:: ZFMODEL1 semantic presentation

K41() is V32() V33() V34() V38() set
K45() is V32() V33() V34() V35() V36() V37() V38() Element of bool K41()
bool K41() is non empty set
omega is V32() V33() V34() V35() V36() V37() V38() set
bool omega is non empty set
bool K45() is non empty set
VAR is non empty V32() V33() V34() V35() V36() V37() Element of bool K45()
5 is ext-real non empty natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
{ b₁ where b₁ is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45() : 5 <= b₁ } is set
bool VAR is non empty set
{} is set
the empty Relation-like non-empty empty-yielding V32() V33() V34() V35() V36() V37() V38() set is empty Relation-like non-empty empty-yielding V32() V33() V34() V35() V36() V37() V38() set
0 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
x. 0 is ext-real natural V14() Element of VAR
5 + 0 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
1 is ext-real non empty natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
x. 1 is ext-real natural V14() Element of VAR
5 + 1 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
2 is ext-real non empty natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
x. 2 is ext-real natural V14() Element of VAR
5 + 2 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
3 is ext-real non empty natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
x. 3 is ext-real natural V14() Element of VAR
5 + 3 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
4 is ext-real non empty natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
x. 4 is ext-real natural V14() Element of VAR
5 + 4 is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
the_axiom_of_extensionality is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(x. 2) 'in' (x. 0) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*1*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
<*(x. 2)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*1*>,<*(x. 2)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
<*(x. 0)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 2)*>),<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 2) 'in' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(x. 1)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 2)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 2) 'in' (x. 0)) => ((x. 2) 'in' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 2) 'in' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*2*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*2*>,((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 0)) '&' ('not' ((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*3*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*3*>,((x. 2) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 0))),('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 0)) '&' ('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 0)) '&' ('not' ((x. 2) 'in' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) => ((x. 2) 'in' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 2) 'in' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 2) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) '&' ('not' ((x. 2) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 1))),('not' ((x. 2) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 1)) '&' ('not' ((x. 2) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 1)) '&' ('not' ((x. 2) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 2) 'in' (x. 0)) => ((x. 2) 'in' (x. 1))) '&' (((x. 2) 'in' (x. 1)) => ((x. 2) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 2) 'in' (x. 0)) => ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 2) 'in' (x. 0)) => ((x. 2) 'in' (x. 1)))),(((x. 2) 'in' (x. 1)) => ((x. 2) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*4*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*(x. 2)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 0) '=' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*0*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*0*>,<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(x. 0)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 0) '=' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 0) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) '&' ('not' ((x. 0) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1)))))),('not' ((x. 0) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) '&' ('not' ((x. 0) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) '&' ('not' ((x. 0) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(x. 1),((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((x. 1),((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*4*>,<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(All ((x. 1),((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*4*>,<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),(All ((x. 1),((All ((x. 2),(((x. 2) 'in' (x. 0)) <=> ((x. 2) 'in' (x. 1))))) => ((x. 0) '=' (x. 1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 0) is Element of E
u . (x. 1) is Element of E
v is set
a is Element of E
u +* ((x. 2),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 2),a)) . (x. 1) is Element of E
u is ext-real natural V14() Element of VAR
(u +* ((x. 2),a)) . u is Element of E
u . u is Element of E
(u +* ((x. 2),a)) . (x. 2) is Element of E
(u +* ((x. 2),a)) . (x. 0) is Element of E
v is set
a is Element of E
u +* ((x. 2),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 2),a)) . (x. 1) is Element of E
u is ext-real natural V14() Element of VAR
(u +* ((x. 2),a)) . u is Element of E
u . u is Element of E
(u +* ((x. 2),a)) . (x. 2) is Element of E
(u +* ((x. 2),a)) . (x. 0) is Element of E
the_axiom_of_pairs is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(x. 3) 'in' (x. 2) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(x. 3)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*1*>,<*(x. 3)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 3)*>),<*(x. 2)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) '=' (x. 0) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*0*>,<*(x. 3)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(x. 3)*>),<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) '=' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(x. 3)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 3) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 3) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((x. 3) '=' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 3) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
('not' ((x. 3) '=' (x. 0))) '&' ('not' ((x. 3) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,('not' ((x. 3) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,('not' ((x. 3) '=' (x. 0)))),('not' ((x. 3) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (('not' ((x. 3) '=' (x. 0))) '&' ('not' ((x. 3) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(('not' ((x. 3) '=' (x. 0))) '&' ('not' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 3) 'in' (x. 2)) => (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 2)) '&' ('not' (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 3) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 2))),('not' (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 2)) '&' ('not' (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 2)) '&' ('not' (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) => ((x. 3) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 3) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 3) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) '&' ('not' ((x. 3) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))),('not' ((x. 3) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) '&' ('not' ((x. 3) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) '&' ('not' ((x. 3) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 3) 'in' (x. 2)) => (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))) '&' ((((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) => ((x. 3) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 3) 'in' (x. 2)) => (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 3) 'in' (x. 2)) => (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))),((((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))) => ((x. 3) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*4*>,<*(x. 3)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(x. 1),(Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(All ((x. 1),(Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),(All ((x. 1),(Ex ((x. 2),(All ((x. 3),(((x. 3) 'in' (x. 2)) <=> (((x. 3) '=' (x. 0)) 'or' ((x. 3) '=' (x. 1))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
u is set
v is Element of E
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Element of E
a is Element of E
