xSQ,S]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[xSQ,S],{}},{[xSQ,S]}} is non empty set
bound_in xSQ is Element of bound_QC-variables Al
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
the_scope_of xSQ is Element of QC-WFF Al
RestrictSub ((bound_in xSQ),xSQ,S) is Relation-like Function-like V52() Element of vSUB Al
ExpandSub ((bound_in xSQ),(the_scope_of xSQ),(RestrictSub ((bound_in xSQ),xSQ,S))) is Relation-like Function-like Element of vSUB Al
[[xSQ,S],(ExpandSub ((bound_in xSQ),(the_scope_of xSQ),(RestrictSub ((bound_in xSQ),xSQ,S))))] is V1() Element of [:[:(QC-WFF Al),(vSUB Al):],(vSUB Al):]
[:[:(QC-WFF Al),(vSUB Al):],(vSUB Al):] is non empty Relation-like set
{[xSQ,S],(ExpandSub ((bound_in xSQ),(the_scope_of xSQ),(RestrictSub ((bound_in xSQ),xSQ,S))))} is non empty set
{{[xSQ,S],(ExpandSub ((bound_in xSQ),(the_scope_of xSQ),(RestrictSub ((bound_in xSQ),xSQ,S))))},{[xSQ,S]}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
A `2 is Element of bound_QC-variables Al
J is Relation-like Function-like second_Q_comp of A
Sub_All (A,J) is Element of QC-Sub-WFF Al
xSQ is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
xSQ `2 is Element of bound_QC-variables Al
S is Relation-like Function-like second_Q_comp of xSQ
Sub_All (xSQ,S) is Element of QC-Sub-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
QC-WFF Al is non empty set
bool (QC-WFF Al) is non empty set
vSUB Al is non empty functional set
(Al,A) is Element of CQC-Sub-WFF Al
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
(Al,(Al,A)) is Element of CQC-WFF Al
All ((A `2),(Al,(Al,A))) is Element of CQC-WFF Al
[(All ((A `2),(Al,(Al,A)))),J] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(All ((A `2),(Al,(Al,A)))),J} is non empty set
{(All ((A `2),(Al,(Al,A))))} is non empty trivial 1 -element set
{{(All ((A `2),(Al,(Al,A)))),J},{(All ((A `2),(Al,(Al,A))))}} is non empty set
xSQ `1 is Element of QC-Sub-WFF Al
(xSQ `1) `1 is Element of QC-WFF Al
All ((xSQ `2),((xSQ `1) `1)) is Element of QC-WFF Al
[(All ((xSQ `2),((xSQ `1) `1))),S] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(All ((xSQ `2),((xSQ `1) `1))),S} is non empty set
{(All ((xSQ `2),((xSQ `1) `1)))} is non empty trivial 1 -element set
{{(All ((xSQ `2),((xSQ `1) `1))),S},{(All ((xSQ `2),((xSQ `1) `1)))}} is non empty set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
A is (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
A `2 is Element of bound_QC-variables Al
J is Relation-like Function-like second_Q_comp of A
(Al,A,J) is Element of CQC-Sub-WFF Al
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
xSQ is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
xSQ `2 is Element of bound_QC-variables Al
S is Relation-like Function-like second_Q_comp of xSQ
Sub_All (xSQ,S) is Element of QC-Sub-WFF Al
Sub_All (A,J) is Element of QC-Sub-WFF Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
Sub_the_bound_of (Al,(Al,J,A),xSQ) is Element of bound_QC-variables Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
xSQ is Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
v is Relation-like Function-like second_Q_comp of xSQ
Sub_All (xSQ,v) is Element of QC-Sub-WFF Al
xSQ `2 is Element of bound_QC-variables Al
(Al,J,A) `2 is Element of bound_QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
Bound_Vars (Al,J) is V52() Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
proj2 (RestrictSub (A,(All (A,(Al,J))),xSQ)) is set
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
(Al,J,A) `2 is Element of bound_QC-variables Al
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A))) is Element of CQC-WFF Al
All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
All (A,(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
bound_in (Al,(Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
(Al,(Al,J,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)) is Relation-like Function-like V52() Element of vSUB Al
the_scope_of (Al,(Al,(Al,J,A),xSQ)) is Element of QC-WFF Al
Dom_Bound_Vars (the_scope_of (Al,(Al,(Al,J,A),xSQ))) is V52() Element of bool (QC-symbols Al)
QC-symbols Al is non empty set
bool (QC-symbols Al) is non empty set
Bound_Vars (the_scope_of (Al,(Al,(Al,J,A),xSQ))) is V52() Element of bool (bound_QC-variables Al)
{ b<sub>1</sub> where b<sub>1</sub> is Element of QC-symbols Al : x. b<sub>1</sub> in Bound_Vars (the_scope_of (Al,(Al,(Al,J,A),xSQ))) } is set
Sub_Var (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) is V52() Element of bool (QC-symbols Al)
(Dom_Bound_Vars (the_scope_of (Al,(Al,(Al,J,A),xSQ)))) \/ (Sub_Var (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)))) is Element of bool (QC-symbols Al)
upVar ((RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))),(the_scope_of (Al,(Al,(Al,J,A),xSQ)))) is Element of QC-symbols Al
NSub ((the_scope_of (Al,(Al,(Al,J,A),xSQ))),(RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)))) is non empty Element of bool (QC-symbols Al)
NAT \ ((Dom_Bound_Vars (the_scope_of (Al,(Al,(Al,J,A),xSQ)))) \/ (Sub_Var (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))))) is V45() V46() V47() V48() V49() V50() V63() Element of bool REAL
the Element of NSub ((the_scope_of (Al,(Al,(Al,J,A),xSQ))),(RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)))) is Element of NSub ((the_scope_of (Al,(Al,(Al,J,A),xSQ))),(RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))))
x. (upVar ((RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))),(the_scope_of (Al,(Al,(Al,J,A),xSQ))))) is Element of bound_QC-variables Al
proj2 (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) is set
{ b₁ where b₁ is Element of QC-symbols Al : x. b₁ in proj2 (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) } is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
proj2 (RestrictSub (A,(All (A,(Al,J))),xSQ)) is set
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
(Al,J,A) `2 is Element of bound_QC-variables Al
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A))) is Element of CQC-WFF Al
All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
All (A,(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
bound_in (Al,(Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
(Al,(Al,J,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)) is Relation-like Function-like V52() Element of vSUB Al
proj2 (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
proj2 (RestrictSub (A,(All (A,(Al,J))),xSQ)) is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
J `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
ExpandSub (A,(Al,J),(RestrictSub (A,(All (A,(Al,J))),xSQ))) is Relation-like Function-like Element of vSUB Al
[(All (A,(Al,J))),xSQ] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
[:(CQC-WFF Al),(vSUB Al):] is non empty Relation-like set
{(All (A,(Al,J))),xSQ} is non empty set
{(All (A,(Al,J)))} is non empty trivial 1 -element set
{{(All (A,(Al,J))),xSQ},{(All (A,(Al,J)))}} is non empty set
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,J,A)) `2 is Relation-like Function-like Element of vSUB Al
QSub Al is Relation-like Function-like set
(Al,J,A) `2 is Element of bound_QC-variables Al
(Al,(Al,(Al,J,A))) is Element of CQC-WFF Al
All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
[(All (((Al,J,A) `2),(Al,(Al,(Al,J,A))))),xSQ] is V1() Element of [:(CQC-WFF Al),(vSUB Al):]
{(All (((Al,J,A) `2),(Al,(Al,(Al,J,A))))),xSQ} is non empty set
{(All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))))} is non empty trivial 1 -element set
{{(All (((Al,J,A) `2),(Al,(Al,(Al,J,A))))),xSQ},{(All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))))}} is non empty set
(QSub Al) . [(All (((Al,J,A) `2),(Al,(Al,(Al,J,A))))),xSQ] is set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
proj1 (QSub Al) is set
[[(All (A,(Al,J))),xSQ],((Al,(Al,J,A)) `2)] is V1() Element of [:[:(CQC-WFF Al),(vSUB Al):],(vSUB Al):]
[:[:(CQC-WFF Al),(vSUB Al):],(vSUB Al):] is non empty Relation-like set
{[(All (A,(Al,J))),xSQ],((Al,(Al,J,A)) `2)} is non empty set
{[(All (A,(Al,J))),xSQ]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[(All (A,(Al,J))),xSQ],((Al,(Al,J,A)) `2)},{[(All (A,(Al,J))),xSQ]}} is non empty set
[[(All (A,(Al,J))),xSQ],(J `2)] is V1() Element of [:[:(CQC-WFF Al),(vSUB Al):],(vSUB Al):]
{[(All (A,(Al,J))),xSQ],(J `2)} is non empty set
{{[(All (A,(Al,J))),xSQ],(J `2)},{[(All (A,(Al,J))),xSQ]}} is non empty set
v is Element of QC-WFF Al
S1 is Relation-like Function-like Element of vSUB Al
[v,S1] is V1() Element of [:(QC-WFF Al),(vSUB Al):]
{v,S1} is non empty set
{v} is non empty trivial 1 -element set
{{v,S1},{v}} is non empty set
z is set
[[v,S1],z] is V1() set
{[v,S1],z} is non empty set
{[v,S1]} is non empty trivial Relation-like Function-like constant 1 -element set
{{[v,S1],z},{[v,S1]}} is non empty set
bound_in (All (A,(Al,J))) is Element of bound_QC-variables Al
the_scope_of (All (A,(Al,J))) is Element of QC-WFF Al
RestrictSub ((bound_in (All (A,(Al,J)))),(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
ExpandSub ((bound_in (All (A,(Al,J)))),(the_scope_of (All (A,(Al,J)))),(RestrictSub ((bound_in (All (A,(Al,J)))),(All (A,(Al,J))),xSQ))) is Relation-like Function-like Element of vSUB Al
Al is non empty Relation-like QC-alphabet
VERUM Al is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
still_not-bound_in (VERUM Al) is Element of bool (bound_QC-variables Al)
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
bool (bound_QC-variables Al) is non empty set
Bound_Vars (VERUM Al) is V52() Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
J ! xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
still_not-bound_in (J ! xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
Bound_Vars (J ! xSQ) is V52() Element of bool (bound_QC-variables Al)
the_arguments_of (J ! xSQ) is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
xSQ -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
S1 is Relation-like NAT -defined QC-variables Al -valued Function-like xSQ -element FinSequence-like FinSequence of QC-variables Al
v is Element of xSQ -ary_QC-pred_symbols Al
v ! S1 is Element of QC-WFF Al
Bound_Vars (the_arguments_of (J ! xSQ)) is Element of bool (bound_QC-variables Al)
len (the_arguments_of (J ! xSQ)) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
{ ((the_arguments_of (J ! xSQ)) . b₁) where b₁ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len (the_arguments_of (J ! xSQ)) & (the_arguments_of (J ! xSQ)) . b₁ in bound_QC-variables Al ) } is set
still_not-bound_in xSQ is Element of bool (bound_QC-variables Al)
variables_in (xSQ,(bound_QC-variables Al)) is Element of bool (bound_QC-variables Al)
<*v*> is Relation-like NAT -defined xSQ -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of xSQ -ary_QC-pred_symbols Al
<*v*> ^ S1 is Relation-like Function-like FinSequence-like set
(<*v*> ^ S1) . 1 is set
<*J*> is Relation-like NAT -defined A -ary_QC-pred_symbols Al -valued Function-like FinSequence-like FinSequence of A -ary_QC-pred_symbols Al
<*J*> ^ xSQ is Relation-like Function-like FinSequence-like set
(<*J*> ^ xSQ) . 1 is set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
bool (bound_QC-variables Al) is non empty set
Bound_Vars A is V52() Element of bool (bound_QC-variables Al)
'not' A is Element of CQC-WFF Al
still_not-bound_in ('not' A) is Element of bool (bound_QC-variables Al)
Bound_Vars ('not' A) is V52() Element of bool (bound_QC-variables Al)
the_argument_of ('not' A) is Element of QC-WFF Al
Bound_Vars (the_argument_of ('not' A)) is V52() Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
bool (bound_QC-variables Al) is non empty set
Bound_Vars A is V52() Element of bool (bound_QC-variables Al)
J is Element of CQC-WFF Al
still_not-bound_in J is Element of bool (bound_QC-variables Al)
Bound_Vars J is V52() Element of bool (bound_QC-variables Al)
A '&' J is Element of CQC-WFF Al
still_not-bound_in (A '&' J) is Element of bool (bound_QC-variables Al)
Bound_Vars (A '&' J) is V52() Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \/ (still_not-bound_in J) is Element of bool (bound_QC-variables Al)
the_left_argument_of (A '&' J) is Element of QC-WFF Al
Bound_Vars (the_left_argument_of (A '&' J)) is V52() Element of bool (bound_QC-variables Al)
the_right_argument_of (A '&' J) is Element of QC-WFF Al
Bound_Vars (the_right_argument_of (A '&' J)) is V52() Element of bool (bound_QC-variables Al)
(Bound_Vars (the_left_argument_of (A '&' J))) \/ (Bound_Vars (the_right_argument_of (A '&' J))) is Element of bool (bound_QC-variables Al)
(Bound_Vars A) \/ (Bound_Vars (the_right_argument_of (A '&' J))) is Element of bool (bound_QC-variables Al)
(Bound_Vars A) \/ (Bound_Vars J) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
Bound_Vars A is V52() Element of bool (bound_QC-variables Al)
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
Bound_Vars (All (J,A)) is V52() Element of bool (bound_QC-variables Al)
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
the_scope_of (All (J,A)) is Element of QC-WFF Al
Bound_Vars (the_scope_of (All (J,A))) is V52() Element of bool (bound_QC-variables Al)
bound_in (All (J,A)) is Element of bound_QC-variables Al
{(bound_in (All (J,A)))} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(Bound_Vars (the_scope_of (All (J,A)))) \/ {(bound_in (All (J,A)))} is non empty Element of bool (bound_QC-variables Al)
(Bound_Vars A) \/ {(bound_in (All (J,A)))} is non empty Element of bool (bound_QC-variables Al)
(Bound_Vars A) \ {J} is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
VERUM Al is Element of CQC-WFF Al
Bound_Vars (VERUM Al) is V52() Element of bool (bound_QC-variables Al)
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
bool (bound_QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
still_not-bound_in (VERUM Al) is Element of bool (bound_QC-variables Al)
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
xSQ is Element of A -ary_QC-pred_symbols Al
J is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ ! J is Element of CQC-WFF Al
still_not-bound_in (xSQ ! J) is Element of bool (bound_QC-variables Al)
Bound_Vars (xSQ ! J) is V52() Element of bool (bound_QC-variables Al)
S is Element of CQC-WFF Al
still_not-bound_in S is Element of bool (bound_QC-variables Al)
Bound_Vars S is V52() Element of bool (bound_QC-variables Al)
'not' S is Element of CQC-WFF Al
still_not-bound_in ('not' S) is Element of bool (bound_QC-variables Al)
Bound_Vars ('not' S) is V52() Element of bool (bound_QC-variables Al)
xSQ is Element of CQC-WFF Al
still_not-bound_in xSQ is Element of bool (bound_QC-variables Al)
Bound_Vars xSQ is V52() Element of bool (bound_QC-variables Al)
v is Element of CQC-WFF Al
still_not-bound_in v is Element of bool (bound_QC-variables Al)
Bound_Vars v is V52() Element of bool (bound_QC-variables Al)
xSQ '&' v is Element of CQC-WFF Al
still_not-bound_in (xSQ '&' v) is Element of bool (bound_QC-variables Al)
Bound_Vars (xSQ '&' v) is V52() Element of bool (bound_QC-variables Al)
S1 is Element of CQC-WFF Al
still_not-bound_in S1 is Element of bool (bound_QC-variables Al)
Bound_Vars S1 is V52() Element of bool (bound_QC-variables Al)
z is Element of bound_QC-variables Al
All (z,S1) is Element of CQC-WFF Al
still_not-bound_in (All (z,S1)) is Element of bool (bound_QC-variables Al)
Bound_Vars (All (z,S1)) is V52() Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is non empty set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is non empty set
J is Element of bound_QC-variables Al
xSQ is Element of A
J .--> xSQ is trivial Relation-like bound_QC-variables Al -defined {J} -defined A -valued Function-like one-to-one constant set
{J} is non empty trivial 1 -element set
