:: STIRL2_1 semantic presentation

REAL is V50() V51() V52() V56() V68() V69() V71() set
NAT is epsilon-transitive epsilon-connected ordinal non empty non trivial V50() V51() V52() V53() V54() V55() V56() non finite V66() V68() cardinal limit_cardinal Element of bool REAL
bool REAL is non empty set
RAT is V50() V51() V52() V53() V56() set
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
the Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
COMPLEX is V50() V56() set
INT is V50() V51() V52() V53() V54() V56() set
[:COMPLEX,COMPLEX:] is Relation-like V40() set
bool [:COMPLEX,COMPLEX:] is non empty set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like V40() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty set
[:REAL,REAL:] is Relation-like V40() V41() V42() set
bool [:REAL,REAL:] is non empty set
[:[:REAL,REAL:],REAL:] is Relation-like V40() V41() V42() set
bool [:[:REAL,REAL:],REAL:] is non empty set
[:RAT,RAT:] is Relation-like RAT -valued V40() V41() V42() set
bool [:RAT,RAT:] is non empty set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued V40() V41() V42() set
bool [:[:RAT,RAT:],RAT:] is non empty set
[:INT,INT:] is Relation-like RAT -valued INT -valued V40() V41() V42() set
bool [:INT,INT:] is non empty set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued V40() V41() V42() set
bool [:[:INT,INT:],INT:] is non empty set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V40() V41() V42() V43() non finite V92() set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued non empty non trivial V40() V41() V42() V43() non finite V92() set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
NAT is epsilon-transitive epsilon-connected ordinal non empty non trivial V50() V51() V52() V53() V54() V55() V56() non finite V66() V68() cardinal limit_cardinal set
bool NAT is non empty non trivial non finite set
bool NAT is non empty non trivial non finite set
[:COMPLEX,REAL:] is Relation-like V40() V41() V42() set
bool [:COMPLEX,REAL:] is non empty set
1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{{},1} is non empty V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() set
2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
3 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
union {} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() set
0 is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer V36() ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of NAT
card {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
{{}} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element set
addnat is Relation-like [:NAT,NAT:] -defined NAT -valued non empty Function-like V24([:NAT,NAT:]) quasi_total V32( NAT ) V40() V41() V42() V43() V92() V93( NAT ) V94( NAT ) Element of bool [:[:NAT,NAT:],NAT:]
K497(NAT,addnat) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 ! is V33() V34() ext-real Element of REAL
Ne is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is ext-real set
Ne is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min ((min Ne),(min Ke)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne \/ Ke is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min (Ne \/ Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min ((min Ke),(min Ne)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke \/ Ne is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
I1 is ext-real set
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min ((min* Ne),(min* Ke)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne \/ Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* (Ne \/ Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
F \/ I1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min (F \/ I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ne /\ Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ne \ Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* (Ne \ Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
min* {Ne} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min {Ne} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne,Ke} is non empty V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() Element of bool NAT
min* {Ne,Ke} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min (Ne,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min {Ne,Ke} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
min {Ne} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ke} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
{Ne} \/ {Ke} is non empty V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() Element of bool NAT
min {Ke} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min ((min {Ne}),(min {Ke})) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne,Ke,F} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool NAT
min* {Ne,Ke,F} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min (Ke,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min (Ne,(min (Ke,F))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min {Ne,Ke,F} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
{Ke,F} is non empty V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() Element of bool NAT
{Ne} \/ {Ke,F} is non empty V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() Element of bool NAT
min {Ne} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min {Ke,F} is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min ((min {Ne}),(min {Ke,F})) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT : not Ne <= b₁ } is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
Ke is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT : not Ne <= b₁ } is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke - 1 is V33() V34() integer V36() ext-real Element of INT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT : not Ke <= b₁ } is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - 1) + 1 is V33() V34() integer V36() ext-real Element of INT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
min* Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT : not Ne <= b₁ } is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
Ke is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
{(Ne - 1)} is non empty trivial V50() V51() V52() V53() V54() finite V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
min* Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is set
[:Ne,Ke:] is Relation-like set
bool [:Ne,Ke:] is non empty set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total finite Element of bool [:Ne,Ke:]
I1 is set
F " I1 is finite set
I2 is set
F " I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
Ne is set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
I1 is set
F . I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom F is Element of bool Ne
bool Ne is non empty set
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is Element of bool Ne
bool Ne is non empty set
dom F is Element of bool Ne
bool Ne is non empty set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
Ke - 1 is V33() V34() integer V36() ext-real Element of INT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{F} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
I1 is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
(Ke,Ne,I1,{F}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,I1,{F}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is set
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
card Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{(I1 + 1)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{(I1 + 1)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{(I1 + 1)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{(I1 + 1)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ne,Ke,F,{(I1 + 1)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{(I1 + 1)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{0} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{0}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{0}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
Ke - Ne is V33() V34() integer V36() ext-real Element of INT
F is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + I1 is V33() V34() integer V36() ext-real Element of INT
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
P1 is V33() V34() integer ext-real set
{P1} is non empty trivial V50() V51() V52() V53() V54() finite V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + P1 is V33() V34() integer V36() ext-real Element of INT
P1 - 1 is V33() V34() integer V36() ext-real Element of INT
{(P1 - 1)} is non empty trivial V50() V51() V52() V53() V54() finite V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{(P1 - 1)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{(P1 - 1)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + (P1 - 1) is V33() V34() integer V36() ext-real Element of INT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{(P2 + 1)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ke,Ne,F,{(P2 + 1)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{(P2 + 1)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ke,Ne,F,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 + P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 + P2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + I1 is V33() V34() integer V36() ext-real Element of INT
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ke,Ne,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke - 1 is V33() V34() integer V36() ext-real Element of INT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + I2 is V33() V34() integer V36() ext-real Element of INT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + I2 is V33() V34() integer V36() ext-real Element of INT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ke,Ne,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke - Ne) + I1 is V33() V34() integer V36() ext-real Element of INT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
id Ne is Relation-like Ne -defined Ne -valued RAT -valued INT -valued Function-like one-to-one V24(Ne) quasi_total V40() V41() V42() V43() V44() V46() finite V92() Element of bool [:Ne,Ne:]
[:Ne,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ne:] is non empty finite V61() set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I1 is set
(Ne,Ke,F,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
I1 is set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ne,Ke,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P2 is set
(Ne,Ke,F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
min* (Ne,Ke,F,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne - Ke is V33() V34() integer V36() ext-real Element of INT
(Ne - Ke) + I2 is V33() V34() integer V36() ext-real Element of INT
P1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke,F,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
(Ne,Ke,F,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
id Ke is Relation-like Ke -defined Ke -valued RAT -valued INT -valued Function-like one-to-one V24(Ke) quasi_total V40() V41() V42() V43() V44() V46() finite V92() Element of bool [:Ke,Ke:]
[:Ke,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ke:] is non empty finite V61() set
F is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
P1 is set
(Ke,Ne,F,P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
P2 is set
{P2} is non empty trivial finite 1 -element set
min* (Ke,Ne,F,{I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P2 is set
(Ke,Ne,F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
F is set
{F} is non empty trivial finite 1 -element set
min* (Ke,Ne,F,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool NAT
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
bool RAT is non empty set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
{0} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
F is Relation-like Function-like set
dom F is set
rng F is set
[:Ne,{0}:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,{0}:] is non empty finite V61() set
I1 is Relation-like Ne -defined {0} -valued Function-like V24(Ne) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,{0}:]
rng I1 is trivial functional V50() V51() V52() V53() V54() V55() finite V61() V68() V69() V70() Element of bool {0}
bool {0} is non empty finite V61() set
I2 is set
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I2,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I2,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool NAT
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
bool RAT is non empty set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
Ke - 1 is V33() V34() integer V36() ext-real Element of INT
I2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
I1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I2
min (P1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:I2,I1:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:I2,I1:] is non empty finite V61() set
P1 is Relation-like I2 -defined I1 -valued non empty Function-like V24(I2) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:I2,I1:]
P2 is set
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom P1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool I2
bool I2 is non empty finite V61() set
min (F,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2,I1,P1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I1
rng P1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool I1
bool I1 is non empty finite V61() set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(I2,I1,P1,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (I2,I1,P1,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min (P2,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(I2,I1,P1,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I1
F is set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2,I1,P1,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I1
min (domF,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(I2,I1,P1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I1
min (F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(I2,I1,P1,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (I2,I1,P1,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{F} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(I2,I1,P1,{F}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (I2,I1,P1,{F}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
F₁() is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₂() is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:F₁(),F₂():] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:F₁(),F₂():] is non empty finite V61() set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:F₁(),F₂():] : P₁[b₁] } is set
{{}} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is set
F is Relation-like F₁() -defined F₂() -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:F₁(),F₂():]
Funcs (F₁(),F₂()) is functional set
Ke is set
F is Relation-like F₁() -defined F₂() -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:F₁(),F₂():]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : S₁[b₁] } is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