{v,a} is set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) +* ((x. 1),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
i is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) +* ((x. 1),a)) . (x. 1) is Element of E
( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) . (x. 0) is Element of E
(( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) +* ((x. 1),a)) . (x. 0) is Element of E
i . (x. 2) is Element of E
j is set
m1 is Element of E
i +* ((x. 3),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(i +* ((x. 3),m1)) . (x. 3) is Element of E
k is ext-real natural V14() Element of VAR
(i +* ((x. 3),m1)) . k is Element of E
i . k is Element of E
(i +* ((x. 3),m1)) . (x. 2) is Element of E
(i +* ((x. 3),m1)) . (x. 0) is Element of E
(i +* ((x. 3),m1)) . (x. 1) is Element of E
i . (x. 1) is Element of E
i . (x. 0) is Element of E
m1 is Element of E
i +* ((x. 3),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(i +* ((x. 3),m1)) . (x. 3) is Element of E
k is ext-real natural V14() Element of VAR
(i +* ((x. 3),m1)) . k is Element of E
i . k is Element of E
(i +* ((x. 3),m1)) . (x. 1) is Element of E
i . (x. 1) is Element of E
(i +* ((x. 3),m1)) . (x. 0) is Element of E
i . (x. 0) is Element of E
(i +* ((x. 3),m1)) . (x. 2) is Element of E
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v . (x. 0) is Element of E
v . (x. 1) is Element of E
{(v . (x. 0)),(v . (x. 1))} is set
a is Element of E
v +* ((x. 2),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 2),a)) . (x. 2) is Element of E
(v +* ((x. 2),a)) . (x. 0) is Element of E
(v +* ((x. 2),a)) . (x. 1) is Element of E
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 3) is Element of E
u . (x. 2) is Element of E
u . (x. 1) is Element of E
u . (x. 0) is Element of E
u is ext-real natural V14() Element of VAR
(v +* ((x. 2),a)) . u is Element of E
v . u is Element of E
E is non empty set
u is set
v is set
{u,v} is set
u is Element of E
v is Element of E
{u,v} is set
the_axiom_of_unions is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(x. 2) 'in' (x. 3) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 2)*>),<*(x. 3)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) 'in' (x. 0) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 3)*>),<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 2) 'in' (x. 3))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 3))),((x. 3) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 2) 'in' (x. 1)) => (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) '&' ('not' (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 1))),('not' (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 1)) '&' ('not' (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 1)) '&' ('not' (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))),('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 2) 'in' (x. 1)) => (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))) '&' ((Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 2) 'in' (x. 1)) => (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 2) 'in' (x. 1)) => (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))),((Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),(Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (Ex ((x. 3),(((x. 2) 'in' (x. 3)) '&' ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Element of E
union v is set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) . (x. 0) is Element of E
e . (x. 1) is Element of E
u is set
e . (x. 0) is Element of E
i is Element of E
e +* ((x. 2),i) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 2),i)) . (x. 2) is Element of E
m1 is ext-real natural V14() Element of VAR
(e +* ((x. 2),i)) . m1 is Element of E
e . m1 is Element of E
(e +* ((x. 2),i)) . (x. 1) is Element of E
m1 is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
m1 . (x. 0) is Element of E
(e +* ((x. 2),i)) . (x. 0) is Element of E
m1 . (x. 2) is Element of E
m1 . (x. 3) is Element of E
m is set
i is set
j is Element of E
m1 is Element of E
e +* ((x. 2),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 2),m1)) +* ((x. 3),j) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((e +* ((x. 2),m1)) +* ((x. 3),j)) . (x. 3) is Element of E
((e +* ((x. 2),m1)) +* ((x. 3),j)) . (x. 0) is Element of E
(e +* ((x. 2),m1)) . (x. 0) is Element of E
(e +* ((x. 2),m1)) . (x. 2) is Element of E
x is ext-real natural V14() Element of VAR
(e +* ((x. 2),m1)) . x is Element of E
e . x is Element of E
((e +* ((x. 2),m1)) +* ((x. 3),j)) . (x. 2) is Element of E
x is ext-real natural V14() Element of VAR
((e +* ((x. 2),m1)) +* ((x. 3),j)) . x is Element of E
(e +* ((x. 2),m1)) . x is Element of E
(e +* ((x. 2),m1)) . (x. 1) is Element of E
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 0) is Element of E
union (u . (x. 0)) is set
v is Element of E
u +* ((x. 1),v) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 1),v)) . (x. 1) is Element of E
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e . (x. 1) is Element of E
e . (x. 2) is Element of E
u is set
i is Element of E
e +* ((x. 3),i) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 3),i)) . (x. 3) is Element of E
(u +* ((x. 1),v)) . (x. 0) is Element of E
(e +* ((x. 3),i)) . (x. 2) is Element of E
(e +* ((x. 3),i)) . (x. 0) is Element of E
e . (x. 0) is Element of E
m1 is ext-real natural V14() Element of VAR
(e +* ((x. 3),i)) . m1 is Element of E
e . m1 is Element of E
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 3) is Element of E
u . (x. 0) is Element of E
u . (x. 2) is Element of E
union (u . (x. 0)) is set
e . (x. 0) is Element of E
(u +* ((x. 1),v)) . (x. 0) is Element of E
e . (x. 2) is Element of E
e is ext-real natural V14() Element of VAR
(u +* ((x. 1),v)) . e is Element of E
u . e is Element of E
E is non empty set
u is set
union u is set
u is Element of E
union u is set
the_axiom_of_infinity is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(x. 1) 'in' (x. 0) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*1*>,<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 1)*>),<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) '=' (x. 2) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(x. 3)*>),<*(x. 2)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((x. 3) '=' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 3) '=' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 3) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 0))),('not' ((x. 3) '=' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 4) 'in' (x. 2) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(x. 4)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*1*>,<*(x. 4)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 4)*>),<*(x. 2)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 4) 'in' (x. 3) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 4)*>),<*(x. 3)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 4) 'in' (x. 3)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 4) 'in' (x. 3))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' ((x. 4) 'in' (x. 3))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' ((x. 4) 'in' (x. 3)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' ((x. 4) 'in' (x. 3)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' ((x. 4) 'in' (x. 3))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*4*>,<*(x. 4)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2))))),(All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' ((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' ((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' ((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' ((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 0)) '&' ('not' (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 0))),('not' (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 0)) '&' ('not' (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 0)) '&' ('not' (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 1) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 1) 'in' (x. 0))),(All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),('not' (((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),('not' (((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 1),('not' (((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),('not' (((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3)))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (Ex ((x. 1),(((x. 1) 'in' (x. 0)) '&' (All ((x. 2),(((x. 2) 'in' (x. 0)) => (Ex ((x. 3),((((x. 3) 'in' (x. 0)) '&' ('not' ((x. 3) '=' (x. 2)))) '&' (All ((x. 4),(((x. 4) 'in' (x. 2)) => ((x. 4) 'in' (x. 3))))))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v . (x. 0) is Element of E
a is Element of E
e is Element of E
v +* ((x. 2),e) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
i is ext-real natural V14() Element of VAR