{J} --> xSQ is non empty Relation-like {J} -defined A -valued {xSQ} -valued Function-like constant total quasi_total Element of bool [:{J},{xSQ}:]
{xSQ} is non empty trivial 1 -element set
[:{J},{xSQ}:] is non empty Relation-like set
bool [:{J},{xSQ}:] is non empty set
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
dom (J .--> xSQ) is trivial Element of bool {J}
bool {J} is non empty set
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
rng (J .--> xSQ) is trivial Element of bool A
bool A is non empty set
{xSQ} is non empty trivial 1 -element Element of bool A
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is set
J is Element of bound_QC-variables Al
xSQ is non empty set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S . A is set
xSQ is Element of xSQ
(Al,xSQ,J,xSQ) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
{J} --> xSQ is non empty Relation-like {J} -defined xSQ -valued {xSQ} -valued Function-like constant total quasi_total Element of bool [:{J},{xSQ}:]
{xSQ} is non empty trivial 1 -element set
[:{J},{xSQ}:] is non empty Relation-like set
bool [:{J},{xSQ}:] is non empty set
(Al,xSQ,S,(Al,xSQ,J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,S,(Al,xSQ,J,xSQ)) . A is set
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
{J} --> xSQ is non empty Relation-like {J} -defined xSQ -valued Function-like constant total quasi_total Element of bool [:{J},xSQ:]
[:{J},xSQ:] is non empty Relation-like set
bool [:{J},xSQ:] is non empty set
[:{J},{xSQ}:] is non empty Relation-like set
dom ({J} --> xSQ) is non empty trivial 1 -element Element of bool {J}
bool {J} is non empty set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of bound_QC-variables Al
xSQ is non empty set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
xSQ is Element of xSQ
(Al,xSQ,A,xSQ) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{A} is non empty trivial 1 -element set
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
{A} --> xSQ is non empty Relation-like {A} -defined xSQ -valued {xSQ} -valued Function-like constant total quasi_total Element of bool [:{A},{xSQ}:]
{xSQ} is non empty trivial 1 -element set
[:{A},{xSQ}:] is non empty Relation-like set
bool [:{A},{xSQ}:] is non empty set
(Al,xSQ,S,(Al,xSQ,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,S,(Al,xSQ,A,xSQ)) . J is Element of xSQ
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
A .--> xSQ is trivial Relation-like bound_QC-variables Al -defined {A} -defined xSQ -valued Function-like one-to-one constant set
dom (A .--> xSQ) is trivial Element of bool {A}
bool {A} is non empty set
(A .--> xSQ) . J is set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
A is Element of CQC-WFF Al
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
xSQ is non empty set
K367(xSQ) is set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like QC-pred_symbols Al -defined K367(xSQ) -valued Function-like quasi_total interpretation of Al,xSQ
xSQ is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v is Element of xSQ
(Al,xSQ,J,v) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
{J} --> v is non empty Relation-like {J} -defined xSQ -valued {v} -valued Function-like constant total quasi_total Element of bool [:{J},{v}:]
{v} is non empty trivial 1 -element set
[:{J},{v}:] is non empty Relation-like set
bool [:{J},{v}:] is non empty set
(Al,xSQ,xSQ,(Al,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S1 is Element of bound_QC-variables Al
(Al,xSQ,xSQ,(Al,xSQ,J,v)) . S1 is Element of xSQ
xSQ . S1 is Element of xSQ
v is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v . J is Element of xSQ
dom v is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
(Al,xSQ,J,(v . J)) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
{J} --> (v . J) is non empty Relation-like {J} -defined xSQ -valued {(v . J)} -valued Function-like constant total quasi_total Element of bool [:{J},{(v . J)}:]
{(v . J)} is non empty trivial 1 -element set
[:{J},{(v . J)}:] is non empty Relation-like set
bool [:{J},{(v . J)}:] is non empty set
(Al,xSQ,xSQ,(Al,xSQ,J,(v . J))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
z is set
v . z is set
(Al,xSQ,xSQ,(Al,xSQ,J,(v . J))) . z is set
q is Element of bound_QC-variables Al
v . q is Element of xSQ
xSQ . q is Element of xSQ
Funcs ((bound_QC-variables Al),xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
z is Relation-like Function-like set
proj1 z is set
proj2 z is set
q is Relation-like Function-like set
proj1 q is set
proj2 q is set
Al is non empty Relation-like QC-alphabet
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-Sub-WFF Al
J is Element of bound_QC-variables Al
(Al,A,J) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{A,J} is non empty set
{A} is non empty trivial 1 -element set
{{A,J},{A}} is non empty set
S is non empty set
Valuations_in (Al,S) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,S
(Al,A) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (J,(Al,A)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,A,J)
RestrictSub (J,(All (J,(Al,A))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (J,(All (J,(Al,A))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined S -valued Function-like quasi_total Element of Valuations_in (Al,S)
(@ (RestrictSub (J,(All (J,(Al,A))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined S -valued Function-like Element of bool [:(bound_QC-variables Al),S:]
[:(bound_QC-variables Al),S:] is non empty Relation-like set
bool [:(bound_QC-variables Al),S:] is non empty set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
J is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
J +* xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like set
J +* xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom (J +* xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom J is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
(dom J) \/ (dom xSQ) is Element of bool (bound_QC-variables Al)
rng (J +* xSQ) is Element of bool A
bool A is non empty set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
proj2 (RestrictSub (A,(All (A,(Al,J))),xSQ)) is set
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
upVar ((RestrictSub (A,(All (A,(Al,J))),xSQ)),(Al,J)) is Element of QC-symbols Al
QC-symbols Al is non empty set
x. (upVar ((RestrictSub (A,(All (A,(Al,J))),xSQ)),(Al,J))) is Element of bound_QC-variables Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,J,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
(Al,J,A) `2 is Element of bound_QC-variables Al
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A))) is Element of CQC-WFF Al
All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
All (A,(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
bound_in (Al,(Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)) is Relation-like Function-like V52() Element of vSUB Al
proj2 (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) is set
the_scope_of (Al,(Al,(Al,J,A),xSQ)) is Element of QC-WFF Al
upVar ((RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))),(the_scope_of (Al,(Al,(Al,J,A),xSQ)))) is Element of QC-symbols Al
x. (upVar ((RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))),(the_scope_of (Al,(Al,(Al,J,A),xSQ))))) is Element of bound_QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
proj2 (RestrictSub (A,(All (A,(Al,J))),xSQ)) is set
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,J,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,(Al,J,A),xSQ)) is Element of CQC-WFF Al
(Al,J,A) `2 is Element of bound_QC-variables Al
(Al,(Al,J,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,J,A))) is Element of CQC-WFF Al
All (((Al,J,A) `2),(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
All (A,(Al,(Al,(Al,J,A)))) is Element of CQC-WFF Al
bound_in (Al,(Al,(Al,J,A),xSQ)) is Element of bound_QC-variables Al
(Al,(Al,J,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2)) is Relation-like Function-like V52() Element of vSUB Al
proj2 (RestrictSub ((bound_in (Al,(Al,(Al,J,A),xSQ))),(Al,(Al,(Al,J,A),xSQ)),((Al,(Al,J,A),xSQ) `2))) is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,S,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,S,A),xSQ)) is Element of bound_QC-variables Al
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
proj1 (RestrictSub (A,(All (A,(Al,S))),xSQ)) is set
S1 is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> S1 is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{S1}:]
{S1} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{S1}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{S1}:] is non empty set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S `2 is Relation-like Function-like Element of vSUB Al
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (S `2)) * (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,S,A,xSQ,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,S1) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> S1 is non empty Relation-like {A} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{A},{S1}:]
[:{A},{S1}:] is non empty Relation-like set
bool [:{A},{S1}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1))),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
ExpandSub (A,(Al,S),(RestrictSub (A,(All (A,(Al,S))),xSQ))) is Relation-like Function-like Element of vSUB Al
[A,A] is V1() Element of [:(bound_QC-variables Al),(bound_QC-variables Al):]
{A,A} is non empty set
{{A,A},{A}} is non empty set
{[A,A]} is non empty trivial Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like constant 1 -element Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
proj2 (RestrictSub (A,(All (A,(Al,S))),xSQ)) is set
p is Relation-like Function-like set
(RestrictSub (A,(All (A,(Al,S))),xSQ)) \/ p is Relation-like set
still_not-bound_in (All (A,(Al,S))) is Element of bool (bound_QC-variables Al)
proj1 xSQ is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (A,(Al,S))) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = A & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is set
(proj1 (RestrictSub (A,(All (A,(Al,S))),xSQ))) /\ {A} is Element of bool (bound_QC-variables Al)
b is set
xSQ | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (A,(Al,S))) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = A & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like Function-like Element of vSUB Al
@ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (A,(Al,S))) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = A & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like bound_QC-variables Al -defined { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (A,(Al,S))) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = A & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom (@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) is Element of bool (bound_QC-variables Al)
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (A,(Al,S))) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = A & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Element of bool (bound_QC-variables Al)
x is Element of bound_QC-variables Al
xSQ . x is set
dom {[A,A]} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
proj1 p is set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) \/ p is Relation-like set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) +* p is Relation-like Function-like set
Funcs ((bound_QC-variables Al),J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
proj2 p is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p is Relation-like J -valued Function-like set
proj1 ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) is set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
A .--> A is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -valued Function-like one-to-one constant set
{A} --> A is non empty Relation-like {A} -defined bound_QC-variables Al -valued {A} -valued Function-like constant total quasi_total Element of bool [:{A},{A}:]
[:{A},{A}:] is non empty Relation-like set
bool [:{A},{A}:] is non empty set
dom (Al,J,A,S1) is trivial Element of bool {A}
bool {A} is non empty set
a is set
(Al,J,A,S1) . a is set
((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) . a is set
p . a is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) . (p . a) is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * ((@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) +* p) is Relation-like J -valued Function-like set
((@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1))) +* ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) is Relation-like J -valued Function-like set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S)) is Element of QC-symbols Al
QC-symbols Al is non empty set
x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))) is Element of bound_QC-variables Al
[A,(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))] is V1() Element of [:(bound_QC-variables Al),(bound_QC-variables Al):]
{A,(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))} is non empty set
{{A,(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))},{A}} is non empty set
{[A,(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))]} is non empty trivial Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like constant 1 -element Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
b is set
x is Element of bound_QC-variables Al
xSQ . x is set
dom {[A,(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))]} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
p is Relation-like Function-like set
proj1 p is set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) \/ p is Relation-like set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) +* p is Relation-like Function-like set
proj2 p is set
{(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p is Relation-like J -valued Function-like set
proj1 ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) is set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
A .--> (x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S)))) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -valued Function-like one-to-one constant set
{A} --> (x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S)))) is non empty Relation-like {A} -defined bound_QC-variables Al -valued {(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))} -valued Function-like constant total quasi_total Element of bool [:{A},{(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))}:]
{(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))} is non empty trivial 1 -element set
[:{A},{(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))}:] is non empty Relation-like set
bool [:{A},{(x. (upVar ((RestrictSub (A,(All (A,(Al,S))),xSQ)),(Al,S))))}:] is non empty set
a is set
(Al,J,A,S1) . a is set
((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) . a is set
p . a is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) . (p . a) is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * ((@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) +* p) is Relation-like J -valued Function-like set
((@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1))) +* ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),S1)) * p) is Relation-like J -valued Function-like set
a is Relation-like Function-like set
proj1 a is set
proj2 a is set
(RestrictSub (A,(All (A,(Al,S))),xSQ)) \/ p is Relation-like set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{xSQ,A} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,A},{xSQ}} is non empty set
v is Relation-like Function-like second_Q_comp of (Al,xSQ,A)
(Al,(Al,xSQ,A),v) is Element of CQC-Sub-WFF Al