card I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ne:] : ( b₁ is onto & b₁ is (Ne,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ne:] : ( b₁ is onto & b₁ is (Ne,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
id Ne is Relation-like Ne -defined Ne -valued RAT -valued INT -valued Function-like one-to-one V24(Ne) quasi_total V40() V41() V42() V43() V44() V46() finite V92() Element of bool [:Ne,Ne:]
{(id Ne)} is non empty trivial functional finite V61() 1 -element Element of bool (bool [:Ne,Ne:])
bool (bool [:Ne,Ne:]) is non empty finite V61() set
F is set
I1 is Relation-like Ne -defined Ne -valued Function-like V24(Ne) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ne:]
F is Relation-like Ne -defined Ne -valued Function-like V24(Ne) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ne:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(0,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:0,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:0,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 0 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ne:] : ( b₁ is onto & b₁ is ( 0 ,Ne) ) } is set
card { b₁ where b₁ is Relation-like 0 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ne:] : ( b₁ is onto & b₁ is ( 0 ,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F is set
I1 is Relation-like non-empty empty-yielding 0 -defined Ne -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V24( 0 ) quasi_total V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element 0 -element V88() V92() Element of bool [:0,Ne:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(0,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:0,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:0,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 0 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ne:] : ( b₁ is onto & b₁ is ( 0 ,Ne) ) } is set
card { b₁ where b₁ is Relation-like 0 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ne:] : ( b₁ is onto & b₁ is ( 0 ,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(0,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:0,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:0,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 0 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ke:] : ( b₁ is onto & b₁ is ( 0 ,Ke) ) } is set
card { b₁ where b₁ is Relation-like 0 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:0,Ke:] : ( b₁ is onto & b₁ is ( 0 ,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is set
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,0:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,0:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,0:] : ( b₁ is onto & b₁ is (Ne, 0 ) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,0:] : ( b₁ is onto & b₁ is (Ne, 0 ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
{{}} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
card {{}} is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
F is set
{F} is non empty trivial finite 1 -element set
I1 is Relation-like non-empty empty-yielding Ne -defined 0 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional quasi_total V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool [:Ne,0:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,0:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,0:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,0:] : ( b₁ is onto & b₁ is (Ne, 0 ) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,0:] : ( b₁ is onto & b₁ is (Ne, 0 ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F is set
I1 is Relation-like non-empty empty-yielding Ne -defined 0 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional quasi_total V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool [:Ne,0:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,1:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,1:] : ( b₁ is onto & b₁ is (Ne,1) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,1:] : ( b₁ is onto & b₁ is (Ne,1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
1 + 0 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
F is Relation-like Ne -defined 1 -valued Function-like V24(Ne) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,1:]
{F} is non empty trivial functional finite V61() 1 -element Element of bool (bool [:Ne,1:])
bool (bool [:Ne,1:]) is non empty finite V61() set
I1 is set
I2 is Relation-like Ne -defined 1 -valued Function-like V24(Ne) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,1:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
1 + 0 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
F₁() is set
F₂() is set
[:F₁(),F₂():] is Relation-like set
bool [:F₁(),F₂():] is non empty set
F₃() is set
F₃() \ F₁() is Element of bool F₃()
bool F₃() is non empty set
F₄() is set
[:F₃(),F₄():] is Relation-like set
bool [:F₃(),F₄():] is non empty set
F₅() is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
Ne is set
F₅() . Ne is set
F₆(Ne) is set
dom F₅() is Element of bool F₁()
bool F₁() is non empty set
rng F₅() is Element of bool F₂()
bool F₂() is non empty set
Ke is set
Ne is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
dom F₅() is Element of bool F₁()
bool F₁() is non empty set
dom Ne is Element of bool F₃()
(dom Ne) /\ F₁() is Element of bool F₃()
Ne | F₁() is Relation-like F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
Ke is set
Ne . Ke is set
F₅() . Ke is set
Ke is set
Ne . Ke is set
F₆(Ke) is set
F₃() is set
F₁() is set
F₃() \ F₁() is Element of bool F₃()
bool F₃() is non empty set
F₄() is set
F₂() is set
[:F₃(),F₄():] is Relation-like set
bool [:F₃(),F₄():] is non empty set
[:F₁(),F₂():] is Relation-like set
bool [:F₁(),F₂():] is non empty set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is set
card { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is epsilon-transitive epsilon-connected ordinal cardinal set
{ b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } is set
card { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F is set
I1 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
I2 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
I2 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
P1 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
P2 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
P2 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng I1 is Element of bool F₂()
bool F₂() is non empty set
[: { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } , { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } :] is Relation-like set
bool [: { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } , { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } :] is non empty set
F is Relation-like { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } -defined { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } -valued Function-like quasi_total Element of bool [: { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } , { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } :]
I1 is set
{{}} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
I2 is set
P1 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
P1 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (P1 | F₁()) is Element of bool F₄()
bool F₄() is non empty set
I2 is set
P1 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
bool RAT is non empty set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool NAT