(v +* ((x. 2),e)) . i is Element of E
v . i is Element of E
(v +* ((x. 2),e)) . (x. 2) is Element of E
(v +* ((x. 2),e)) . (x. 0) is Element of E
i is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
i . (x. 0) is Element of E
i . (x. 3) is Element of E
j is Element of E
m1 is set
m is Element of E
i +* ((x. 4),m) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(i +* ((x. 4),m)) . (x. 4) is Element of E
x is ext-real natural V14() Element of VAR
(i +* ((x. 4),m)) . x is Element of E
i . x is Element of E
(i +* ((x. 4),m)) . (x. 2) is Element of E
i . (x. 2) is Element of E
(i +* ((x. 4),m)) . (x. 3) is Element of E
i . (x. 2) is Element of E
u is Element of E
the Element of u is Element of u
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e +* ((x. 0),u) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Element of E
(e +* ((x. 0),u)) +* ((x. 1),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 0),u)) . (x. 0) is Element of E
j is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
j . (x. 2) is Element of E
j . (x. 0) is Element of E
((e +* ((x. 0),u)) +* ((x. 1),a)) . (x. 0) is Element of E
m1 is Element of E
j +* ((x. 3),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(j +* ((x. 3),m1)) . (x. 3) is Element of E
k is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
k . (x. 4) is Element of E
k . (x. 2) is Element of E
k . (x. 3) is Element of E
(j +* ((x. 3),m1)) . (x. 2) is Element of E
(j +* ((x. 3),m1)) . (x. 0) is Element of E
k is ext-real natural V14() Element of VAR
(j +* ((x. 3),m1)) . k is Element of E
j . k is Element of E
((e +* ((x. 0),u)) +* ((x. 1),a)) . (x. 1) is Element of E
j is ext-real natural V14() Element of VAR
((e +* ((x. 0),u)) +* ((x. 1),a)) . j is Element of E
(e +* ((x. 0),u)) . j is Element of E
j is ext-real natural V14() Element of VAR
(e +* ((x. 0),u)) . j is Element of E
e . j is Element of E
E is non empty set
u is Element of E
v is set
a is set
e is Element of E
u is Element of E
i is set
u is set
v is Element of E
a is Element of E
e is set
u is Element of E
v is Element of E
the_axiom_of_power_sets is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 3) 'in' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 3) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 2)) '&' ('not' ((x. 3) 'in' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 2))),('not' ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 2)) '&' ('not' ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 2)) '&' ('not' ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 2) 'in' (x. 1)) => (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 2) 'in' (x. 1)) '&' ('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 2) 'in' (x. 1))),('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 2) 'in' (x. 1)) '&' ('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 2) 'in' (x. 1)) '&' ('not' (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))),('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) '&' ('not' ((x. 2) 'in' (x. 1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 2) 'in' (x. 1)) => (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))) '&' ((All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 2) 'in' (x. 1)) => (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 2) 'in' (x. 1)) => (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))),((All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))) => ((x. 2) 'in' (x. 1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),('not' (All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),(Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),(Ex ((x. 1),(All ((x. 2),(((x. 2) 'in' (x. 1)) <=> (All ((x. 3),(((x. 3) 'in' (x. 2)) => ((x. 3) 'in' (x. 0))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Element of E
bool v is non empty set
E /\ (bool v) is set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
( the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] +* ((x. 0),v)) . (x. 0) is Element of E
e . (x. 1) is Element of E
u is set
i is Element of E
e +* ((x. 2),i) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 2),i)) . (x. 2) is Element of E
m1 is ext-real natural V14() Element of VAR
(e +* ((x. 2),i)) . m1 is Element of E
e . m1 is Element of E
(e +* ((x. 2),i)) . (x. 1) is Element of E
m1 is set
m is Element of E
(e +* ((x. 2),i)) +* ((x. 3),m) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((e +* ((x. 2),i)) +* ((x. 3),m)) . (x. 3) is Element of E
x is ext-real natural V14() Element of VAR
((e +* ((x. 2),i)) +* ((x. 3),m)) . x is Element of E
(e +* ((x. 2),i)) . x is Element of E
((e +* ((x. 2),i)) +* ((x. 3),m)) . (x. 2) is Element of E
((e +* ((x. 2),i)) +* ((x. 3),m)) . (x. 0) is Element of E
(e +* ((x. 2),i)) . (x. 0) is Element of E
e . (x. 0) is Element of E
u is set
i is Element of E
e +* ((x. 2),i) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 2),i)) . (x. 2) is Element of E
m1 is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
m1 . (x. 3) is Element of E
m1 . (x. 2) is Element of E
(e +* ((x. 2),i)) . (x. 0) is Element of E
e . (x. 0) is Element of E
m1 . (x. 0) is Element of E
(e +* ((x. 2),i)) . (x. 1) is Element of E
m1 is ext-real natural V14() Element of VAR
(e +* ((x. 2),i)) . m1 is Element of E
e . m1 is Element of E
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 0) is Element of E
bool (u . (x. 0)) is non empty set
E /\ (bool (u . (x. 0))) is set
v is Element of E
u +* ((x. 1),v) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 1),v)) . (x. 1) is Element of E
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e . (x. 2) is Element of E
e . (x. 1) is Element of E
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 3) is Element of E
u . (x. 2) is Element of E
(u +* ((x. 1),v)) . (x. 0) is Element of E
e . (x. 0) is Element of E
u . (x. 0) is Element of E
e . (x. 2) is Element of E
u is set
i is Element of E
e +* ((x. 3),i) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(e +* ((x. 3),i)) . (x. 3) is Element of E
m1 is ext-real natural V14() Element of VAR
(e +* ((x. 3),i)) . m1 is Element of E
e . m1 is Element of E
(e +* ((x. 3),i)) . (x. 2) is Element of E
(e +* ((x. 3),i)) . (x. 0) is Element of E
e . (x. 0) is Element of E
(u +* ((x. 1),v)) . (x. 0) is Element of E
e . (x. 1) is Element of E
e is ext-real natural V14() Element of VAR
(u +* ((x. 1),v)) . e is Element of E
u . e is Element of E
E is non empty set
u is set
bool u is non empty set
E /\ (bool u) is set
u is Element of E
bool u is non empty set
E /\ (bool u) is set
E is ext-real natural set
u is ext-real natural V14() Element of VAR
v is non empty set
[:VAR,v:] is non empty Relation-like set
bool [:VAR,v:] is non empty set
a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
len a is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
Free a is V32() V33() V34() V35() V36() V37() Element of bool VAR
All (u,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*u*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*u*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
e is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
Var1 a is ext-real natural V14() Element of VAR
Var2 a is ext-real natural V14() Element of VAR
{(Var1 a),(Var2 a)} is V32() V33() V34() V35() V36() V37() set
(Var1 a) '=' (Var2 a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(Var1 a)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*0*>,<*(Var1 a)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
<*(Var2 a)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(Var1 a)*>),<*(Var2 a)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
e . (Var1 a) is Element of v
e . (Var2 a) is Element of v
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
u . (Var1 a) is Element of v
u . (Var2 a) is Element of v
bound_in a is ext-real natural V14() Element of VAR
the_scope_of a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((bound_in a),(the_scope_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(bound_in a)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*(bound_in a)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(bound_in a)*>),(the_scope_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Free (the_scope_of a) is V32() V33() V34() V35() V36() V37() Element of bool VAR
{(bound_in a)} is V32() V33() V34() V35() V36() V37() set
(Free (the_scope_of a)) \ {(bound_in a)} is V32() V33() V34() V35() V36() V37() Element of bool VAR
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
i is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
i . (bound_in a) is Element of v
e +* ((bound_in a),(i . (bound_in a))) is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
m1 is ext-real natural V14() Element of VAR
i . m1 is Element of v
(e +* ((bound_in a),(i . (bound_in a)))) . m1 is Element of v
e . m1 is Element of v
u . m1 is Element of v