@ (Al,(Al,xSQ,A),v) is Element of [:(QC-WFF Al),(vSUB Al):]
QC-WFF Al is non empty set
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,xSQ,A),v)) is Element of bound_QC-variables Al
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,xSQ) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,q) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> q is non empty Relation-like {A} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{A},{q}:]
[:{A},{q}:] is non empty Relation-like set
bool [:{A},{q}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))),(Al,J,A,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)),(Al,J,(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))),(Al,J,A,q))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
xSQ `2 is Relation-like Function-like Element of vSUB Al
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (xSQ `2)) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
xSQ `2 is Relation-like Function-like Element of vSUB Al
@ (xSQ `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (xSQ `2)) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)),(Al,xSQ,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,xSQ) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,q) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> q is non empty Relation-like {A} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{A},{q}:]
[:{A},{q}:] is non empty Relation-like set
bool [:{A},{q}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))),(Al,J,A,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,S,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
QC-WFF Al is non empty set
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,S,A),xSQ)) is Element of bound_QC-variables Al
(Al,S,A,xSQ,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(Al,S) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:] is non empty set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,A,xSQ,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
Funcs ((bound_QC-variables Al),J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
rng (@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom xSQ is Element of bool (bound_QC-variables Al)
x is Relation-like Function-like set
proj1 x is set
proj2 x is set
dom (Al,S,A,xSQ,J,xSQ) is Element of bool (bound_QC-variables Al)
dom (@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) is Element of bool (bound_QC-variables Al)
dom (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) is Element of bool (bound_QC-variables Al)
x is Relation-like Function-like set
proj1 x is set
proj2 x is set
dom (Al,S,A,xSQ,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))) is Element of bool (bound_QC-variables Al)
x is set
(Al,S,A,xSQ,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))) . x is set
(Al,S,A,xSQ,J,xSQ) . x is set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) . x is set
proj2 (RestrictSub (A,(All (A,(Al,S))),xSQ)) is set
b is Element of bound_QC-variables Al
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) . b is Element of J
xSQ . b is Element of J
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{xSQ,A} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,A},{xSQ}} is non empty set
v is Relation-like Function-like second_Q_comp of (Al,xSQ,A)
(Al,(Al,xSQ,A),v) is Element of CQC-Sub-WFF Al
@ (Al,(Al,xSQ,A),v) is Element of [:(QC-WFF Al),(vSUB Al):]
QC-WFF Al is non empty set
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,xSQ,A),v)) is Element of bound_QC-variables Al
(Al,xSQ,A,v,J,S) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(Al,xSQ) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * S is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,A,q) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> q is non empty Relation-like {A} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{A},{q}:]
[:{A},{q}:] is non empty Relation-like set
bool [:{A},{q}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)),(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,q))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{q}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * (Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,q) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> q is non empty Relation-like {A} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{A},{q}:]
[:{A},{q}:] is non empty Relation-like set
bool [:{A},{q}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))),(Al,J,A,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q)),(Al,J,(Al,xSQ,A,v,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),q))),(Al,J,A,q))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Relation-like NAT -defined QC-variables Al -valued Function-like FinSequence-like FinSequence of QC-variables Al
rng A is Element of bool (QC-variables Al)
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
variables_in (A,(bound_QC-variables Al)) is Element of bool (bound_QC-variables Al)
len A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
{ (A . b<sub>1</sub>) where b<sub>1</sub> is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len A & A . b<sub>1</sub> in bound_QC-variables Al ) } is set
J is set
dom A is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V52() cardinal set
A . xSQ is set
Seg (len A) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
J is set
xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A . xSQ is set
Seg (len A) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
dom A is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of bound_QC-variables Al
{A} is non empty trivial 1 -element set
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
dom xSQ is Element of bool (bound_QC-variables Al)
S is Element of J
(Al,J,A,S) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
{A} --> S is non empty Relation-like {A} -defined J -valued {S} -valued Function-like constant total quasi_total Element of bool [:{A},{S}:]
{S} is non empty trivial 1 -element set
[:{A},{S}:] is non empty Relation-like set
bool [:{A},{S}:] is non empty set
dom (Al,J,A,S) is trivial Element of bool {A}
bool {A} is non empty set
Funcs ((bound_QC-variables Al),J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like Function-like set
proj1 xSQ is set
proj2 xSQ is set
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
xSQ *' S is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
still_not-bound_in S is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
xSQ | (still_not-bound_in S) is Relation-like bound_QC-variables Al -defined still_not-bound_in S -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
S * (xSQ | (still_not-bound_in S)) is Relation-like NAT -defined J -valued Function-like Element of bool [:NAT,J:]
[:NAT,J:] is non empty Relation-like V52() set
bool [:NAT,J:] is non empty V52() set
rng S is Element of bool (QC-variables Al)
dom (xSQ | (still_not-bound_in S)) is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
(dom xSQ) /\ (still_not-bound_in S) is Element of bool (bound_QC-variables Al)
(bound_QC-variables Al) /\ (still_not-bound_in S) is Element of bool (bound_QC-variables Al)
dom (S * (xSQ | (still_not-bound_in S))) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
dom S is V45() V46() V47() V48() V49() V50() V63() A -element Element of bool NAT
len S is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Seg (len S) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
xSQ is Relation-like Function-like FinSequence-like set
len xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
proj1 xSQ is set
Seg A is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
v is ext-real epsilon-transitive epsilon-connected ordinal natural V52() cardinal set
xSQ . v is set
(xSQ *' S) . v is set
S1 is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
S . S1 is set
(xSQ | (still_not-bound_in S)) . (S . S1) is set
xSQ . (S . S1) is set
(xSQ *' S) . S1 is set
len (xSQ *' S) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
S ! xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
still_not-bound_in (S ! xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
v is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
v | (still_not-bound_in (S ! xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (S ! xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 | (still_not-bound_in (S ! xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (S ! xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
still_not-bound_in xSQ is Element of bool (bound_QC-variables Al)
S1 *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
xSQ . S is Element of K367(J)
Valid ((S ! xSQ),xSQ) is Relation-like Valuations_in (Al,J) -defined K370() -valued Function-like quasi_total Element of Funcs ((Valuations_in (Al,J)),K370())
Funcs ((Valuations_in (Al,J)),K370()) is non empty FUNCTION_DOMAIN of Valuations_in (Al,J),K370()
(Valid ((S ! xSQ),xSQ)) . S1 is Element of K370()
(Valid ((S ! xSQ),xSQ)) . v is Element of K370()
v *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
S1 | (still_not-bound_in xSQ) is Relation-like bound_QC-variables Al -defined still_not-bound_in xSQ -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
xSQ * (S1 | (still_not-bound_in xSQ)) is Relation-like NAT -defined J -valued Function-like Element of bool [:NAT,J:]
[:NAT,J:] is non empty Relation-like V52() set
bool [:NAT,J:] is non empty V52() set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
'not' A is Element of CQC-WFF Al
still_not-bound_in ('not' A) is Element of bool (bound_QC-variables Al)
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S | (still_not-bound_in ('not' A)) is Relation-like bound_QC-variables Al -defined still_not-bound_in ('not' A) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ | (still_not-bound_in ('not' A)) is Relation-like bound_QC-variables Al -defined still_not-bound_in ('not' A) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of CQC-WFF Al
still_not-bound_in J is Element of bool (bound_QC-variables Al)
A '&' J is Element of CQC-WFF Al
still_not-bound_in (A '&' J) is Element of bool (bound_QC-variables Al)
xSQ is non empty set
K367(xSQ) is set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like QC-pred_symbols Al -defined K367(xSQ) -valued Function-like quasi_total interpretation of Al,xSQ
(still_not-bound_in A) \/ (still_not-bound_in J) is Element of bool (bound_QC-variables Al)
v is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v | (still_not-bound_in (A '&' J)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (A '&' J) -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
S1 is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S1 | (still_not-bound_in (A '&' J)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (A '&' J) -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
v | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
S1 | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
v | (still_not-bound_in J) is Relation-like bound_QC-variables Al -defined still_not-bound_in J -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
S1 | (still_not-bound_in J) is Relation-like bound_QC-variables Al -defined still_not-bound_in J -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of J
(Al,J,A,S) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
{A} --> S is non empty Relation-like {A} -defined J -valued {S} -valued Function-like constant total quasi_total Element of bool [:{A},{S}:]
{S} is non empty trivial 1 -element set
[:{A},{S}:] is non empty Relation-like set
bool [:{A},{S}:] is non empty set
(Al,J,xSQ,(Al,J,A,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is set
xSQ | xSQ is Relation-like bound_QC-variables Al -defined xSQ -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom (xSQ | xSQ) is Element of bool xSQ
bool xSQ is non empty set
(Al,J,xSQ,(Al,J,A,S)) | xSQ is Relation-like bound_QC-variables Al -defined xSQ -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom ((Al,J,xSQ,(Al,J,A,S)) | xSQ) is Element of bool xSQ
dom (Al,J,xSQ,(Al,J,A,S)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
(dom (Al,J,xSQ,(Al,J,A,S))) /\ xSQ is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
(dom xSQ) /\ xSQ is Element of bool (bound_QC-variables Al)
(bound_QC-variables Al) /\ xSQ is Element of bool (QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
xSQ is non empty set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
xSQ | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
v is Element of xSQ
(Al,xSQ,J,v) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> v is non empty Relation-like {J} -defined xSQ -valued {v} -valued Function-like constant total quasi_total Element of bool [:{J},{v}:]
{v} is non empty trivial 1 -element set
[:{J},{v}:] is non empty Relation-like set
bool [:{J},{v}:] is non empty set
(Al,xSQ,S,(Al,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,xSQ,(Al,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom (S | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
dom ((Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
dom ((Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
S1 is set
((Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A)) . S1 is set
((Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A)) . S1 is set
(Al,xSQ,S,(Al,xSQ,J,v)) . S1 is set
(Al,xSQ,xSQ,(Al,xSQ,J,v)) . S1 is set
(S | (still_not-bound_in A)) . S1 is set
S . S1 is set
dom (xSQ | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
xSQ . S1 is set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(still_not-bound_in (All (J,A))) \/ {J} is non empty Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
{J} \/ ((still_not-bound_in A) \ {J}) is non empty Element of bool (bound_QC-variables Al)
{J} \/ (still_not-bound_in A) is non empty Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
xSQ is non empty set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S | ((still_not-bound_in A) \ {J}) is Relation-like bound_QC-variables Al -defined (still_not-bound_in A) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
xSQ | ((still_not-bound_in A) \ {J}) is Relation-like bound_QC-variables Al -defined (still_not-bound_in A) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
v is Element of xSQ
(Al,xSQ,J,v) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> v is non empty Relation-like {J} -defined xSQ -valued {v} -valued Function-like constant total quasi_total Element of bool [:{J},{v}:]
{v} is non empty trivial 1 -element set
[:{J},{v}:] is non empty Relation-like set
bool [:{J},{v}:] is non empty set
(Al,xSQ,S,(Al,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,xSQ,(Al,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom ((Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
dom ((Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A)) is Element of bool (bound_QC-variables Al)
S1 is set
((Al,xSQ,S,(Al,xSQ,J,v)) | (still_not-bound_in A)) . S1 is set
((Al,xSQ,xSQ,(Al,xSQ,J,v)) | (still_not-bound_in A)) . S1 is set
(Al,xSQ,S,(Al,xSQ,J,v)) . S1 is set
(Al,xSQ,xSQ,(Al,xSQ,J,v)) . S1 is set
dom (xSQ | ((still_not-bound_in A) \ {J})) is Element of bool ((still_not-bound_in A) \ {J})
bool ((still_not-bound_in A) \ {J}) is non empty set
(xSQ | ((still_not-bound_in A) \ {J})) . S1 is set
xSQ . S1 is set
S . S1 is set
dom (S | ((still_not-bound_in A) \ {J})) is Element of bool ((still_not-bound_in A) \ {J})
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
xSQ is non empty set
K367(xSQ) is set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
S is Relation-like QC-pred_symbols Al -defined K367(xSQ) -valued Function-like quasi_total interpretation of Al,xSQ