I2 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
P1 is set
I2 . P1 is set
F₅(P1) is set
I2 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (I2 | F₁()) is Element of bool F₄()
bool F₄() is non empty set
I2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
I2 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
I2 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (I2 | F₁()) is Element of bool F₄()
bool F₄() is non empty set
I1 is set
I2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
rng I2 is Element of bool F₂()
bool F₂() is non empty set
P1 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
P1 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng F is Element of bool { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) }
bool { b₁ where b₁ is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():] : ( P₁[b₁,F₃(),F₄()] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in F₃() \ F₁() or b₁ . b₂ = F₅(b₂) ) ) ) } is non empty set
I1 is set
I2 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
I2 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (I2 | F₁()) is Element of bool F₄()
bool F₄() is non empty set
dom (I2 | F₁()) is Element of bool F₁()
bool F₁() is non empty set
dom I2 is Element of bool F₃()
(dom I2) /\ F₁() is Element of bool F₃()
[:F₁(),(rng (I2 | F₁())):] is Relation-like set
bool [:F₁(),(rng (I2 | F₁())):] is non empty set
P1 is Relation-like F₁() -defined rng (I2 | F₁()) -valued Function-like quasi_total Element of bool [:F₁(),(rng (I2 | F₁())):]
P2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
dom F is Element of bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] }
bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is non empty set
F . P2 is set
F is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
F | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (F | F₁()) is Element of bool F₄()
domF is set
dom P2 is Element of bool F₁()
P2 . domF is set
F . domF is set
I2 . domF is set
F . domF is set
F₅(domF) is set
I2 . domF is set
F . domF is set
I2 . domF is set
F . domF is set
I2 . domF is set
I1 is set
I2 is set
F . I1 is set
F . I2 is set
dom F is Element of bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] }
bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is non empty set
P1 is Relation-like F₃() -defined F₄() -valued Function-like quasi_total Element of bool [:F₃(),F₄():]
P1 | F₁() is Relation-like F₃() -defined F₁() -defined F₃() -defined F₄() -valued Function-like Element of bool [:F₃(),F₄():]
rng (P1 | F₁()) is Element of bool F₄()
bool F₄() is non empty set
P2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
F is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():]
dom F is Element of bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] }
bool { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is non empty set
F₂() is set
F₁() is set
F₃() is set
{F₃()} is non empty trivial finite 1 -element set
F₁() \/ {F₃()} is non empty set
F₄() is set
{F₄()} is non empty trivial finite 1 -element set
F₂() \/ {F₄()} is non empty set
[:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] is Relation-like non empty set
bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] is non empty set
[:F₁(),F₂():] is Relation-like set
bool [:F₁(),F₂():] is non empty set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is set
card { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total Element of bool [:F₁(),F₂():] : P₁[b₁,F₁(),F₂()] } is epsilon-transitive epsilon-connected ordinal cardinal set
{ b₁ where b₁ is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] : ( P₁[b₁,F₁() \/ {F₃()},F₂() \/ {F₄()}] & rng (b₁ | F₁()) c= F₂() & b₁ . F₃() = F₄() ) } is set
card { b₁ where b₁ is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] : ( P₁[b₁,F₁() \/ {F₃()},F₂() \/ {F₄()}] & rng (b₁ | F₁()) c= F₂() & b₁ . F₃() = F₄() ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(F₁() \/ {F₃()}) \ F₁() is Element of bool (F₁() \/ {F₃()})
bool (F₁() \/ {F₃()}) is non empty set
F is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
F . F₃() is set
{F₃()} \ F₁() is trivial finite Element of bool {F₃()}
bool {F₃()} is non empty finite V61() set
I1 is set
F . I1 is set
F is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
F | F₁() is Relation-like F₁() -defined F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued Function-like Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
F . F₃() is set
{ b₁ where b₁ is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] : ( P₁[b₁,F₁() \/ {F₃()},F₂() \/ {F₄()}] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in (F₁() \/ {F₃()}) \ F₁() or b₁ . b₂ = H₁(b₂) ) ) ) } is set
I2 is set
I2 is set
P1 is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
P1 | F₁() is Relation-like F₁() -defined F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued Function-like Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
rng (P1 | F₁()) is Element of bool (F₂() \/ {F₄()})
bool (F₂() \/ {F₄()}) is non empty set
P1 . F₃() is set
I2 is set
P1 is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
P1 | F₁() is Relation-like F₁() -defined F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued Function-like Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):]
rng (P1 | F₁()) is Element of bool (F₂() \/ {F₄()})
bool (F₂() \/ {F₄()}) is non empty set
P1 . F₃() is set
P2 is set
P1 . P2 is set
card { b₁ where b₁ is Relation-like F₁() \/ {F₃()} -defined F₂() \/ {F₄()} -valued non empty Function-like V24(F₁() \/ {F₃()}) quasi_total Element of bool [:(F₁() \/ {F₃()}),(F₂() \/ {F₄()}):] : ( P₁[b₁,F₁() \/ {F₃()},F₂() \/ {F₄()}] & rng (b₁ | F₁()) c= F₂() & ( for b₂ being set holds
( not b₂ in (F₁() \/ {F₃()}) \ F₁() or b₁ . b₂ = H₁(b₂) ) ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + 1):] is non empty finite V61() set
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
{Ke} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + 1),F,{Ke}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + 1),F,{Ke}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne + 1) - 1 is V33() V34() integer V36() ext-real Element of INT
rng F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ke + 1)
min* ((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:(Ne + 1),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),Ke:] is non empty finite V61() set
F is Relation-like Ne + 1 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ke:]
((Ne + 1),Ke,F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{((Ne + 1),Ke,F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),Ke,F,{((Ne + 1),Ke,F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
I1 is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ne + F),(Ke + I1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + F),(Ke + I1):] is non empty finite V61() set
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
P1 is Relation-like Ne + F -defined Ke + I1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + F),(Ke + I1):]
P1 | Ne is Relation-like Ne -defined Ne + F -defined RAT -valued Ke + I1 -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + F),(Ke + I1):]
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I2,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{F} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{F}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I2,{F}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng P1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke + I1)