len (the_scope_of a) is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
m1 is ext-real natural V14() Element of VAR
(e +* ((bound_in a),(i . (bound_in a)))) . m1 is Element of v
e . m1 is Element of v
All (u,(the_scope_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(the_scope_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
i is ext-real natural V14() Element of VAR
u . i is Element of v
e . i is Element of v
All (u,(bound_in a),(the_scope_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All (u,(All ((bound_in a),(the_scope_of a)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(All ((bound_in a),(the_scope_of a)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
the_left_argument_of a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
the_right_argument_of a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(the_left_argument_of a) '&' (the_right_argument_of a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(the_left_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(the_left_argument_of a)),(the_right_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
len (the_right_argument_of a) is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
len (the_left_argument_of a) is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
Free (the_left_argument_of a) is V32() V33() V34() V35() V36() V37() Element of bool VAR
Free (the_right_argument_of a) is V32() V33() V34() V35() V36() V37() Element of bool VAR
(Free (the_left_argument_of a)) \/ (Free (the_right_argument_of a)) is V32() V33() V34() V35() V36() V37() Element of bool VAR
All (u,(the_right_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(the_right_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All (u,(the_left_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(the_left_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
(Var1 a) 'in' (Var2 a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*1*>,<*(Var1 a)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(Var1 a)*>),<*(Var2 a)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
u . (Var1 a) is Element of v
u . (Var2 a) is Element of v
the_argument_of a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (the_argument_of a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(the_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
len (the_argument_of a) is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
Free (the_argument_of a) is V32() V33() V34() V35() V36() V37() Element of bool VAR
u is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
All (u,(the_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(the_argument_of a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is ext-real natural V14() Element of VAR
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
All (E,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*E*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*E*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*E*>),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is non empty set
[:VAR,v:] is non empty Relation-like set
bool [:VAR,v:] is non empty set
a is Relation-like VAR -defined v -valued Function-like V29( VAR ,v) Element of bool [:VAR,v:]
len u is ext-real natural V14() V32() V33() V34() V35() V36() V37() Element of K45()
E is ext-real natural V14() Element of VAR
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All (E,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*E*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*E*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*E*>),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
the_scope_of (All (E,u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
bound_in (All (E,u)) is ext-real natural V14() Element of VAR
All ((bound_in (All (E,u))),(the_scope_of (All (E,u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(bound_in (All (E,u)))*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*(bound_in (All (E,u)))*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(bound_in (All (E,u)))*>),(the_scope_of (All (E,u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is ext-real natural V14() Element of VAR
u is ext-real natural V14() Element of VAR
{E,u} is V32() V33() V34() V35() V36() V37() set
v is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free v is V32() V33() V34() V35() V36() V37() Element of bool VAR
All (E,u,v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All (u,v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*u*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*u*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All (E,(All (u,v))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*E*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*E*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*E*>),(All (u,v))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
a is non empty set
[:VAR,a:] is non empty Relation-like set
bool [:VAR,a:] is non empty set
e is Relation-like VAR -defined a -valued Function-like V29( VAR ,a) Element of bool [:VAR,a:]
bound_in (All (u,v)) is ext-real natural V14() Element of VAR
the_scope_of (All (u,v)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (All (u,v)) is V32() V33() V34() V35() V36() V37() Element of bool VAR
{u} is V32() V33() V34() V35() V36() V37() set
(Free v) \ {u} is V32() V33() V34() V35() V36() V37() Element of bool VAR
E is ext-real natural V14() Element of VAR
u is ext-real natural V14() Element of VAR
v is ext-real natural V14() Element of VAR
{E,u,v} is non empty V32() V33() V34() V35() V36() V37() set
a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free a is V32() V33() V34() V35() V36() V37() Element of bool VAR
All (E,u,v,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All (u,v,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All (v,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*v*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*v*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*v*>),a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All (u,(All (v,a))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*u*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*u*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*u*>),(All (v,a))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All (E,(All (u,v,a))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*E*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*E*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*E*>),(All (u,v,a))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
e is non empty set
[:VAR,e:] is non empty Relation-like set
bool [:VAR,e:] is non empty set
u is Relation-like VAR -defined e -valued Function-like V29( VAR ,e) Element of bool [:VAR,e:]
bound_in (All (u,(All (v,a)))) is ext-real natural V14() Element of VAR
i is set
{u,v} is V32() V33() V34() V35() V36() V37() set
the_scope_of (All (v,a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
{v} is V32() V33() V34() V35() V36() V37() set
(Free a) \ {v} is V32() V33() V34() V35() V36() V37() Element of bool VAR
{u} is V32() V33() V34() V35() V36() V37() set
((Free a) \ {v}) \ {u} is V32() V33() V34() V35() V36() V37() Element of bool VAR
bound_in (All (v,a)) is ext-real natural V14() Element of VAR
the_scope_of (All (u,(All (v,a)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (All (u,v,a)) is V32() V33() V34() V35() V36() V37() Element of bool VAR
Free (All (v,a)) is V32() V33() V34() V35() V36() V37() Element of bool VAR
(Free (All (v,a))) \ {u} is V32() V33() V34() V35() V36() V37() Element of bool VAR
u is non empty set
[:VAR,u:] is non empty Relation-like set
bool [:VAR,u:] is non empty set
E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free E is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(x. 4) '=' (x. 0) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*0*>,<*(x. 4)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(x. 4)*>),<*(x. 0)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
E => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,E),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (E '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(E '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' E))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(E => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(E => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(E => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(E <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
a is set
e is set
e is set
u is set
[e,u] is V26() set
{e,u} is set
{e} is set
{{e,u},{e}} is set
i is set
[e,i] is V26() set
{e,i} is set
{{e,i},{e}} is set
j is Element of u
v +* ((x. 3),j) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
x is ext-real natural V14() Element of VAR
(v +* ((x. 3),j)) . x is Element of u
v . x is Element of u