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
v is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v | (still_not-bound_in (All (J,A))) is Relation-like bound_QC-variables Al -defined still_not-bound_in (All (J,A)) -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
S1 is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S1 | (still_not-bound_in (All (J,A))) is Relation-like bound_QC-variables Al -defined still_not-bound_in (All (J,A)) -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
v | ((still_not-bound_in A) \ {J}) is Relation-like bound_QC-variables Al -defined (still_not-bound_in A) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
S1 | ((still_not-bound_in A) \ {J}) is Relation-like bound_QC-variables Al -defined (still_not-bound_in A) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z is Element of xSQ
(Al,xSQ,J,z) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> z is non empty Relation-like {J} -defined xSQ -valued {z} -valued Function-like constant total quasi_total Element of bool [:{J},{z}:]
{z} is non empty trivial 1 -element set
[:{J},{z}:] is non empty Relation-like set
bool [:{J},{z}:] is non empty set
(Al,xSQ,v,(Al,xSQ,J,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,v,(Al,xSQ,J,z)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,S1,(Al,xSQ,J,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,S1,(Al,xSQ,J,z)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z is Element of xSQ
(Al,xSQ,J,z) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> z is non empty Relation-like {J} -defined xSQ -valued {z} -valued Function-like constant total quasi_total Element of bool [:{J},{z}:]
{z} is non empty trivial 1 -element set
[:{J},{z}:] is non empty Relation-like set
bool [:{J},{z}:] is non empty set
(Al,xSQ,S1,(Al,xSQ,J,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,v,(Al,xSQ,J,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,v,(Al,xSQ,J,z)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,S1,(Al,xSQ,J,z)) | (still_not-bound_in A) is Relation-like bound_QC-variables Al -defined still_not-bound_in A -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z is Element of xSQ
(Al,xSQ,J,z) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> z is non empty Relation-like {J} -defined xSQ -valued {z} -valued Function-like constant total quasi_total Element of bool [:{J},{z}:]
{z} is non empty trivial 1 -element set
[:{J},{z}:] is non empty Relation-like set
bool [:{J},{z}:] is non empty set
(Al,xSQ,v,(Al,xSQ,J,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
q is Element of xSQ
(Al,xSQ,J,q) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} --> q is non empty Relation-like {J} -defined xSQ -valued {q} -valued Function-like constant total quasi_total Element of bool [:{J},{q}:]
{q} is non empty trivial 1 -element set
[:{J},{q}:] is non empty Relation-like set
bool [:{J},{q}:] is non empty set
(Al,xSQ,S1,(Al,xSQ,J,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
VERUM Al is Element of CQC-WFF Al
still_not-bound_in (VERUM Al) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
xSQ -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
xSQ | (still_not-bound_in (VERUM Al)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (VERUM Al) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
S is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
S | (still_not-bound_in (VERUM Al)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (VERUM Al) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
z is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
S1 is Element of xSQ -ary_QC-pred_symbols Al
v is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like xSQ -element FinSequence-like FinSequence of QC-variables Al
S1 ! v is Element of CQC-WFF Al
still_not-bound_in (S1 ! v) is Element of bool (bound_QC-variables Al)
z | (still_not-bound_in (S1 ! v)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (S1 ! v) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
q is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
q | (still_not-bound_in (S1 ! v)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (S1 ! v) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
p is Element of CQC-WFF Al
still_not-bound_in p is Element of bool (bound_QC-variables Al)
a is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
'not' p is Element of CQC-WFF Al
still_not-bound_in ('not' p) is Element of bool (bound_QC-variables Al)
a | (still_not-bound_in ('not' p)) is Relation-like bound_QC-variables Al -defined still_not-bound_in ('not' p) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
x is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
x | (still_not-bound_in ('not' p)) is Relation-like bound_QC-variables Al -defined still_not-bound_in ('not' p) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
b is Element of CQC-WFF Al
still_not-bound_in b is Element of bool (bound_QC-variables Al)
x is Element of CQC-WFF Al
still_not-bound_in x is Element of bool (bound_QC-variables Al)
e2 is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
b '&' x is Element of CQC-WFF Al
still_not-bound_in (b '&' x) is Element of bool (bound_QC-variables Al)
e2 | (still_not-bound_in (b '&' x)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (b '&' x) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
c<sub>17</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>17</sub> | (still_not-bound_in (b '&' x)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (b '&' x) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
c<sub>18</sub> is Element of CQC-WFF Al
still_not-bound_in c<sub>18</sub> is Element of bool (bound_QC-variables Al)
c<sub>20</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>19</sub> is Element of bound_QC-variables Al
All (c<sub>19</sub>,c<sub>18</sub>) is Element of CQC-WFF Al
still_not-bound_in (All (c<sub>19</sub>,c<sub>18</sub>)) is Element of bool (bound_QC-variables Al)
c<sub>20</sub> | (still_not-bound_in (All (c<sub>19</sub>,c<sub>18</sub>))) is Relation-like bound_QC-variables Al -defined still_not-bound_in (All (c<sub>19</sub>,c<sub>18</sub>)) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
c<sub>21</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>21</sub> | (still_not-bound_in (All (c<sub>19</sub>,c<sub>18</sub>))) is Relation-like bound_QC-variables Al -defined still_not-bound_in (All (c<sub>19</sub>,c<sub>18</sub>)) -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
still_not-bound_in (Al,S) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
@ (Al,(Al,S,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,S,A),xSQ)) is Element of bound_QC-variables Al
(Al,S,A,xSQ,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
v is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> v is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {v} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{v}:]
{v} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{v}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{v}:] is non empty set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,A,v) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> v is non empty Relation-like {A} -defined J -valued {v} -valued Function-like constant total quasi_total Element of bool [:{A},{v}:]
[:{A},{v}:] is non empty Relation-like set
bool [:{A},{v}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,S) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,S) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom (Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) is Element of bool (bound_QC-variables Al)
dom (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) is Element of bool (bound_QC-variables Al)
dom (Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) is Element of bool (bound_QC-variables Al)
(dom (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v))) \/ (dom (Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
dom (Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) is Element of bool (bound_QC-variables Al)
proj2 (RestrictSub (A,(All (A,(Al,S))),xSQ)) is set
b is set
(Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) . b is set
(Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) . b is set
dom (Al,J,A,v) is trivial Element of bool {A}
bool {A} is non empty set
dom (Al,S,A,xSQ,J,xSQ) is Element of bool (bound_QC-variables Al)
(dom (Al,S,A,xSQ,J,xSQ)) \/ (dom (Al,J,A,v)) is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) . b is set
x is Element of bound_QC-variables Al
xSQ . x is Element of J
(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) . b is set
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
dom ((Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S))) is Element of bool (bound_QC-variables Al)
((dom (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v))) \/ (dom (Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)))) /\ (still_not-bound_in (Al,S)) is Element of bool (bound_QC-variables Al)
Bound_Vars (Al,S) is V52() Element of bool (bound_QC-variables Al)
b is set
((Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S))) . b is set
((Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S))) . b is set
xSQ | (still_not-bound_in (Al,S)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,S) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,S) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(xSQ | (still_not-bound_in (Al,S))),((Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) | (still_not-bound_in (Al,S)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,S) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) | (still_not-bound_in (Al,S))),((Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) | (still_not-bound_in (Al,S))) is Element of bool (bound_QC-variables Al)
dom ((Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S))) is Element of bool (bound_QC-variables Al)
(dom ((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) | (still_not-bound_in (Al,S)))) \/ (dom ((Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S)))) is Element of bool (bound_QC-variables Al)
(dom (Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v))) /\ (still_not-bound_in (Al,S)) is Element of bool (bound_QC-variables Al)
(dom xSQ) /\ (still_not-bound_in (Al,S)) is Element of bool (bound_QC-variables Al)
((Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) | (still_not-bound_in (Al,S))) . b is set
(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)) . b is set
xSQ . b is set
(xSQ | (still_not-bound_in (Al,S))) . b is set
((Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)) | (still_not-bound_in (Al,S))) . b is set
dom ((Al,J,xSQ,(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v))) | (still_not-bound_in (Al,S))) is Element of bool (bound_QC-variables Al)
(dom (Al,J,(Al,J,xSQ,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),v)),(Al,J,(Al,S,A,xSQ,J,xSQ),(Al,J,A,v)))) /\ (still_not-bound_in (Al,S)) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{xSQ,A} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,A},{xSQ}} is non empty set
v is Relation-like Function-like second_Q_comp of (Al,xSQ,A)
(Al,(Al,xSQ,A),v) is Element of CQC-Sub-WFF Al
@ (Al,(Al,xSQ,A),v) is Element of [:(QC-WFF Al),(vSUB Al):]
QC-WFF Al is non empty set
vSUB Al is non empty functional set
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,xSQ,A),v)) is Element of bound_QC-variables Al
(Al,xSQ,A,v,J,S) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(Al,xSQ) is Element of CQC-WFF Al
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * S is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
still_not-bound_in (Al,xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
p is Element of J
(Al,J,A,p) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> p is non empty Relation-like {A} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{A},{p}:]
{p} is non empty trivial 1 -element set
[:{A},{p}:] is non empty Relation-like set
bool [:{A},{p}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:]
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)),(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)),(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) | (still_not-bound_in (Al,xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) | (still_not-bound_in (Al,xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
still_not-bound_in (Al,xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
p is Element of J
(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,xSQ,A),v)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,xSQ,A),v)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:]
{p} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,xSQ,A),v)))},{p}:] is non empty set
(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,A,p) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> p is non empty Relation-like {A} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{A},{p}:]
[:{A},{p}:] is non empty Relation-like set
bool [:{A},{p}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)),(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,J,S,(Al,J,(S_Bound (@ (Al,(Al,xSQ,A),v))),p)),(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) | (still_not-bound_in (Al,xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,p))) | (still_not-bound_in (Al,xSQ)) is Relation-like bound_QC-variables Al -defined still_not-bound_in (Al,xSQ) -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,S,A,xSQ,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom (Al,S,A,xSQ,J,xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
proj1 (RestrictSub (A,(All (A,(Al,S))),xSQ)) is set
rng (@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
dom (@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) is Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{xSQ,A} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,A},{xSQ}} is non empty set
v is Relation-like Function-like second_Q_comp of (Al,xSQ,A)
(Al,xSQ,A,v,J,S) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(Al,xSQ) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * S is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,xSQ,A,v,J,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 is Element of J
(Al,J,A,S1) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> S1 is non empty Relation-like {A} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{A},{S1}:]
{S1} is non empty trivial 1 -element set
[:{A},{S1}:] is non empty Relation-like set
bool [:{A},{S1}:] is non empty set
(Al,J,(Al,J,S,(Al,xSQ,A,v,J,S)),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,S1))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 is Element of J
(Al,J,A,S1) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> S1 is non empty Relation-like {A} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{A},{S1}:]
{S1} is non empty trivial 1 -element set
[:{A},{S1}:] is non empty Relation-like set
bool [:{A},{S1}:] is non empty set
(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,xSQ,A,v,J,S),(Al,J,A,S1))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,(Al,J,S,(Al,xSQ,A,v,J,S)),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Element of CQC-Sub-WFF Al
(Al,xSQ,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{xSQ,A} is non empty set
{xSQ} is non empty trivial 1 -element set
{{xSQ,A},{xSQ}} is non empty set
(Al,xSQ) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
v is Relation-like Function-like second_Q_comp of (Al,xSQ,A)
(Al,xSQ,A,v,J,S) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