bool (Ke + I1) is non empty finite V61() set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{domF} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
(Ne,Ke,I2,{domF}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I2,{domF}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ne + F),(Ke + I1),P1,{domF}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + F),(Ke + I1),P1,{domF}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
m is set
(Ne,Ke,I2,m) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke,I2,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + F),(Ke + I1),P1,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + I1
dom P1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + F)
bool (Ne + F) is non empty finite V61() set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,Ke,I2,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + F),(Ke + I1),P1,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + I1
((Ne + F),(Ke + I1),P1,(min* ((Ne + F),(Ke + I1),P1,{domF}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + I1
(Ne,Ke,I2,(min* ((Ne + F),(Ke + I1),P1,{domF}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + F),(Ke + I1),P1,{F}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + F),(Ke + I1),P1,{F}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ne + F),(Ke + I1),P1,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + F),(Ke + I1),P1,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + 1):] is non empty finite V61() set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke + 1 -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
rng (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool RAT
bool RAT is non empty set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I1 is set
rng F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ke + 1)
dom (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 is set
(F | Ne) . P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
(dom F) /\ Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ne + 1),(Ke + 1),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,P2)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
min* ((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F | Ne) . P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
(dom F) /\ Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
I2 is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ke + 1)
P2 is set
((Ne + 1),(Ke + 1),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
(Ne,Ke,I1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
(dom F) /\ Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
dom (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(F | Ne) . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I1,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:(Ne + 1),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),Ke:] is non empty finite V61() set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is Relation-like Ne + 1 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ke:]
((Ne + 1),Ke,F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{((Ne + 1),Ke,F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),Ke,F,{((Ne + 1),Ke,F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ke:]
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
Ke + 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I1,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
P1 is set
((Ne + 1),Ke,F,P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(Ne,Ke,I1,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + 1),Ke,F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{I2} is non empty trivial finite 1 -element set
((Ne + 1),Ke,F,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
((Ne + 1),Ke,F,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(Ne,Ke,I1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + F):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + F):] is non empty finite V61() set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I2 is Relation-like Ne + 1 -defined Ke + F -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + F):]
I2 | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke + F -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + F):]
rng I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke + F)
bool (Ke + F) is non empty finite V61() set
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,Ke,I1,P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + 1),(Ke + F),I2,P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
((Ne + 1),(Ke + F),I2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
P2 is set
((Ne + 1),(Ke + F),I2,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(Ne,Ke,I1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + 1),(Ke + F),I2,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + F),I2,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + F),I2,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
((Ne + 1),(Ke + F),I2,(min* ((Ne + 1),(Ke + F),I2,{P1}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
(Ne + 1) - 1 is V33() V34() integer V36() ext-real Element of INT
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(Ne,Ke,I1,(min* ((Ne + 1),(Ke + F),I2,{P1}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
((Ne + 1),(Ke + F),I2,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + F),I2,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
P2 is set
(Ne,Ke,I1,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
((Ne + 1),(Ke + F),I2,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
(Ne,Ke,I1,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
(Ne,Ke,I1,(min* (Ne,Ke,I1,{P1}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + 1),(Ke + F),I2,(min* (Ne,Ke,I1,{P1}))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + F
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + F),I2,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + F),I2,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + F),I2,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + F),I2,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,Ke,I1,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* (Ne,Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
(Ne - 1) + 1 is V33() V34() integer V36() ext-real Element of INT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + 1):] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I1 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
I1 | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke + 1 -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),I1,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),I1,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),I1,{((Ne + 1),(Ke + 1),I1,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
rng I1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ke + 1)
I2 is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
P2 is set
(Ne,Ke,F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom I1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),I1,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
dom I1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + 1),I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + 1),I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),(Ke + 1),I1,{I2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),(Ke + 1),I1,{I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
((Ne + 1),(Ke + 1),I1,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