x is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(v +* ((x. 3),j)) . (x. 3) is Element of u
x . (x. 3) is Element of u
m1 is Element of u
x +* ((x. 4),m1) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(x +* ((x. 4),m1)) . (x. 4) is Element of u
x is ext-real natural V14() Element of VAR
(x +* ((x. 4),m1)) . x is Element of u
v . x is Element of u
(v +* ((x. 3),j)) . x is Element of u
x . x is Element of u
x is ext-real natural V14() Element of VAR
(x +* ((x. 4),m1)) . x is Element of u
x . x is Element of u
(x +* ((x. 4),m1)) . (x. 3) is Element of u
[e,u] `1 is set
[e,u] `2 is set
(x +* ((x. 4),m1)) . (x. 0) is Element of u
m is Element of u
x +* ((x. 4),m) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(x +* ((x. 4),m)) . (x. 4) is Element of u
y is ext-real natural V14() Element of VAR
(x +* ((x. 4),m)) . y is Element of u
v . y is Element of u
(v +* ((x. 3),j)) . y is Element of u
x . y is Element of u
y is ext-real natural V14() Element of VAR
(x +* ((x. 4),m)) . y is Element of u
x . y is Element of u
(x +* ((x. 4),m)) . (x. 3) is Element of u
[e,i] `1 is set
[e,i] `2 is set
x . (x. 0) is Element of u
(x +* ((x. 4),m)) . (x. 0) is Element of u
e is Relation-like Function-like set
proj2 e is set
u is set
proj1 e is set
i is set
e . i is set
[i,u] is V26() set
{i,u} is set
{i} is set
{{i,u},{i}} is set
proj1 e is set
u is set
i is Element of u
v +* ((x. 3),i) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
m1 is ext-real natural V14() Element of VAR
(v +* ((x. 3),i)) . m1 is Element of u
v . m1 is Element of u
m1 is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
m1 . (x. 0) is Element of u
(v +* ((x. 3),i)) . (x. 3) is Element of u
m1 +* ((x. 4),(m1 . (x. 0))) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
x is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
x . (x. 3) is Element of u
[i,(m1 . (x. 0))] is V26() set
{i,(m1 . (x. 0))} is set
{i} is set
{{i,(m1 . (x. 0))},{i}} is set
[i,(m1 . (x. 0))] `1 is set
x . (x. 4) is Element of u
[i,(m1 . (x. 0))] `2 is set
(m1 +* ((x. 4),(m1 . (x. 0)))) . (x. 4) is Element of u
k is ext-real natural V14() Element of VAR
x . k is Element of u
(m1 +* ((x. 4),(m1 . (x. 0)))) . k is Element of u
m1 . k is Element of u
m1 . (x. 3) is Element of u
(m1 +* ((x. 4),(m1 . (x. 0)))) . (x. 3) is Element of u
(v +* ((x. 3),i)) . k is Element of u
v . k is Element of u
k is ext-real natural V14() Element of VAR
(m1 +* ((x. 4),(m1 . (x. 0)))) . k is Element of u
m1 . k is Element of u
(m1 +* ((x. 4),(m1 . (x. 0)))) . (x. 0) is Element of u
All ((x. 0),E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is set
i is set
[u,i] is V26() set
{u,i} is set
{u} is set
{{u,i},{u}} is set
u is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
i is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
i . (x. 3) is Element of u
u . (i . (x. 3)) is Element of u
i . (x. 4) is Element of u
All ((x. 0),E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
j is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j . (x. 3) is Element of u
[(i . (x. 3)),(i . (x. 4))] is V26() set
{(i . (x. 3)),(i . (x. 4))} is set
{(i . (x. 3))} is set
{{(i . (x. 3)),(i . (x. 4))},{(i . (x. 3))}} is set
[(i . (x. 3)),(i . (x. 4))] `1 is set
j . (x. 4) is Element of u
[(i . (x. 3)),(i . (x. 4))] `2 is set
m1 is ext-real natural V14() Element of VAR
j . m1 is Element of u
i . m1 is Element of u
v . m1 is Element of u
[(i . (x. 3)),(i . (x. 4))] is V26() set
{(i . (x. 3)),(i . (x. 4))} is set
{(i . (x. 3))} is set
{{(i . (x. 3)),(i . (x. 4))},{(i . (x. 3))}} is set
[(i . (x. 3)),(i . (x. 4))] `1 is set
[(i . (x. 3)),(i . (x. 4))] `2 is set
dom u is Element of bool u
bool u is non empty set
a is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
e is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
u is Element of u
a . u is set
e . u is set
v +* ((x. 3),u) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j is ext-real natural V14() Element of VAR
(v +* ((x. 3),u)) . j is Element of u
v . j is Element of u
j is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j . (x. 3) is Element of u
(v +* ((x. 3),u)) . (x. 3) is Element of u
j . (x. 0) is Element of u
j +* ((x. 4),(j . (x. 0))) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
m is ext-real natural V14() Element of VAR
(j +* ((x. 4),(j . (x. 0)))) . m is Element of u
v . m is Element of u
(v +* ((x. 3),u)) . m is Element of u
j . m is Element of u
(j +* ((x. 4),(j . (x. 0)))) . (x. 4) is Element of u
(j +* ((x. 4),(j . (x. 0)))) . (x. 0) is Element of u
(j +* ((x. 4),(j . (x. 0)))) . (x. 3) is Element of u
m is ext-real natural V14() Element of VAR
(j +* ((x. 4),(j . (x. 0)))) . m is Element of u
j . m is Element of u
a . ((j +* ((x. 4),(j . (x. 0)))) . (x. 3)) is Element of u
a . u is Element of u
e . u is Element of u
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
Var1 u is ext-real natural V14() Element of VAR
Var2 u is ext-real natural V14() Element of VAR
{(Var1 u),(Var2 u)} is V32() V33() V34() V35() V36() V37() set
v . (Var1 u) is Element of E
a . (Var1 u) is Element of E
v . (Var2 u) is Element of E
a . (Var2 u) is Element of E
(Var1 u) 'in' (Var2 u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(Var1 u)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*1*>,<*(Var1 u)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
<*(Var2 u)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(Var1 u)*>),<*(Var2 u)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Var1 u) '=' (Var2 u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*0*>,<*(Var1 u)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*0*>,<*(Var1 u)*>),<*(Var2 u)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
the_left_argument_of u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (the_left_argument_of u) is V32() V33() V34() V35() V36() V37() Element of bool VAR
the_right_argument_of u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (the_right_argument_of u) is V32() V33() V34() V35() V36() V37() Element of bool VAR
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
(the_left_argument_of u) '&' (the_right_argument_of u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(the_left_argument_of u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(the_left_argument_of u)),(the_right_argument_of u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(Free (the_left_argument_of u)) \/ (Free (the_right_argument_of u)) is V32() V33() V34() V35() V36() V37() Element of bool VAR
e is ext-real natural V14() Element of VAR
v . e is Element of E
a . e is Element of E
e is ext-real natural V14() Element of VAR
v . e is Element of E
a . e is Element of E
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
the_scope_of u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (the_scope_of u) is V32() V33() V34() V35() V36() V37() Element of bool VAR
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
bound_in u is ext-real natural V14() Element of VAR
All ((bound_in u),(the_scope_of u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
<*(bound_in u)*> is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),<*4*>,<*(bound_in u)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(bound_in u)*>),(the_scope_of u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
{(bound_in u)} is V32() V33() V34() V35() V36() V37() set
(Free (the_scope_of u)) \ {(bound_in u)} is V32() V33() V34() V35() V36() V37() Element of bool VAR
e is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
e . (bound_in u) is Element of E
v +* ((bound_in u),(e . (bound_in u))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
i is ext-real natural V14() Element of VAR
(v +* ((bound_in u),(e . (bound_in u)))) . i is Element of E
e . i is Element of E
v . i is Element of E
a . i is Element of E
i is ext-real natural V14() Element of VAR
(v +* ((bound_in u),(e . (bound_in u)))) . i is Element of E
v . i is Element of E
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
the_argument_of u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free (the_argument_of u) is V32() V33() V34() V35() V36() V37() Element of bool VAR
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
'not' (the_argument_of u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(the_argument_of u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free E is V32() V33() V34() V35() V36() V37() Element of bool VAR
{(x. 3),(x. 4)} is V32() V33() V34() V35() V36() V37() set
u is non empty set
E <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
E => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