All (A,(Al,xSQ)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,xSQ))),v) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (A,(All (A,(Al,xSQ))),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,xSQ))),v))) * S is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,xSQ,A,v,J,S)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 is Element of J
(Al,J,A,S1) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> S1 is non empty Relation-like {A} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{A},{S1}:]
{S1} is non empty trivial 1 -element set
[:{A},{S1}:] is non empty Relation-like set
bool [:{A},{S1}:] is non empty set
(Al,J,(Al,J,S,(Al,xSQ,A,v,J,S)),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 is Element of J
(Al,J,A,S1) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> S1 is non empty Relation-like {A} -defined J -valued {S1} -valued Function-like constant total quasi_total Element of bool [:{A},{S1}:]
{S1} is non empty trivial 1 -element set
[:{A},{S1}:] is non empty Relation-like set
bool [:{A},{S1}:] is non empty set
(Al,J,(Al,J,S,(Al,xSQ,A,v,J,S)),(Al,J,A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
Al is non empty Relation-like QC-alphabet
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
still_not-bound_in xSQ is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom xSQ is Element of bool (bound_QC-variables Al)
(Al,J,S,xSQ) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,S,xSQ) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
v is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom v is Element of bool (bound_QC-variables Al)
(Al,J,xSQ,v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,J,(Al,J,xSQ,v),S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
len ((Al,J,S,xSQ) *' xSQ) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
dom ((Al,J,S,xSQ) *' xSQ) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
Seg A is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
len ((Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) *' xSQ) is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
p is ext-real epsilon-transitive epsilon-connected ordinal natural V52() cardinal set
((Al,J,S,xSQ) *' xSQ) . p is set
((Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) *' xSQ) . p is set
dom ((Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) *' xSQ) is V45() V46() V47() V48() V49() V50() V63() Element of bool NAT
dom xSQ is V45() V46() V47() V48() V49() V50() V63() A -element Element of bool NAT
a is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
xSQ . a is set
dom (Al,J,(Al,J,xSQ,v),S1) is Element of bool (bound_QC-variables Al)
len xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
x is Element of bound_QC-variables Al
{ (xSQ . b<sub>1</sub>) where b<sub>1</sub> is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT : ( 1 <= b<sub>1</sub> & b<sub>1</sub> <= len xSQ & xSQ . b<sub>1</sub> in bound_QC-variables Al ) } is set
variables_in (xSQ,(bound_QC-variables Al)) is Element of bool (bound_QC-variables Al)
(Al,J,(Al,J,xSQ,v),S1) . x is set
(Al,J,xSQ,v) . x is set
dom (Al,J,xSQ,v) is Element of bool (bound_QC-variables Al)
xSQ . x is set
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) . x is set
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) . x is Element of J
(Al,J,S,xSQ) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,xSQ) . x is set
((Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) *' xSQ) . a is set
(Al,J,S,xSQ) . x is Element of J
S1 . x is set
S . x is Element of J
(Al,J,S,xSQ) . (xSQ . a) is set
S . (xSQ . a) is set
((Al,J,S,xSQ) *' xSQ) . a is set
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) . (xSQ . a) is set
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
A -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Element of A -ary_QC-pred_symbols Al
xSQ is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like A -element FinSequence-like FinSequence of QC-variables Al
S ! xSQ is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
still_not-bound_in (S ! xSQ) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
v is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,J,v,S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
z is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom z is Element of bool (bound_QC-variables Al)
(Al,J,S1,z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
q is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom q is Element of bool (bound_QC-variables Al)
(Al,J,(Al,J,S1,z),q) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,v,(Al,J,(Al,J,S1,z),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
still_not-bound_in xSQ is Element of bool (bound_QC-variables Al)
p is Element of bound_QC-variables Al
(Al,J,v,(Al,J,(Al,J,S1,z),q)) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
xSQ . S is Element of K367(J)
Valid ((S ! xSQ),xSQ) is Relation-like Valuations_in (Al,J) -defined K370() -valued Function-like quasi_total Element of Funcs ((Valuations_in (Al,J)),K370())
Funcs ((Valuations_in (Al,J)),K370()) is non empty FUNCTION_DOMAIN of Valuations_in (Al,J),K370()
(Valid ((S ! xSQ),xSQ)) . (Al,J,v,(Al,J,(Al,J,S1,z),q)) is Element of K370()
(Valid ((S ! xSQ),xSQ)) . (Al,J,v,S1) is Element of K370()
(Al,J,v,S1) *' xSQ is Relation-like NAT -defined J -valued Function-like FinSequence-like FinSequence of J
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
'not' A is Element of CQC-WFF Al
still_not-bound_in ('not' A) is Element of bool (bound_QC-variables Al)
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom xSQ is Element of bool (bound_QC-variables Al)
(Al,J,S,xSQ) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
v is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom v is Element of bool (bound_QC-variables Al)
(Al,J,xSQ,v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,J,(Al,J,xSQ,v),S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S,(Al,J,(Al,J,xSQ,v),S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
z is Element of bound_QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-pred_symbols Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of CQC-WFF Al
still_not-bound_in J is Element of bool (bound_QC-variables Al)
A '&' J is Element of CQC-WFF Al
still_not-bound_in (A '&' J) is Element of bool (bound_QC-variables Al)
xSQ is non empty set
K367(xSQ) is set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
S is Relation-like QC-pred_symbols Al -defined K367(xSQ) -valued Function-like quasi_total interpretation of Al,xSQ
xSQ is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom v is Element of bool (bound_QC-variables Al)
(Al,xSQ,xSQ,v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S1 is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,xSQ,v,S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom z is Element of bool (bound_QC-variables Al)
(Al,xSQ,(Al,xSQ,v,S1),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
q is Element of bound_QC-variables Al
(still_not-bound_in A) \/ (still_not-bound_in J) is Element of bool (bound_QC-variables Al)
q is Element of bound_QC-variables Al
p is Element of bound_QC-variables Al
q is Element of bound_QC-variables Al
p is Element of bound_QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
xSQ is non empty set
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
S is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom S is Element of bool (bound_QC-variables Al)
(dom S) \ {J} is Element of bool (bound_QC-variables Al)
xSQ is Element of bound_QC-variables Al
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
{J} \/ ((still_not-bound_in A) \ {J}) is non empty Element of bool (bound_QC-variables Al)
{J} \/ (still_not-bound_in A) is non empty Element of bool (bound_QC-variables Al)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of bound_QC-variables Al
{A} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom S is Element of bool (bound_QC-variables Al)
(Al,J,xSQ,S) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
xSQ is Relation-like Function-like set
proj1 xSQ is set
(proj1 xSQ) \ {A} is Element of bool (proj1 xSQ)
bool (proj1 xSQ) is non empty set
xSQ | ((proj1 xSQ) \ {A}) is Relation-like Function-like set
v is Element of bound_QC-variables Al
(xSQ | ((proj1 xSQ) \ {A})) . v is set
(Al,J,xSQ,S) . v is Element of J
(proj1 xSQ) /\ ((proj1 xSQ) \ {A}) is Element of bool (proj1 xSQ)
xSQ . v is set
xSQ . v is Element of J
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
xSQ is non empty set
K367(xSQ) is set
Valuations_in (Al,xSQ) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,xSQ
[:(bound_QC-variables Al),xSQ:] is non empty Relation-like set
bool [:(bound_QC-variables Al),xSQ:] is non empty set
S is Relation-like QC-pred_symbols Al -defined K367(xSQ) -valued Function-like quasi_total interpretation of Al,xSQ
xSQ is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
v is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom v is Element of bool (bound_QC-variables Al)
(Al,xSQ,xSQ,v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
S1 is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,xSQ,v,S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z is Relation-like bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom z is Element of bool (bound_QC-variables Al)
(Al,xSQ,(Al,xSQ,v,S1),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(dom S1) \ {J} is Element of bool (bound_QC-variables Al)
S1 | ((dom S1) \ {J}) is Relation-like bound_QC-variables Al -defined (dom S1) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(dom z) \ {J} is Element of bool (bound_QC-variables Al)
z | ((dom z) \ {J}) is Relation-like bound_QC-variables Al -defined (dom z) \ {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
dom (z | ((dom z) \ {J})) is Element of bool ((dom z) \ {J})
bool ((dom z) \ {J}) is non empty set
a is Element of bound_QC-variables Al
(z | ((dom z) \ {J})) . a is set
(Al,xSQ,xSQ,v) . a is Element of xSQ
dom (S1 | ((dom S1) \ {J})) is Element of bool ((dom S1) \ {J})
bool ((dom S1) \ {J}) is non empty set
a is Element of bound_QC-variables Al
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
dom (Al,xSQ,J,a) is trivial Element of bool {J}
bool {J} is non empty set
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
dom (Al,xSQ,J,a) is trivial Element of bool {J}
bool {J} is non empty set
(Al,xSQ,xSQ,v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,J,a)),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,J,a)),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,J,a),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,(Al,xSQ,J,a),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,(Al,xSQ,J,a),(z | ((dom z) \ {J}))))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(z | ((dom z) \ {J})),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,(z | ((dom z) \ {J})),(Al,xSQ,J,a))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(S1 | ((dom S1) \ {J})),(Al,xSQ,(z | ((dom z) \ {J})),(Al,xSQ,J,a)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(S1 | ((dom S1) \ {J})),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(S1 | ((dom S1) \ {J})),(z | ((dom z) \ {J}))),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(S1 | ((dom S1) \ {J})),(z | ((dom z) \ {J}))),(Al,xSQ,J,a))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
S1 . J is set
J .--> (S1 . J) is trivial Relation-like bound_QC-variables Al -defined {J} -defined Function-like one-to-one constant set
{J} --> (S1 . J) is non empty Relation-like {J} -defined {(S1 . J)} -valued Function-like constant total quasi_total Element of bool [:{J},{(S1 . J)}:]
{(S1 . J)} is non empty trivial 1 -element set
[:{J},{(S1 . J)}:] is non empty Relation-like set
bool [:{J},{(S1 . J)}:] is non empty set
(S1 | ((dom S1) \ {J})) +* (J .--> (S1 . J)) is Relation-like bound_QC-variables Al -defined Function-like set
z | (dom z) is Relation-like bound_QC-variables Al -defined dom z -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(z | ((dom z) \ {J})) +* {} is Relation-like Function-like set
dom (J .--> (S1 . J)) is trivial Element of bool {J}
proj1 {} is empty Relation-like non-empty empty-yielding Function-like one-to-one constant functional ext-real non positive non negative epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V45() V46() V47() V48() V49() V50() V51() V52() V63() V64() V65() V66() cardinal {} -element Function-yielding V82() set
(Al,xSQ,S1,z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,S1,z),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,S1,z),(Al,xSQ,J,a))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
z . J is set
J .--> (z . J) is trivial Relation-like bound_QC-variables Al -defined {J} -defined Function-like one-to-one constant set
{J} --> (z . J) is non empty Relation-like {J} -defined {(z . J)} -valued Function-like constant total quasi_total Element of bool [:{J},{(z . J)}:]
{(z . J)} is non empty trivial 1 -element set
[:{J},{(z . J)}:] is non empty Relation-like set
bool [:{J},{(z . J)}:] is non empty set
dom (J .--> (z . J)) is trivial Element of bool {J}
(z | ((dom z) \ {J})) +* (J .--> (z . J)) is Relation-like bound_QC-variables Al -defined Function-like set
S1 | (dom S1) is Relation-like bound_QC-variables Al -defined dom S1 -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(S1 | ((dom S1) \ {J})) +* {} is Relation-like Function-like set
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,S1,z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,S1,z)),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,xSQ,v),S1),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,(Al,xSQ,xSQ,v),S1),z),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,xSQ,(Al,xSQ,v,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,v,S1)),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,v,S1)),z),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
dom (Al,xSQ,J,a) is trivial Element of bool {J}
bool {J} is non empty set
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)),(Al,xSQ,J,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
a is Element of xSQ
(Al,xSQ,J,a) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} is non empty trivial 1 -element set
{J} --> a is non empty Relation-like {J} -defined xSQ -valued {a} -valued Function-like constant total quasi_total Element of bool [:{J},{a}:]
{a} is non empty trivial 1 -element set
[:{J},{a}:] is non empty Relation-like set
bool [:{J},{a}:] is non empty set
(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,a),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
x is Element of xSQ
(Al,xSQ,J,x) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} --> x is non empty Relation-like {J} -defined xSQ -valued {x} -valued Function-like constant total quasi_total Element of bool [:{J},{x}:]
{x} is non empty trivial 1 -element set
[:{J},{x}:] is non empty Relation-like set
bool [:{J},{x}:] is non empty set
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,J,x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
b is Element of xSQ
(Al,xSQ,J,b) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} --> b is non empty Relation-like {J} -defined xSQ -valued {b} -valued Function-like constant total quasi_total Element of bool [:{J},{b}:]
{b} is non empty trivial 1 -element set
[:{J},{b}:] is non empty Relation-like set
bool [:{J},{b}:] is non empty set
(Al,xSQ,(Al,xSQ,J,b),(S1 | ((dom S1) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,(Al,xSQ,J,b),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J}))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like Element of bool [:(bound_QC-variables Al),xSQ:]
(Al,xSQ,(Al,xSQ,xSQ,v),(Al,xSQ,(Al,xSQ,(Al,xSQ,J,b),(S1 | ((dom S1) \ {J}))),(z | ((dom z) \ {J})))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