dom I1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
(Ne,Ke,F,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
[:(Ne + 1),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),Ke:] is non empty finite V61() set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I1 is Relation-like Ne + 1 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ke:]
I1 | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ke:]
((Ne + 1),Ke,I1,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{((Ne + 1),Ke,I1,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),Ke,I1,{((Ne + 1),Ke,I1,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
I2 is set
(Ne,Ke,F,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
((Ne + 1),Ke,I1,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
P1 is set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is set
(Ne,Ke,F,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
((Ne + 1),Ke,I1,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
Ke + 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{P2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),Ke,I1,{P2}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),Ke,I1,{P2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{P1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ne + 1),Ke,I1,{P1}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
min* ((Ne + 1),Ke,I1,{P1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke \/ {Ne} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is set
card { b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is epsilon-transitive epsilon-connected ordinal cardinal set
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
I2 is set
P1 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P1,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P1,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P1,{((Ne + 1),(Ke + 1),P1,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
dom P1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
{0} is non empty trivial functional V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
((Ne + 1),(Ke + 1),P1,0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
(Ne,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : S₁[b₁,Ne,Ke] } is set
Ne \/ {Ne} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
{Ke} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke \/ {Ke} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
[:(Ne \/ {Ne}),(Ke \/ {Ke}):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne \/ {Ne} -defined Ke \/ {Ke} -valued non empty Function-like V24(Ne \/ {Ne}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):] : ( S₁[b₁,Ne \/ {Ne},Ke \/ {Ke}] & rng (b₁ | Ne) c= Ke & b₁ . Ne = Ke ) } is set
P2 is Relation-like Ne \/ {Ne} -defined Ke \/ {Ke} -valued non empty Function-like V24(Ne \/ {Ne}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):]
P2 . Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 | Ne is Relation-like Ne -defined Ne \/ {Ne} -defined RAT -valued Ke \/ {Ke} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):]
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke + 1 -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
rng (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool RAT
bool RAT is non empty set
dom (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
dom F is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (Ne + 1)
bool (Ne + 1) is non empty finite V61() set
(dom F) /\ Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne + 1)
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:m,I1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:m,I1:] is non empty finite V61() set
domF is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
I2 is Relation-like m -defined I1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:m,I1:]
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:domF,m:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:domF,m:] is non empty finite V61() set
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
I1 is Relation-like domF -defined m -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:domF,m:]
(domF,m,I1,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of m
{(domF,m,I1,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(domF,m,I1,{(domF,m,I1,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
(Ne,Ke,I2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{(Ne,Ke,I2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{(Ne,Ke,I2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
(Ne,Ke,I2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{(Ne,Ke,I2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,I2,{(Ne,Ke,I2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : S₁[b₁,Ne,Ke] } is epsilon-transitive epsilon-connected ordinal cardinal set
card { b₁ where b₁ is Relation-like Ne \/ {Ne} -defined Ke \/ {Ke} -valued non empty Function-like V24(Ne \/ {Ne}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):] : ( S₁[b₁,Ne \/ {Ne},Ke \/ {Ke}] & rng (b₁ | Ne) c= Ke & b₁ . Ne = Ke ) } is epsilon-transitive epsilon-connected ordinal cardinal set
P2 is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:F,domF:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:F,domF:] is non empty finite V61() set
m is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
P2 is set
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F | Ne is Relation-like Ne -defined Ne + 1 -defined RAT -valued Ke + 1 -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
rng (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool RAT
bool RAT is non empty set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:domF,m:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:domF,m:] is non empty finite V61() set
P2 is set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
domF is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:]
(Ne,Ke,domF,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke
{(Ne,Ke,domF,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ne,Ke,domF,{(Ne,Ke,domF,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P2 is set
F is Relation-like Ne \/ {Ne} -defined Ke \/ {Ke} -valued non empty Function-like V24(Ne \/ {Ne}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):]
F | Ne is Relation-like Ne -defined Ne \/ {Ne} -defined RAT -valued Ke \/ {Ke} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ne \/ {Ne}),(Ke \/ {Ke}):]
rng (F | Ne) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke \/ {Ke})
bool (Ke \/ {Ke}) is non empty finite V61() set
F . Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),domF,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),domF,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),domF,{((Ne + 1),(Ke + 1),domF,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),Ne:] is non empty finite V61() set
{Ke} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) & not ((Ke + 1),Ne,b₁,{((Ke + 1),Ne,b₁,Ke)}) = {Ke} & ((Ke + 1),Ne,b₁,Ke) = F ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) & not ((Ke + 1),Ne,b₁,{((Ke + 1),Ne,b₁,Ke)}) = {Ke} & ((Ke + 1),Ne,b₁,Ke) = F ) } is epsilon-transitive epsilon-connected ordinal cardinal set
{ b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : S₁[b₁,Ke,Ne] } is set
Ke \/ {Ke} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
{F} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ne \/ {F} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