E '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,E),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (E '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(E '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' E is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' E))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(E => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => E) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(E => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(E => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => E)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(E <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(E <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(E <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
[:u,u:] is non empty Relation-like set
bool [:u,u:] is non empty set
[:VAR,u:] is non empty Relation-like set
bool [:VAR,u:] is non empty set
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(E,u, the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]) is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
a is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
e is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
e . (x. 3) is Element of u
a . (e . (x. 3)) is Element of u
e . (x. 4) is Element of u
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3))) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4))) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j is ext-real natural V14() Element of VAR
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . j is Element of u
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] . j is Element of u
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) . j is Element of u
m is ext-real natural V14() Element of VAR
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . m is Element of u
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] . m is Element of u
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) . m is Element of u
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) . (x. 3) is Element of u
m is ext-real natural V14() Element of VAR
e . m is Element of u
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . m is Element of u
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 4) is Element of u
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 3) is Element of u
a . ((( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 3)) is Element of u
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) . (x. 3) is Element of u
j is ext-real natural V14() Element of VAR
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . j is Element of u
e . j is Element of u
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 4) is Element of u
(( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 3) is Element of u
a . ((( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),(e . (x. 3)))) +* ((x. 4),(e . (x. 4)))) . (x. 3)) is Element of u
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
a is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
e is Relation-like u -defined u -valued Function-like V29(u,u) Element of bool [:u,u:]
u is Element of u
a . u is set
e . u is set
the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),u) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
j . (x. 3) is Element of u
( the Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:] +* ((x. 3),u)) . (x. 3) is Element of u
j . (x. 0) is Element of u
j +* ((x. 4),(j . (x. 0))) is Relation-like VAR -defined u -valued Function-like V29( VAR ,u) Element of bool [:VAR,u:]
(j +* ((x. 4),(j . (x. 0)))) . (x. 3) is Element of u
(j +* ((x. 4),(j . (x. 0)))) . (x. 4) is Element of u
(j +* ((x. 4),(j . (x. 0)))) . (x. 0) is Element of u
m is ext-real natural V14() Element of VAR
(j +* ((x. 4),(j . (x. 0)))) . m is Element of u
j . m is Element of u
a . ((j +* ((x. 4),(j . (x. 0)))) . (x. 3)) is Element of u
a . u is Element of u
e . u is Element of u
{(x. 0),(x. 1),(x. 2)} is non empty V32() V33() V34() V35() V36() V37() set
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:] is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v is Relation-like Function-like set
a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free a is V32() V33() V34() V35() V36() V37() Element of bool VAR
a <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
a => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
a '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,a),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (a '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(a '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' a is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' a))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(a => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => a) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(a => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(a => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => a)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(a <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(a <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(a <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(a <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(a <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(a <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(a,E) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
[:E,E:] is non empty Relation-like set
bool [:E,E:] is non empty set
(a,E, the Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
e is set
e is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 3) is Element of E
e . (u . (x. 3)) is Element of E
u . (x. 4) is Element of E
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
the_axiom_of_substitution_for u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(x. 3) 'in' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 3)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 3) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
a is Element of E
v +* ((x. 1),a) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u is set
{(x. 1),(x. 2)} is V32() V33() V34() V35() V36() V37() set
u is ext-real natural V14() Element of VAR
(v +* ((x. 1),a)) . u is Element of E
v . u is Element of E
u is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u . (x. 2) is Element of E
(v +* ((x. 1),a)) . (x. 1) is Element of E
(u,E,v) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
[:E,E:] is non empty Relation-like set
bool [:E,E:] is non empty set
(u,E,v) .: a is Element of bool E
bool E is non empty set
j is set
dom (u,E,v) is Element of bool E
m1 is set
(u,E,v) . m1 is set
k is Element of E
u +* ((x. 4),k) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
m is Element of E
(u +* ((x. 4),k)) +* ((x. 3),m) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 3) is Element of E
u . (x. 1) is Element of E
((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 1) is Element of E
(u +* ((x. 4),k)) . (x. 1) is Element of E
v +* ((x. 3),m) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 4),k)) . (x. 4) is Element of E
(v +* ((x. 3),m)) +* ((x. 4),k) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),m)) . (x. 3) is Element of E
((v +* ((x. 3),m)) +* ((x. 4),k)) +* ((x. 1),(((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 1))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((v +* ((x. 3),m)) +* ((x. 4),k)) . (x. 4) is Element of E
((v +* ((x. 3),m)) +* ((x. 4),k)) . (x. 3) is Element of E
y is ext-real natural V14() Element of VAR
((u +* ((x. 4),k)) +* ((x. 3),m)) . y is Element of E
(((v +* ((x. 3),m)) +* ((x. 4),k)) +* ((x. 1),(((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 1)))) . y is Element of E
(((v +* ((x. 3),m)) +* ((x. 4),k)) +* ((x. 1),(((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 1)))) . (x. 4) is Element of E
((v +* ((x. 3),m)) +* ((x. 4),k)) . y is Element of E
(v +* ((x. 3),m)) . y is Element of E
v . y is Element of E
(v +* ((x. 1),a)) . y is Element of E
u . y is Element of E
(u +* ((x. 4),k)) . y is Element of E
y is ext-real natural V14() Element of VAR
(((v +* ((x. 3),m)) +* ((x. 4),k)) +* ((x. 1),(((u +* ((x. 4),k)) +* ((x. 3),m)) . (x. 1)))) . y is Element of E
((v +* ((x. 3),m)) +* ((x. 4),k)) . y is Element of E
y is ext-real natural V14() Element of VAR
((v +* ((x. 3),m)) +* ((x. 4),k)) . y is Element of E
v . y is Element of E
(v +* ((x. 3),m)) . y is Element of E
(u,E,v) . (((v +* ((x. 3),m)) +* ((x. 4),k)) . (x. 3)) is Element of E
All ((x. 1),(x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
y is ext-real natural V14() Element of VAR
(u +* ((x. 4),k)) . y is Element of E
u . y is Element of E
(u +* ((x. 4),k)) . (x. 2) is Element of E
y is ext-real natural V14() Element of VAR
(u +* ((x. 4),k)) . y is Element of E
((u +* ((x. 4),k)) +* ((x. 3),m)) . y is Element of E
j is set
m1 is Element of E
u +* ((x. 4),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u +* ((x. 4),m1)) . (x. 4) is Element of E
k is ext-real natural V14() Element of VAR
(u +* ((x. 4),m1)) . k is Element of E
u . k is Element of E
(u +* ((x. 4),m1)) . (x. 2) is Element of E