x is Element of xSQ
(Al,xSQ,J,x) is trivial Relation-like bound_QC-variables Al -defined {J} -defined bound_QC-variables Al -defined xSQ -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),xSQ:]
{J} --> x is non empty Relation-like {J} -defined xSQ -valued {x} -valued Function-like constant total quasi_total Element of bool [:{J},{x}:]
{x} is non empty trivial 1 -element set
[:{J},{x}:] is non empty Relation-like set
bool [:{J},{x}:] is non empty set
(Al,xSQ,(Al,xSQ,xSQ,(Al,xSQ,(Al,xSQ,v,S1),z)),(Al,xSQ,J,x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined xSQ -valued Function-like quasi_total Element of Valuations_in (Al,xSQ)
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
VERUM Al is Element of CQC-WFF Al
still_not-bound_in (VERUM Al) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
S1 is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
S1 -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom xSQ is Element of bool (bound_QC-variables Al)
v is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom v is Element of bool (bound_QC-variables Al)
xSQ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
S is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom S is Element of bool (bound_QC-variables Al)
(Al,A,xSQ,S) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,A,S,xSQ) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,(Al,A,S,xSQ),v) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,xSQ,(Al,A,(Al,A,S,xSQ),v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
x is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom x is Element of bool (bound_QC-variables Al)
q is Element of S1 -ary_QC-pred_symbols Al
z is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like S1 -element FinSequence-like FinSequence of QC-variables Al
q ! z is Element of CQC-WFF Al
still_not-bound_in (q ! z) is Element of bool (bound_QC-variables Al)
b is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom b is Element of bool (bound_QC-variables Al)
p is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
a is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom a is Element of bool (bound_QC-variables Al)
(Al,A,p,a) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,A,a,x) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,(Al,A,a,x),b) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,p,(Al,A,(Al,A,a,x),b)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
x is Element of CQC-WFF Al
still_not-bound_in x is Element of bool (bound_QC-variables Al)
c<sub>18</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>18</sub> is Element of bool (bound_QC-variables Al)
'not' x is Element of CQC-WFF Al
still_not-bound_in ('not' x) is Element of bool (bound_QC-variables Al)
c<sub>19</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>19</sub> is Element of bool (bound_QC-variables Al)
e2 is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>17</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>17</sub> is Element of bool (bound_QC-variables Al)
(Al,A,e2,c<sub>17</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,A,c<sub>17</sub>,c<sub>18</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,(Al,A,c<sub>17</sub>,c<sub>18</sub>),c<sub>19</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,e2,(Al,A,(Al,A,c<sub>17</sub>,c<sub>18</sub>),c<sub>19</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>20</sub> is Element of CQC-WFF Al
still_not-bound_in c<sub>20</sub> is Element of bool (bound_QC-variables Al)
c<sub>21</sub> is Element of CQC-WFF Al
still_not-bound_in c<sub>21</sub> is Element of bool (bound_QC-variables Al)
c<sub>24</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>24</sub> is Element of bool (bound_QC-variables Al)
c<sub>20</sub> '&' c<sub>21</sub> is Element of CQC-WFF Al
still_not-bound_in (c<sub>20</sub> '&' c<sub>21</sub>) is Element of bool (bound_QC-variables Al)
c<sub>25</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>25</sub> is Element of bool (bound_QC-variables Al)
c<sub>22</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>23</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>23</sub> is Element of bool (bound_QC-variables Al)
(Al,A,c<sub>22</sub>,c<sub>23</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,A,c<sub>23</sub>,c<sub>24</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,(Al,A,c<sub>23</sub>,c<sub>24</sub>),c<sub>25</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c<sub>22</sub>,(Al,A,(Al,A,c<sub>23</sub>,c<sub>24</sub>),c<sub>25</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>26</sub> is Element of CQC-WFF Al
still_not-bound_in c<sub>26</sub> is Element of bool (bound_QC-variables Al)
c<sub>30</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>30</sub> is Element of bool (bound_QC-variables Al)
c<sub>27</sub> is Element of bound_QC-variables Al
All (c<sub>27</sub>,c<sub>26</sub>) is Element of CQC-WFF Al
still_not-bound_in (All (c<sub>27</sub>,c<sub>26</sub>)) is Element of bool (bound_QC-variables Al)
c<sub>31</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>31</sub> is Element of bool (bound_QC-variables Al)
c<sub>28</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>29</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
dom c<sub>29</sub> is Element of bool (bound_QC-variables Al)
(Al,A,c<sub>28</sub>,c<sub>29</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,A,c<sub>29</sub>,c<sub>30</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,(Al,A,c<sub>29</sub>,c<sub>30</sub>),c<sub>31</sub>) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c<sub>28</sub>,(Al,A,(Al,A,c<sub>29</sub>,c<sub>30</sub>),c<sub>31</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is set
xSQ is set
xSQ is Element of bound_QC-variables Al
S is set
J is set
xSQ is set
S is set
xSQ is Element of bound_QC-variables Al
xSQ is Element of bound_QC-variables Al
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
vSUB Al is non empty functional set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
still_not-bound_in A is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
J is Relation-like Function-like Element of vSUB Al
@ J is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
xSQ is set
S is set
v is Element of bound_QC-variables Al
xSQ is set
(@ J) . v is set
xSQ is set
S is set
xSQ is set
v is Element of bound_QC-variables Al
(@ J) . v is set
v is Element of bound_QC-variables Al
(@ J) . v is set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
vSUB Al is non empty functional set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is Element of CQC-WFF Al
(Al,A) is set
J is Relation-like Function-like Element of vSUB Al
@ J is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ J) | (Al,A) is Relation-like bound_QC-variables Al -defined (Al,A) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ J) | (Al,A)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
(Al,A,J) is set
(@ J) | (Al,A,J) is Relation-like bound_QC-variables Al -defined (Al,A,J) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ J) | (Al,A,J)) is Element of bool (bound_QC-variables Al)
(dom ((@ J) | (Al,A))) /\ (dom ((@ J) | (Al,A,J))) is Element of bool (bound_QC-variables Al)
xSQ is set
dom (@ J) is Element of bool (bound_QC-variables Al)
(dom (@ J)) /\ (Al,A) is Element of bool (bound_QC-variables Al)
(dom (@ J)) /\ (Al,A,J) is Element of bool (bound_QC-variables Al)
(dom (@ J)) /\ ((dom (@ J)) /\ (Al,A)) is Element of bool (bound_QC-variables Al)
((dom (@ J)) /\ ((dom (@ J)) /\ (Al,A))) /\ (Al,A,J) is Element of bool (bound_QC-variables Al)
(dom (@ J)) /\ (dom (@ J)) is Element of bool (bound_QC-variables Al)
((dom (@ J)) /\ (dom (@ J))) /\ (Al,A) is Element of bool (bound_QC-variables Al)
(((dom (@ J)) /\ (dom (@ J))) /\ (Al,A)) /\ (Al,A,J) is Element of bool (bound_QC-variables Al)
(Al,A) /\ (Al,A,J) is set
(dom (@ J)) /\ ((Al,A) /\ (Al,A,J)) is Element of bool (bound_QC-variables Al)
still_not-bound_in A is Element of bool (bound_QC-variables Al)
S is Element of bound_QC-variables Al
xSQ is Element of bound_QC-variables Al
(@ J) . xSQ is set
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
A is Element of CQC-WFF Al
J is Element of bound_QC-variables Al
All (J,A) is Element of CQC-WFF Al
(Al,(All (J,A))) is set
xSQ is Relation-like Function-like Element of vSUB Al
RestrictSub (J,(All (J,A)),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (J,(All (J,A)),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
@ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) | (Al,(All (J,A))) is Relation-like bound_QC-variables Al -defined (Al,(All (J,A))) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(All (J,A)),xSQ) is set
(@ xSQ) | (Al,(All (J,A)),xSQ) is Relation-like bound_QC-variables Al -defined (Al,(All (J,A)),xSQ) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (J,A)))),((@ xSQ) | (Al,(All (J,A)),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) \ (Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (J,A)))),((@ xSQ) | (Al,(All (J,A)),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
still_not-bound_in (All (J,A)) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
proj1 xSQ is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is set
xSQ is set
dom ((@ xSQ) | (Al,(All (J,A)))) is Element of bool (bound_QC-variables Al)
dom ((@ xSQ) | (Al,(All (J,A)),xSQ)) is Element of bool (bound_QC-variables Al)
xSQ | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like Function-like Element of vSUB Al
(@ xSQ) | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like bound_QC-variables Al -defined { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
rng (@ xSQ) is Element of bool (bound_QC-variables Al)
[: { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } ,(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [: { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } ,(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
v is set
S1 is set
[v,S1] is V1() set
{v,S1} is non empty set
{v} is non empty trivial 1 -element set
{{v,S1},{v}} is non empty set
z is Element of bound_QC-variables Al
(@ xSQ) . z is set
q is Element of bound_QC-variables Al
xSQ . q is set
[:(Al,(All (J,A)),xSQ),(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [:(Al,(All (J,A)),xSQ),(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
z is Element of bound_QC-variables Al
q is Element of bound_QC-variables Al
xSQ . q is set
[:(Al,(All (J,A))),(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [:(Al,(All (J,A))),(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
((@ xSQ) | (Al,(All (J,A)))) \/ ((@ xSQ) | (Al,(All (J,A)),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | (Al,(All (J,A)))) is Element of bool (bound_QC-variables Al)
dom ((@ xSQ) | (Al,(All (J,A)),xSQ)) is Element of bool (bound_QC-variables Al)
xSQ is set
v is set
S1 is set
[v,S1] is V1() set
{v,S1} is non empty set
{v} is non empty trivial 1 -element set
{{v,S1},{v}} is non empty set
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(@ xSQ) . v is set
rng (@ xSQ) is Element of bool (bound_QC-variables Al)
((@ xSQ) | (Al,(All (J,A)))) \/ ((@ xSQ) | (Al,(All (J,A)),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(Al,(All (J,A))),(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [:(Al,(All (J,A))),(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
z is Element of bound_QC-variables Al
[z,S1] is V1() set
{z,S1} is non empty set
{z} is non empty trivial 1 -element set
{{z,S1},{z}} is non empty set
still_not-bound_in A is Element of bool (bound_QC-variables Al)
{J} is non empty trivial 1 -element Element of bool (bound_QC-variables Al)
(still_not-bound_in A) \ {J} is Element of bool (bound_QC-variables Al)
[:(Al,(All (J,A)),xSQ),(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [:(Al,(All (J,A)),xSQ),(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) . z is set
xSQ . z is set
[: { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } ,(rng (@ xSQ)):] is Relation-like set
(@ xSQ) /\ [: { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } ,(rng (@ xSQ)):] is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like bound_QC-variables Al -defined { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
xSQ | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in (All (J,A)) & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like Function-like Element of vSUB Al
Al is non empty Relation-like QC-alphabet
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
vSUB Al is non empty functional set
A is Element of CQC-WFF Al
(Al,A) is set
J is Element of bound_QC-variables Al
xSQ is Relation-like Function-like Element of vSUB Al
RestrictSub (J,A,xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (J,A,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
dom (@ (RestrictSub (J,A,xSQ))) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
@ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) | (Al,A) is Relation-like bound_QC-variables Al -defined (Al,A) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | (Al,A)) is Element of bool (bound_QC-variables Al)
(Al,A,xSQ) is set
(@ xSQ) | (Al,A,xSQ) is Relation-like bound_QC-variables Al -defined (Al,A,xSQ) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | (Al,A,xSQ)) is Element of bool (bound_QC-variables Al)
(dom ((@ xSQ) | (Al,A))) \/ (dom ((@ xSQ) | (Al,A,xSQ))) is Element of bool (bound_QC-variables Al)
still_not-bound_in A is Element of bool (bound_QC-variables Al)
proj1 xSQ is set
{ b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is set
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ (Al,A,xSQ) is Element of bool (bound_QC-variables Al)
xSQ | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like Function-like Element of vSUB Al
(@ xSQ) | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Relation-like bound_QC-variables Al -defined { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ { b<sub>1</sub> where b<sub>1</sub> is Element of bound_QC-variables Al : ( b<sub>1</sub> in still_not-bound_in A & b<sub>1</sub> is Element of proj1 xSQ & not b<sub>1</sub> = J & not b<sub>1</sub> = xSQ . b<sub>1</sub> ) } is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ (Al,A) is Element of bool (bound_QC-variables Al)
xSQ is set
v is Element of bound_QC-variables Al
(@ xSQ) . v is set
S1 is Element of bound_QC-variables Al
xSQ . S1 is set
v is Element of bound_QC-variables Al
S1 is Element of bound_QC-variables Al
xSQ . S1 is set
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is Element of CQC-Sub-WFF Al
(Al,J,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{J,A} is non empty set
{J} is non empty trivial 1 -element set
{{J,A},{J}} is non empty set
(Al,J) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,J)) is Element of CQC-WFF Al
(Al,(All (A,(Al,J)))) is set
xSQ is Relation-like Function-like second_Q_comp of (Al,J,A)
(Al,(Al,J,A),xSQ) is Element of CQC-Sub-WFF Al
(Al,(Al,J,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ ((Al,(Al,J,A),xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
RestrictSub (A,(All (A,(Al,J))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,J))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
@ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ xSQ) | (Al,(All (A,(Al,J)))) is Relation-like bound_QC-variables Al -defined (Al,(All (A,(Al,J)))) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,J))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,J)))))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(All (A,(Al,J))),xSQ) is set