[:(Ke \/ {Ke}),(Ne \/ {F}):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ke \/ {Ke}),(Ne \/ {F}):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke \/ {Ke} -defined Ne \/ {F} -valued non empty Function-like V24(Ke \/ {Ke}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):] : ( S₁[b₁,Ke \/ {Ke},Ne \/ {F}] & rng (b₁ | Ke) c= Ne & b₁ . Ke = F ) } is set
F is Relation-like Ke \/ {Ke} -defined Ne \/ {F} -valued non empty Function-like V24(Ke \/ {Ke}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):]
F . Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F | Ke is Relation-like Ke -defined Ke \/ {Ke} -defined RAT -valued Ne \/ {F} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):]
domF is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,domF,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,domF,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,domF,{((Ke + 1),Ne,domF,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
domF | Ke is Relation-like Ke -defined Ke + 1 -defined RAT -valued Ne -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
dom (domF | Ke) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
dom domF is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
(dom domF) /\ Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke + 1)
rng (domF | Ke) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:I1,I2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:I1,I2:] is non empty finite V61() set
m is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
P1 is Relation-like I1 -defined I2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:I1,I2:]
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:m,I1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:m,I1:] is non empty finite V61() set
domF is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
I2 is Relation-like m -defined I1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:m,I1:]
(m,I1,I2,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of I1
{(m,I1,I2,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(m,I1,I2,{(m,I1,I2,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P1 is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
(Ke,Ne,P1,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{(Ke,Ne,P1,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,P1,{(Ke,Ne,P1,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P1 is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
(Ke,Ne,P1,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{(Ke,Ne,P1,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,P1,{(Ke,Ne,P1,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card { b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : S₁[b₁,Ke,Ne] } is epsilon-transitive epsilon-connected ordinal cardinal set
card { b₁ where b₁ is Relation-like Ke \/ {Ke} -defined Ne \/ {F} -valued non empty Function-like V24(Ke \/ {Ke}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):] : ( S₁[b₁,Ke \/ {Ke},Ne \/ {F}] & rng (b₁ | Ke) c= Ne & b₁ . Ke = F ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F is set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:domF,m:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:domF,m:] is non empty finite V61() set
I1 is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
domF is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
F is set
domF is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,domF,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,domF,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,domF,{((Ke + 1),Ne,domF,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
[:m,I1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:m,I1:] is non empty finite V61() set
domF | Ke is Relation-like Ke -defined Ke + 1 -defined RAT -valued Ne -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
rng (domF | Ke) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
F is set
domF is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
m is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:]
(Ke,Ne,m,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{(Ke,Ne,m,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(Ke,Ne,m,{(Ke,Ne,m,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is set
domF is Relation-like Ke \/ {Ke} -defined Ne \/ {F} -valued non empty Function-like V24(Ke \/ {Ke}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):]
domF | Ke is Relation-like Ke -defined Ke \/ {Ke} -defined RAT -valued Ne \/ {F} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:(Ke \/ {Ke}),(Ne \/ {F}):]
rng (domF | Ke) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ne \/ {F})
bool (Ne \/ {F}) is non empty finite V61() set
domF . Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
m is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,m,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,m,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,m,{((Ke + 1),Ne,m,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
Ne is Relation-like Function-like set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne | Ke is Relation-like Function-like finite set
rng (Ne | Ke) is finite set
union (rng (Ne | Ke)) is set
Ne . Ke is set
(union (rng (Ne | Ke))) \/ (Ne . Ke) is set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ne | (Ke + 1) is Relation-like Function-like finite set
rng (Ne | (Ke + 1)) is finite set
union (rng (Ne | (Ke + 1))) is set
F is set
I1 is set
dom (Ne | Ke) is finite set
I2 is set
(Ne | Ke) . I2 is set
Ne . I2 is set
dom Ne is set
(dom Ne) /\ Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() set
(dom Ne) /\ (Ke + 1) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() set
dom (Ne | (Ke + 1)) is finite set
(Ne | (Ke + 1)) . I2 is set
dom Ne is set
(dom Ne) /\ (Ke + 1) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() set
dom (Ne | (Ke + 1)) is finite set
(Ne | (Ke + 1)) . Ke is set
F is set
I1 is set
dom (Ne | (Ke + 1)) is finite set
I2 is set
(Ne | (Ke + 1)) . I2 is set
dom Ne is set
(dom Ne) /\ (Ke + 1) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(dom Ne) /\ Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() set
dom (Ne | Ke) is finite set
(Ne | Ke) . P1 is set
Ne . P1 is set
(Ne | (Ke + 1)) . P1 is set
Ne . P1 is set
(Ne | (Ke + 1)) . P1 is set
F₂() is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₁() is non empty set
Ne is set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Element of F₁()
[:F₂(),F₁():] is Relation-like set
bool [:F₂(),F₁():] is non empty set
Ne is Relation-like F₂() -defined F₁() -valued Function-like V24(F₂()) quasi_total finite Element of bool [:F₂(),F₁():]
dom Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool F₂()
bool F₂() is non empty finite V61() set
Ke is Relation-like NAT -defined F₁() -valued T-Sequence-like Function-like finite V88() set
dom Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke . F is set
Ne is non empty set
Ke is Relation-like NAT -defined Ne -valued T-Sequence-like Function-like finite V88() set
dom Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
rng Ke is finite Element of bool Ne
bool Ne is non empty set
union (rng Ke) is set
card (union (rng Ke)) is epsilon-transitive epsilon-connected ordinal cardinal set
len Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke . F is set
card (Ke . F) is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
card I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Relation-like NAT -defined NAT -valued T-Sequence-like Function-like V40() V41() V42() V43() finite V88() V92() set
dom F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