k is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
k . (x. 1) is Element of E
(u +* ((x. 4),m1)) . (x. 1) is Element of E
k . (x. 3) is Element of E
v +* ((x. 3),(k . (x. 3))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 4) is Element of E
((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1) is Element of E
k +* ((x. 1),(((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),(k . (x. 3)))) . (x. 3) is Element of E
y is ext-real natural V14() Element of VAR
((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . y is Element of E
(k +* ((x. 1),(((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1)))) . y is Element of E
(k +* ((x. 1),(((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1)))) . (x. 3) is Element of E
(k +* ((x. 1),(((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1)))) . (x. 4) is Element of E
k . (x. 4) is Element of E
k . y is Element of E
(u +* ((x. 4),m1)) . y is Element of E
u . y is Element of E
(v +* ((x. 1),a)) . y is Element of E
v . y is Element of E
(v +* ((x. 3),(k . (x. 3)))) . y is Element of E
y is ext-real natural V14() Element of VAR
((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . y is Element of E
v . y is Element of E
(v +* ((x. 3),(k . (x. 3)))) . y is Element of E
((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 3) is Element of E
(u,E,v) . (((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 3)) is Element of E
All ((x. 1),(x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u . (x. 1) is Element of E
dom (u,E,v) is Element of bool E
y is ext-real natural V14() Element of VAR
(k +* ((x. 1),(((v +* ((x. 3),(k . (x. 3)))) +* ((x. 4),m1)) . (x. 1)))) . y is Element of E
k . y is Element of E
(u,E,v) . (k . (x. 3)) is Element of E
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is set
the_axiom_of_substitution_for u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u,E,v) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
a . (x. 1) is Element of E
(u,E,v) .: (a . (x. 1)) is Element of bool E
e is Element of E
a +* ((x. 2),e) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(a +* ((x. 2),e)) . (x. 2) is Element of E
i is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
i . (x. 4) is Element of E
i . (x. 2) is Element of E
dom (u,E,v) is Element of bool E
j is set
(u,E,v) . j is set
m1 is Element of E
i +* ((x. 3),m1) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(i +* ((x. 3),m1)) . (x. 3) is Element of E
v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 4) is Element of E
(i +* ((x. 3),m1)) . (x. 1) is Element of E
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) +* ((x. 1),((i +* ((x. 3),m1)) . (x. 1))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) . (x. 3) is Element of E
x is ext-real natural V14() Element of VAR
(i +* ((x. 3),m1)) . x is Element of E
(((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) +* ((x. 1),((i +* ((x. 3),m1)) . (x. 1)))) . x is Element of E
(i +* ((x. 3),m1)) . (x. 4) is Element of E
(((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) +* ((x. 1),((i +* ((x. 3),m1)) . (x. 1)))) . (x. 3) is Element of E
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 3) is Element of E
i . x is Element of E
(a +* ((x. 2),e)) . x is Element of E
a . x is Element of E
v . x is Element of E
(v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) . x is Element of E
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . x is Element of E
x is ext-real natural V14() Element of VAR
(((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) +* ((x. 1),((i +* ((x. 3),m1)) . (x. 1)))) . x is Element of E
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . x is Element of E
x is ext-real natural V14() Element of VAR
((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . x is Element of E
v . x is Element of E
(v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) . x is Element of E
(u,E,v) . (((v +* ((x. 3),((i +* ((x. 3),m1)) . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 3)) is Element of E
All ((x. 1),(x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
All ((x. 2),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(All ((x. 2),u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(a +* ((x. 2),e)) . (x. 1) is Element of E
i . (x. 1) is Element of E
x is ext-real natural V14() Element of VAR
(i +* ((x. 3),m1)) . x is Element of E
i . x is Element of E
j is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
j . (x. 3) is Element of E
v +* ((x. 3),(j . (x. 3))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 4) is Element of E
((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 1) is Element of E
j +* ((x. 1),(((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 1))) is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(v +* ((x. 3),(j . (x. 3)))) . (x. 3) is Element of E
x is ext-real natural V14() Element of VAR
((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . x is Element of E
(j +* ((x. 1),(((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 1)))) . x is Element of E
((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 3) is Element of E
(j +* ((x. 1),(((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 1)))) . (x. 4) is Element of E
j . (x. 4) is Element of E
(v +* ((x. 3),(j . (x. 3)))) . x is Element of E
v . x is Element of E
a . x is Element of E
(a +* ((x. 2),e)) . x is Element of E
i . x is Element of E
j . x is Element of E
j . (x. 1) is Element of E
x is ext-real natural V14() Element of VAR
((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . x is Element of E
v . x is Element of E
(v +* ((x. 3),(j . (x. 3)))) . x is Element of E
x is ext-real natural V14() Element of VAR
(j +* ((x. 1),(((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 1)))) . x is Element of E
j . x is Element of E
(u,E,v) . (((v +* ((x. 3),(j . (x. 3)))) +* ((x. 4),(i . (x. 4)))) . (x. 3)) is Element of E
i is ext-real natural V14() Element of VAR
(a +* ((x. 2),e)) . i is Element of E
a . i is Element of E
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u,E,v) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
a is Element of E
(u,E,v) .: a is Element of bool E
e is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free e is V32() V33() V34() V35() V36() V37() Element of bool VAR
the_axiom_of_substitution_for e is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
e <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
e => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
e '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,e),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (e '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(e '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => e is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' e is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' e)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' e)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(e => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(e => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(e => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => e)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(e <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' e is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' e) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' e)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' e)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(e <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' e))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
i is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u,E,i) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
j is Element of E
(u,E,i) .: j is Element of bool E
m1 is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free m1 is V32() V33() V34() V35() V36() V37() Element of bool VAR
the_axiom_of_substitution_for m1 is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
m1 <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
m1 => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
m1 '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,m1),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (m1 '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(m1 '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => m1 is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' m1 is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' m1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' m1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(m1 => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(m1 => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(m1 => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => m1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(m1 <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' m1 is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' m1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' m1)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' m1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(m1 <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' m1))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