(@ xSQ) | (Al,(All (A,(Al,J))),xSQ) is Relation-like bound_QC-variables Al -defined (Al,(All (A,(Al,J))),xSQ) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,J))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,J)))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | (Al,(All (A,(Al,J))))) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom ((@ xSQ) | (Al,(All (A,(Al,J))),xSQ)) is Element of bool (bound_QC-variables Al)
(Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
((@ xSQ) | (Al,(All (A,(Al,J))))) \/ ((@ xSQ) | (Al,(All (A,(Al,J))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
Sub_All ((Al,J,A),xSQ) is Element of QC-Sub-WFF Al
(@ xSQ) \ (Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom xSQ is Element of bool (bound_QC-variables Al)
(dom ((@ xSQ) | (Al,(All (A,(Al,J)))))) \/ (dom ((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) is Element of bool (bound_QC-variables Al)
dom (Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) is Element of bool (bound_QC-variables Al)
(Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) \/ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ))) \/ (@ xSQ) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),xSQ,(Al,(bound_QC-variables Al),((@ xSQ) | (Al,(All (A,(Al,J))))),((@ xSQ) | (Al,(All (A,(Al,J))),xSQ)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
still_not-bound_in (All (A,(Al,S))) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,S,A,xSQ,J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom (Al,S,A,xSQ,J,xSQ) is Element of bool (bound_QC-variables Al)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,S,A),xSQ),J,xSQ) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,(Al,S,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,(Al,S,A),xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,(Al,S,A),xSQ) `2)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,(Al,(Al,S,A),xSQ),J,xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
@ xSQ is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(All (A,(Al,S)))) is set
(@ xSQ) | (Al,(All (A,(Al,S)))) is Relation-like bound_QC-variables Al -defined (Al,(All (A,(Al,S)))) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,S)))))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(All (A,(Al,S))),xSQ) is set
(@ xSQ) | (Al,(All (A,(Al,S))),xSQ) is Relation-like bound_QC-variables Al -defined (Al,(All (A,(Al,S))),xSQ) -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,S)))))),((@ xSQ) | (Al,(All (A,(Al,S))),xSQ))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(Al,(bound_QC-variables Al),(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,S)))))),((@ xSQ) | (Al,(All (A,(Al,S))),xSQ))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
((@ xSQ) | (Al,(All (A,(Al,S))))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom S1 is Element of bool (bound_QC-variables Al)
(Al,J,(Al,S,A,xSQ,J,xSQ),S1) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
z is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom z is Element of bool (bound_QC-variables Al)
(Al,J,(Al,J,(Al,S,A,xSQ,J,xSQ),S1),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,xSQ,(Al,J,(Al,J,(Al,S,A,xSQ,J,xSQ),S1),z)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
rng ((@ xSQ) | (Al,(All (A,(Al,S))))) is Element of bool (bound_QC-variables Al)
dom xSQ is Element of bool (bound_QC-variables Al)
q is Element of bound_QC-variables Al
dom ((@ xSQ) | (Al,(All (A,(Al,S))))) is Element of bool (bound_QC-variables Al)
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ (Al,(All (A,(Al,S)))) is Element of bool (bound_QC-variables Al)
p is Element of bound_QC-variables Al
rng ((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) is Element of bool (bound_QC-variables Al)
q is Element of bound_QC-variables Al
z . q is set
xSQ . q is Element of J
dom ((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) is Element of bool (bound_QC-variables Al)
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ (Al,(All (A,(Al,S))),xSQ) is Element of bool (bound_QC-variables Al)
((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) . q is set
xSQ . (((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) . q) is set
p is Element of bound_QC-variables Al
(@ xSQ) . p is set
proj1 xSQ is set
{ b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } is set
xSQ | { b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } is Relation-like Function-like Element of vSUB Al
(@ xSQ) | { b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } is Relation-like bound_QC-variables Al -defined { b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } -defined bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
dom ((@ xSQ) | { b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } ) is Element of bool (bound_QC-variables Al)
dom (@ xSQ) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ { b₁ where b₁ is Element of bound_QC-variables Al : ( b₁ in still_not-bound_in (All (A,(Al,S))) & b₁ is Element of proj1 xSQ & not b₁ = A & not b₁ = xSQ . b₁ ) } is Element of bool (bound_QC-variables Al)
dom ((@ xSQ) | (Al,(All (A,(Al,S))),xSQ)) is Element of bool (bound_QC-variables Al)
(dom (@ xSQ)) /\ (Al,(All (A,(Al,S))),xSQ) is Element of bool (bound_QC-variables Al)
p is set
a is Element of bound_QC-variables Al
(@ xSQ) . a is set
x is Element of bound_QC-variables Al
xSQ . x is set
(Al,(bound_QC-variables Al),(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))),((@ xSQ) | (Al,(All (A,(Al,S)))))) * xSQ is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,((@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * xSQ),(((@ xSQ) | (Al,(All (A,(Al,S))))) * xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
(Al,S) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
All (A,(Al,S)) is Element of CQC-WFF Al
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
Sub_All ((Al,S,A),xSQ) is Element of QC-Sub-WFF Al
(Al,(Al,(Al,S,A),xSQ)) is Element of CQC-WFF Al
(Al,S,A) `2 is Element of bound_QC-variables Al
(Al,(Al,S,A)) is Element of CQC-Sub-WFF Al
(Al,(Al,(Al,S,A))) is Element of CQC-WFF Al
All (((Al,S,A) `2),(Al,(Al,(Al,S,A)))) is Element of CQC-WFF Al
All (A,(Al,(Al,(Al,S,A)))) is Element of CQC-WFF Al
S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,A,xSQ,J,S1) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
vSUB Al is non empty functional set
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S1,(Al,S,A,xSQ,J,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,(Al,(Al,S,A),xSQ),J,S1) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,(Al,S,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,(Al,S,A),xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,(Al,S,A),xSQ) `2)) * S1 is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S1,(Al,(Al,(Al,S,A),xSQ),J,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
still_not-bound_in (All (A,(Al,S))) is Element of bool (bound_QC-variables Al)
bool (bound_QC-variables Al) is non empty set
dom (Al,S,A,xSQ,J,S1) is Element of bool (bound_QC-variables Al)
z is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom z is Element of bool (bound_QC-variables Al)
q is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
dom q is Element of bool (bound_QC-variables Al)
(Al,J,(Al,S,A,xSQ,J,S1),z) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,(Al,S,A,xSQ,J,S1),z),q) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,S1,(Al,J,(Al,J,(Al,S,A,xSQ,J,S1),z),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
Al is non empty Relation-like QC-alphabet
QC-variables Al is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
bool (QC-variables Al) is non empty set
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
A is Element of bound_QC-variables Al
J is non empty set
K367(J) is set
Valuations_in (Al,J) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,J
xSQ is Relation-like QC-pred_symbols Al -defined K367(J) -valued Function-like quasi_total interpretation of Al,J
S is Element of CQC-Sub-WFF Al
(Al,S,A) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{S,A} is non empty set
{S} is non empty trivial 1 -element set
{{S,A},{S}} is non empty set
CQC_Sub S is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
xSQ is Relation-like Function-like second_Q_comp of (Al,S,A)
(Al,(Al,S,A),xSQ) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,(Al,S,A),xSQ) is Element of CQC-WFF Al
v is Relation-like bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,(Al,(Al,S,A),xSQ),J,v) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
[:(bound_QC-variables Al),J:] is non empty Relation-like set
bool [:(bound_QC-variables Al),J:] is non empty set
(Al,(Al,S,A),xSQ) `2 is Relation-like Function-like Element of vSUB Al
vSUB Al is non empty functional set
@ ((Al,(Al,S,A),xSQ) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((Al,(Al,S,A),xSQ) `2)) * v is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,v,(Al,(Al,(Al,S,A),xSQ),J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
@ (Al,(Al,S,A),xSQ) is Element of [:(QC-WFF Al),(vSUB Al):]
[:(QC-WFF Al),(vSUB Al):] is non empty Relation-like set
S_Bound (@ (Al,(Al,S,A),xSQ)) is Element of bound_QC-variables Al
q is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> q is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:]
{q} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{q}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,S) is Element of CQC-WFF Al
All (A,(Al,S)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,q) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> q is non empty Relation-like {A} -defined J -valued {q} -valued Function-like constant total quasi_total Element of bool [:{A},{q}:]
[:{A},{q}:] is non empty Relation-like set
bool [:{A},{q}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))),(Al,J,A,q)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q)),(Al,J,(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),q))),(Al,J,A,q))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
p is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:]
{p} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S `2 is Relation-like Function-like Element of vSUB Al
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)),(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
All ((S_Bound (@ (Al,(Al,S,A),xSQ))),(CQC_Sub S)) is Element of CQC-WFF Al
p is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:]
{p} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
p is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:]
{p} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S `2 is Relation-like Function-like Element of vSUB Al
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)),(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
p is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> p is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {p} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:]
{p} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{p}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S `2 is Relation-like Function-like Element of vSUB Al
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)),(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),p)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,(Al,(Al,S,A),xSQ)) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,(Al,(Al,S,A),xSQ)) is Element of CQC-WFF Al
(Al,(Al,(Al,S,A),xSQ),(CQC_Sub (Al,(Al,(Al,S,A),xSQ)))) is Element of CQC-WFF Al
(Al,(Al,(Al,S,A),xSQ),(CQC_Sub S)) is Element of CQC-WFF Al
(Al,S,A,xSQ,J,v) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,S) is Element of CQC-WFF Al
All (A,(Al,S)) is Element of CQC-WFF Al
RestrictSub (A,(All (A,(Al,S))),xSQ) is Relation-like Function-like V52() Element of vSUB Al
@ (RestrictSub (A,(All (A,(Al,S))),xSQ)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * v is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
a is Element of J
(Al,J,A,a) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> a is non empty Relation-like {A} -defined J -valued {a} -valued Function-like constant total quasi_total Element of bool [:{A},{a}:]
{a} is non empty trivial 1 -element set
[:{A},{a}:] is non empty Relation-like set
bool [:{A},{a}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,v,(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,a))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
x is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> x is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {x} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:]
{x} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,A,x) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} --> x is non empty Relation-like {A} -defined J -valued {x} -valued Function-like constant total quasi_total Element of bool [:{A},{x}:]
[:{A},{x}:] is non empty Relation-like set
bool [:{A},{x}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)),(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,x))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,v,(Al,S,A,xSQ,J,v)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
a is Element of J
(Al,J,A,a) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> a is non empty Relation-like {A} -defined J -valued {a} -valued Function-like constant total quasi_total Element of bool [:{A},{a}:]
{a} is non empty trivial 1 -element set
[:{A},{a}:] is non empty Relation-like set
bool [:{A},{a}:] is non empty set
(Al,J,(Al,J,v,(Al,S,A,xSQ,J,v)),(Al,J,A,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
a is Element of J
(Al,J,A,a) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> a is non empty Relation-like {A} -defined J -valued {a} -valued Function-like constant total quasi_total Element of bool [:{A},{a}:]
{a} is non empty trivial 1 -element set
[:{A},{a}:] is non empty Relation-like set
bool [:{A},{a}:] is non empty set
(Al,J,(Al,J,v,(Al,S,A,xSQ,J,v)),(Al,J,A,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
a is Element of J
(Al,J,A,a) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> a is non empty Relation-like {A} -defined J -valued {a} -valued Function-like constant total quasi_total Element of bool [:{A},{a}:]
{a} is non empty trivial 1 -element set
[:{A},{a}:] is non empty Relation-like set
bool [:{A},{a}:] is non empty set
(Al,J,(Al,J,v,(Al,S,A,xSQ,J,v)),(Al,J,A,a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
a is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),a) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} is non empty trivial 1 -element set
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> a is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {a} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{a}:]
{a} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{a}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{a}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),a)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
x is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> x is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {x} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:]
{x} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
b is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> b is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {b} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{b}:]
{b} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{b}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{b}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
S `2 is Relation-like Function-like Element of vSUB Al
@ (S `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (S `2)) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b)),(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),b)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
x is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> x is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {x} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:]
{x} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{x}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(@ (S `2)) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)),(Al,S,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),x)))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
e2 is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> e2 is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {e2} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{e2}:]
{e2} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{e2}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{e2}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2))) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(@ (RestrictSub (A,(All (A,(Al,S))),xSQ))) * (Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2)) is Relation-like bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,A,e2) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} is non empty trivial 1 -element set
{A} --> e2 is non empty Relation-like {A} -defined J -valued {e2} -valued Function-like constant total quasi_total Element of bool [:{A},{e2}:]
[:{A},{e2}:] is non empty Relation-like set
bool [:{A},{e2}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2))),(Al,J,A,e2)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2)),(Al,J,(Al,S,A,xSQ,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),e2))),(Al,J,A,e2))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
c<sub>17</sub> is Element of J
(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),c<sub>17</sub>) is trivial Relation-like bound_QC-variables Al -defined {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{(S_Bound (@ (Al,(Al,S,A),xSQ)))} --> c<sub>17</sub> is non empty Relation-like {(S_Bound (@ (Al,(Al,S,A),xSQ)))} -defined J -valued {c<sub>17</sub>} -valued Function-like constant total quasi_total Element of bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{c<sub>17</sub>}:]
{c<sub>17</sub>} is non empty trivial 1 -element set
[:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{c<sub>17</sub>}:] is non empty Relation-like set
bool [:{(S_Bound (@ (Al,(Al,S,A),xSQ)))},{c<sub>17</sub>}:] is non empty set
(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),c<sub>17</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
(Al,J,A,c<sub>17</sub>) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} --> c<sub>17</sub> is non empty Relation-like {A} -defined J -valued {c<sub>17</sub>} -valued Function-like constant total quasi_total Element of bool [:{A},{c<sub>17</sub>}:]
[:{A},{c<sub>17</sub>}:] is non empty Relation-like set
bool [:{A},{c<sub>17</sub>}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,c<sub>17</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,(Al,J,v,(Al,J,(S_Bound (@ (Al,(Al,S,A),xSQ))),c<sub>17</sub>)),(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,c<sub>17</sub>))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
c<sub>18</sub> is Element of J
(Al,J,A,c<sub>18</sub>) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} --> c<sub>18</sub> is non empty Relation-like {A} -defined J -valued {c<sub>18</sub>} -valued Function-like constant total quasi_total Element of bool [:{A},{c<sub>18</sub>}:]
{c<sub>18</sub>} is non empty trivial 1 -element set
[:{A},{c<sub>18</sub>}:] is non empty Relation-like set
bool [:{A},{c<sub>18</sub>}:] is non empty set
(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,c<sub>18</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like Element of bool [:(bound_QC-variables Al),J:]
(Al,J,v,(Al,J,(Al,S,A,xSQ,J,v),(Al,J,A,c<sub>18</sub>))) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
c<sub>19</sub> is Element of J
(Al,J,A,c<sub>19</sub>) is trivial Relation-like bound_QC-variables Al -defined {A} -defined bound_QC-variables Al -defined J -valued Function-like one-to-one constant Element of bool [:(bound_QC-variables Al),J:]
{A} --> c<sub>19</sub> is non empty Relation-like {A} -defined J -valued {c<sub>19</sub>} -valued Function-like constant total quasi_total Element of bool [:{A},{c<sub>19</sub>}:]
{c<sub>19</sub>} is non empty trivial 1 -element set
[:{A},{c<sub>19</sub>}:] is non empty Relation-like set
bool [:{A},{c<sub>19</sub>}:] is non empty set
(Al,J,(Al,J,v,(Al,S,A,xSQ,J,v)),(Al,J,A,c<sub>19</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined J -valued Function-like quasi_total Element of Valuations_in (Al,J)
F<sub>1</sub>() is non empty Relation-like QC-alphabet
QC-Sub-WFF F<sub>1</sub>() is non empty F<sub>1</sub>() -Sub-closed set
CQC-Sub-WFF F<sub>1</sub>() is non empty Element of bool (QC-Sub-WFF F<sub>1</sub>())
bool (QC-Sub-WFF F<sub>1</sub>()) is non empty set
QC-variables F<sub>1</sub>() is non empty set
bound_QC-variables F<sub>1</sub>() is non empty Element of bool (QC-variables F<sub>1</sub>())
bool (QC-variables F<sub>1</sub>()) is non empty set
QC-pred_symbols F<sub>1</sub>() is non empty set
vSUB F<sub>1</sub>() is non empty functional set
Al is Element of CQC-Sub-WFF F<sub>1</sub>()
J is Element of bound_QC-variables F<sub>1</sub>()
(F<sub>1</sub>(),Al,J) is V1() (F<sub>1</sub>()) Element of [:(QC-Sub-WFF F<sub>1</sub>()),(bound_QC-variables F<sub>1</sub>()):]
[:(QC-Sub-WFF F<sub>1</sub>()),(bound_QC-variables F<sub>1</sub>()):] is non empty Relation-like set
{Al,J} is non empty set
{Al} is non empty trivial 1 -element set
{{Al,J},{Al}} is non empty set
xSQ is Relation-like Function-like second_Q_comp of (F<sub>1</sub>(),Al,J)
Sub_All ((F<sub>1</sub>(),Al,J),xSQ) is Element of QC-Sub-WFF F<sub>1</sub>()
(F<sub>1</sub>(),(F<sub>1</sub>(),Al,J),xSQ) is Element of CQC-Sub-WFF F<sub>1</sub>()
Al is Element of CQC-Sub-WFF F<sub>1</sub>()
Al `2 is Relation-like Function-like Element of vSUB F₁()
A is Element of CQC-Sub-WFF F₁()
A `2 is Relation-like Function-like Element of vSUB F<sub>1</sub>()
Sub_& (Al,A) is Element of QC-Sub-WFF F<sub>1</sub>()
(F<sub>1</sub>(),Al,A) is Element of CQC-Sub-WFF F<sub>1</sub>()
Al is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
Al -ary_QC-pred_symbols F<sub>1</sub>() is non empty Element of bool (QC-pred_symbols F<sub>1</sub>())
bool (QC-pred_symbols F<sub>1</sub>()) is non empty set
z is Element of CQC-Sub-WFF F<sub>1</sub>()
q is Element of bound_QC-variables F<sub>1</sub>()
(F<sub>1</sub>(),z,q) is V1() (F<sub>1</sub>()) Element of [:(QC-Sub-WFF F<sub>1</sub>()),(bound_QC-variables F<sub>1</sub>()):]
[:(QC-Sub-WFF F<sub>1</sub>()),(bound_QC-variables F<sub>1</sub>()):] is non empty Relation-like set
{z,q} is non empty set
{z} is non empty trivial 1 -element set
{{z,q},{z}} is non empty set
J is Element of Al -ary_QC-pred_symbols F<sub>1</sub>()
A is Relation-like NAT -defined QC-variables F<sub>1</sub>() -valued bound_QC-variables F<sub>1</sub>() -valued Function-like Al -element FinSequence-like FinSequence of QC-variables F<sub>1</sub>()
xSQ is Relation-like Function-like Element of vSUB F<sub>1</sub>()
(Al,F<sub>1</sub>(),J,A,xSQ) is Sub_atomic Element of CQC-Sub-WFF F<sub>1</sub>()
S is Element of CQC-Sub-WFF F<sub>1</sub>()
xSQ is Element of CQC-Sub-WFF F<sub>1</sub>()
(F<sub>1</sub>(),xSQ) is Sub_negative Element of CQC-Sub-WFF F<sub>1</sub>()
v is Element of CQC-Sub-WFF F<sub>1</sub>()
v `2 is Relation-like Function-like Element of vSUB F₁()
S1 is Element of CQC-Sub-WFF F₁()
S1 `2 is Relation-like Function-like Element of vSUB F<sub>1</sub>()
Sub_& (v,S1) is Element of QC-Sub-WFF F<sub>1</sub>()
p is Relation-like Function-like second_Q_comp of (F<sub>1</sub>(),z,q)
Sub_All ((F<sub>1</sub>(),z,q),p) is Element of QC-Sub-WFF F<sub>1</sub>()
Al is non empty Relation-like QC-alphabet
QC-pred_symbols Al is non empty set
QC-Sub-WFF Al is non empty Al -Sub-closed set
CQC-Sub-WFF Al is non empty Element of bool (QC-Sub-WFF Al)
bool (QC-Sub-WFF Al) is non empty set
bound_QC-variables Al is non empty Element of bool (QC-variables Al)
QC-variables Al is non empty set
bool (QC-variables Al) is non empty set
A is non empty set
K367(A) is set
Valuations_in (Al,A) is non empty FUNCTION_DOMAIN of bound_QC-variables Al,A
J is Relation-like QC-pred_symbols Al -defined K367(A) -valued Function-like quasi_total interpretation of Al,A
vSUB Al is non empty functional set
xSQ is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
xSQ -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
bool (QC-pred_symbols Al) is non empty set
z is ext-real epsilon-transitive epsilon-connected ordinal natural V31() V32() V43() V44() V45() V46() V47() V48() V49() V50() V52() V63() V64() V65() cardinal Element of NAT
z -ary_QC-pred_symbols Al is non empty Element of bool (QC-pred_symbols Al)
c<sub>24</sub> is Element of CQC-Sub-WFF Al
c<sub>25</sub> is Element of bound_QC-variables Al
(Al,c<sub>24</sub>,c<sub>25</sub>) is V1() (Al) Element of [:(QC-Sub-WFF Al),(bound_QC-variables Al):]
[:(QC-Sub-WFF Al),(bound_QC-variables Al):] is non empty Relation-like set
{c<sub>24</sub>,c<sub>25</sub>} is non empty set
{c<sub>24</sub>} is non empty trivial 1 -element set
{{c<sub>24</sub>,c<sub>25</sub>},{c<sub>24</sub>}} is non empty set
xSQ is Element of xSQ -ary_QC-pred_symbols Al
S is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like xSQ -element FinSequence-like FinSequence of QC-variables Al
v is Relation-like Function-like Element of vSUB Al
(xSQ,Al,xSQ,S,v) is Sub_atomic Element of CQC-Sub-WFF Al
CQC_Sub (xSQ,Al,xSQ,S,v) is Element of CQC-WFF Al
QC-WFF Al is non empty set
CQC-WFF Al is non empty Element of bool (QC-WFF Al)
bool (QC-WFF Al) is non empty set
S1 is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(xSQ,Al,xSQ,S,v),A,S1) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
[:(bound_QC-variables Al),A:] is non empty Relation-like set
bool [:(bound_QC-variables Al),A:] is non empty set
(xSQ,Al,xSQ,S,v) `2 is Relation-like Function-like Element of vSUB Al
@ ((xSQ,Al,xSQ,S,v) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
[:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty Relation-like set
bool [:(bound_QC-variables Al),(bound_QC-variables Al):] is non empty set
(@ ((xSQ,Al,xSQ,S,v) `2)) * S1 is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,S1,(Al,(xSQ,Al,xSQ,S,v),A,S1)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
p is Element of z -ary_QC-pred_symbols Al
q is Relation-like NAT -defined bound_QC-variables Al -valued QC-variables Al -valued Function-like z -element FinSequence-like FinSequence of QC-variables Al
a is Relation-like Function-like Element of vSUB Al
(z,Al,p,q,a) is Sub_atomic Element of CQC-Sub-WFF Al
x is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(z,Al,p,q,a),A,x) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(z,Al,p,q,a) `2 is Relation-like Function-like Element of vSUB Al
@ ((z,Al,p,q,a) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((z,Al,p,q,a) `2)) * x is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,x,(Al,(z,Al,p,q,a),A,x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
CQC_Sub (z,Al,p,q,a) is Element of CQC-WFF Al
b is Element of CQC-Sub-WFF Al
CQC_Sub b is Element of CQC-WFF Al
x is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,b,A,x) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
b `2 is Relation-like Function-like Element of vSUB Al
@ (b `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ (b `2)) * x is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,x,(Al,b,A,x)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
e2 is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,b,A,e2) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(@ (b `2)) * e2 is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,e2,(Al,b,A,e2)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>17</sub> is Element of CQC-Sub-WFF Al
CQC_Sub c<sub>17</sub> is Element of CQC-WFF Al
(Al,c<sub>17</sub>) is Sub_negative Element of CQC-Sub-WFF Al
CQC_Sub (Al,c<sub>17</sub>) is Element of CQC-WFF Al
c<sub>18</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,c<sub>17</sub>),A,c<sub>18</sub>) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,c<sub>17</sub>) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,c₁₇) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,c<sub>17</sub>) `2)) * c₁₈ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c₁₈,(Al,(Al,c₁₇),A,c₁₈)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c₁₉ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,c₁₇),A,c₁₉) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(@ ((Al,c₁₇) `2)) * c<sub>19</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c<sub>19</sub>,(Al,(Al,c<sub>17</sub>),A,c<sub>19</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c<sub>20</sub> is Element of CQC-Sub-WFF Al
c<sub>20</sub> `2 is Relation-like Function-like Element of vSUB Al
c₂₁ is Element of CQC-Sub-WFF Al
c₂₁ `2 is Relation-like Function-like Element of vSUB Al
CQC_Sub c<sub>20</sub> is Element of CQC-WFF Al
CQC_Sub c<sub>21</sub> is Element of CQC-WFF Al
(Al,c<sub>20</sub>,c<sub>21</sub>) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,c<sub>20</sub>,c<sub>21</sub>) is Element of CQC-WFF Al
c<sub>22</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,c<sub>20</sub>,c<sub>21</sub>),A,c<sub>22</sub>) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,c<sub>20</sub>,c<sub>21</sub>) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,c₂₀,c₂₁) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,c<sub>20</sub>,c<sub>21</sub>) `2)) * c₂₂ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c₂₂,(Al,(Al,c₂₀,c₂₁),A,c₂₂)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c₂₃ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,c₂₀,c₂₁),A,c₂₃) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(@ ((Al,c₂₀,c₂₁) `2)) * c<sub>23</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c<sub>23</sub>,(Al,(Al,c<sub>20</sub>,c<sub>21</sub>),A,c<sub>23</sub>)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
CQC_Sub c<sub>24</sub> is Element of CQC-WFF Al
c<sub>26</sub> is Relation-like Function-like second_Q_comp of (Al,c<sub>24</sub>,c<sub>25</sub>)
(Al,(Al,c<sub>24</sub>,c<sub>25</sub>),c<sub>26</sub>) is Element of CQC-Sub-WFF Al
CQC_Sub (Al,(Al,c<sub>24</sub>,c<sub>25</sub>),c<sub>26</sub>) is Element of CQC-WFF Al
c<sub>27</sub> is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,(Al,c<sub>24</sub>,c<sub>25</sub>),c<sub>26</sub>),A,c<sub>27</sub>) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,(Al,c<sub>24</sub>,c<sub>25</sub>),c<sub>26</sub>) `2 is Relation-like Function-like Element of vSUB Al
@ ((Al,(Al,c₂₄,c₂₅),c₂₆) `2) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -valued Function-like Element of bool [:(bound_QC-variables Al),(bound_QC-variables Al):]
(@ ((Al,(Al,c<sub>24</sub>,c<sub>25</sub>),c<sub>26</sub>) `2)) * c₂₇ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c₂₇,(Al,(Al,(Al,c₂₄,c₂₅),c₂₆),A,c₂₇)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
c₂₈ is Relation-like bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)
(Al,(Al,(Al,c₂₄,c₂₅),c₂₆),A,c₂₈) is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(@ ((Al,(Al,c₂₄,c₂₅),c₂₆) `2)) * c₂₈ is Relation-like bound_QC-variables Al -defined A -valued Function-like Element of bool [:(bound_QC-variables Al),A:]
(Al,A,c₂₈,(Al,(Al,(Al,c₂₄,c₂₅),c₂₆),A,c₂₈)) is Relation-like bound_QC-variables Al -defined bound_QC-variables Al -defined A -valued Function-like quasi_total Element of Valuations_in (Al,A)