u is Relation-like Function-like set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
v is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free v is V32() V33() V34() V35() V36() V37() Element of bool VAR
a is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
v <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
v => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
v '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,v),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (v '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(v '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => v is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' v is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' v)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' v)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' v))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(v => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => v) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(v => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(v => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => v)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(v <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(v <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(v <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(v <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(v <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(v <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(v,E,a) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
[:E,E:] is non empty Relation-like set
bool [:E,E:] is non empty set
e is set
u .: e is set
u is Element of E
(v,E,a) .: u is Element of bool E
bool E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
(u,E,v) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
[:E,E:] is non empty Relation-like set
bool [:E,E:] is non empty set
a is Element of E
(u,E,v) .: a is Element of bool E
bool E is non empty set
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
the_axiom_of_substitution_for u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) 'in' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 3)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 3) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
E is non empty set
u is Element of E
v is Element of E
a is set
e is Element of E
a is set
e is Element of E
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Element of E
v is Element of E
a is Element of E
e is Element of E
{a,e} is set
u is Element of E
union u is set
i is Element of E
bool i is non empty set
E /\ (bool i) is set
j is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free j is V32() V33() V34() V35() V36() V37() Element of bool VAR
m1 is Relation-like VAR -defined E -valued Function-like V29( VAR ,E) Element of bool [:VAR,E:]
j <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
j => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
j '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,j) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,j),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (j '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(j '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => j is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' j is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,j) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' j) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' j)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' j)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' j))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(j => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => j) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(j => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(j => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => j)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(j <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(j <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(j <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(j <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(j <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(j <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(j,E,m1) is Relation-like E -defined E -valued Function-like V29(E,E) Element of bool [:E,E:]
[:E,E:] is non empty Relation-like set
bool [:E,E:] is non empty set
m is Element of E
(j,E,m1) .: m is Element of bool E
bool E is non empty set
E is non empty set
[:VAR,E:] is non empty Relation-like set
bool [:VAR,E:] is non empty set
u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
Free u is V32() V33() V34() V35() V36() V37() Element of bool VAR
the_axiom_of_substitution_for u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u <=> ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u => ((x. 4) '=' (x. 0)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
u '&' ('not' ((x. 4) '=' (x. 0))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,u),('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (u '&' ('not' ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(u '&' ('not' ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) => u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) '=' (x. 0)) '&' ('not' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) '=' (x. 0))),('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) '=' (x. 0)) '&' ('not' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) '=' (x. 0)) '&' ('not' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(u => ((x. 4) '=' (x. 0))) '&' (((x. 4) '=' (x. 0)) => u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(u => ((x. 4) '=' (x. 0)))),(((x. 4) '=' (x. 0)) => u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(u <=> ((x. 4) '=' (x. 0)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 0)*>),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 0),('not' (All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(x. 3) 'in' (x. 1) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*1*>,<*(x. 3)*>),<*(x. 1)*>) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 3) 'in' (x. 1)) '&' u is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,((x. 3) 'in' (x. 1))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 3) 'in' (x. 1))),u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (((x. 3) 'in' (x. 1)) '&' u) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 3) 'in' (x. 1)) '&' u)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 3)*>),('not' (((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 3),('not' (((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,((x. 4) 'in' (x. 2))),('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(((x. 4) 'in' (x. 2)) '&' ('not' (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' ((x. 4) 'in' (x. 2)) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))),('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) '&' ('not' ((x. 4) 'in' (x. 2))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))) '&' ((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(((x. 4) 'in' (x. 2)) => (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))),((Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))) => ((x. 4) 'in' (x. 2)))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 4)*>),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 2)*>),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' (All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 2),('not' (All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),K139(K45(),<*4*>,<*(x. 1)*>),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) => (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
'not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,(All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
K139(K45(),K139(K45(),<*3*>,(All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0)))))))))),('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
'not' ((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u)))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like ZF-formula-like FinSequence of K45()
K139(K45(),<*2*>,((All ((x. 3),(Ex ((x. 0),(All ((x. 4),(u <=> ((x. 4) '=' (x. 0))))))))) '&' ('not' (All ((x. 1),(Ex ((x. 2),(All ((x. 4),(((x. 4) 'in' (x. 2)) <=> (Ex ((x. 3),(((x. 3) 'in' (x. 1)) '&' u))))))))))))) is Relation-like K45() -defined K45() -valued Function-like FinSequence-like FinSequence of K45()
v is Element of E