Sum F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of COMPLEX
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F . I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke . I1 is set
card (Ke . I1) is epsilon-transitive epsilon-connected ordinal cardinal set
addnat "**" F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
len F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
len F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
bool [:NAT,NAT:] is non empty non trivial non finite set
F . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(len F) - 1 is V33() V34() integer V36() ext-real Element of INT
I1 is Relation-like NAT -defined NAT -valued non empty Function-like V24( NAT ) quasi_total V40() V41() V42() V43() V92() Element of bool [:NAT,NAT:]
I1 . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 . ((len F) - 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke | (I2 + 1) is Relation-like I2 + 1 -defined NAT -defined Ne -valued rng Ke -valued T-Sequence-like Function-like finite V88() set
rng Ke is finite set
rng (Ke | (I2 + 1)) is finite Element of bool Ne
union (rng (Ke | (I2 + 1))) is set
card (union (rng (Ke | (I2 + 1)))) is epsilon-transitive epsilon-connected ordinal cardinal set
I1 . I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke | ((I2 + 1) + 1) is Relation-like (I2 + 1) + 1 -defined NAT -defined Ne -valued rng Ke -valued T-Sequence-like Function-like finite V88() set
rng (Ke | ((I2 + 1) + 1)) is finite Element of bool Ne
union (rng (Ke | ((I2 + 1) + 1))) is set
card (union (rng (Ke | ((I2 + 1) + 1)))) is epsilon-transitive epsilon-connected ordinal cardinal set
I1 . (I2 + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F . (I2 + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
addnat . ((I1 . I2),(F . (I2 + 1))) is set
Ke . (I2 + 1) is set
(union (rng (Ke | (I2 + 1)))) /\ (Ke . (I2 + 1)) is set
m is set
I1 is set
dom (Ke | (I2 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
I2 is set
(Ke | (I2 + 1)) . I2 is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke | (I2 + 1)) . P1 is set
Ke . P1 is set
(dom Ke) /\ (I2 + 1) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
m is finite set
card m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 . I2) + (card m) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
domF is finite set
domF \/ m is finite set
card (domF \/ m) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke | (len F) is Relation-like len F -defined NAT -defined Ne -valued rng Ke -valued T-Sequence-like Function-like finite V88() set
rng Ke is finite set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke | (0 + 1) is Relation-like 0 + 1 -defined NAT -defined Ne -valued rng Ke -valued T-Sequence-like Function-like finite V88() set
rng (Ke | (0 + 1)) is finite Element of bool Ne
union (rng (Ke | (0 + 1))) is set
card (union (rng (Ke | (0 + 1)))) is epsilon-transitive epsilon-connected ordinal cardinal set
Ke | 0 is Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined RAT -valued Ne -valued rng Ke -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
rng (Ke | 0) is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool Ne
union (rng (Ke | 0)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke . 0 is set
(union (rng (Ke | 0))) \/ (Ke . 0) is set
len F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₂() is finite set
card F₂() is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(card F₂()),F₂():] is Relation-like finite set
bool [:(card F₂()),F₂():] is non empty finite V61() set
F₄() is Relation-like card F₂() -defined F₂() -valued Function-like quasi_total finite Element of bool [:(card F₂()),F₂():]
F₃() is set
F₁() is finite set
[:F₁(),F₂():] is Relation-like finite set
bool [:F₁(),F₂():] is non empty finite V61() set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : P₁[b₁] } is set
card { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : P₁[b₁] } is epsilon-transitive epsilon-connected ordinal cardinal set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . a₁ ) } is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Funcs (F₁(),F₂()) is functional set
bool (Funcs (F₁(),F₂())) is non empty set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₄() . F is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . F ) } is set
I2 is set
P1 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():]
P1 . F₃() is set
F is Relation-like NAT -defined bool (Funcs (F₁(),F₂())) -valued T-Sequence-like Function-like finite V88() set
dom F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F . I1 is set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F . I2 is set
(F . I1) /\ (F . I2) is set
P1 is set
F₄() . I1 is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I1 ) } is set
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F₄() . I2 is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I2 ) } is set
dom F₄() is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (card F₂())
bool (card F₂()) is non empty finite V61() set
P2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():]
P2 . F₃() is set
F is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():]
F . F₃() is set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F . I1 is set
rng F is finite Element of bool (bool (Funcs (F₁(),F₂())))
bool (bool (Funcs (F₁(),F₂()))) is non empty set
rng F is finite Element of bool (bool (Funcs (F₁(),F₂())))
bool (bool (Funcs (F₁(),F₂()))) is non empty set
union (rng F) is set
card (union (rng F)) is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is Relation-like NAT -defined NAT -valued T-Sequence-like Function-like V40() V41() V42() V43() finite V88() V92() set
dom I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
Sum I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of COMPLEX
P1 is set
P2 is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():]
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F₄() is finite Element of bool F₂()
bool F₂() is non empty finite V61() set
dom P2 is finite Element of bool F₁()
bool F₁() is non empty finite V61() set
P2 . F₃() is set
rng P2 is finite Element of bool F₂()
dom F₄() is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (card F₂())
bool (card F₂()) is non empty finite V61() set
F is set
F₄() . F is set
F . F is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . F ) } is set
P1 is set
P2 is set
F is set
F . F is set
F₄() . F is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . F ) } is set
domF is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():]
domF . F₃() is set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 . I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₄() . I2 is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I2 ) } is set
card { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I2 ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F . I2 is set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 . I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F₄() . I2 is set
{ b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I2 ) } is set
card { b₁ where b₁ is Relation-like F₁() -defined F₂() -valued Function-like quasi_total finite Element of bool [:F₁(),F₂():] : ( P₁[b₁] & b₁ . F₃() = F₄() . I2 ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ne:] : ( b₁ is onto & b₁ is (Ke,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
Ne * (Ke,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),Ne:] is non empty finite V61() set
{Ke} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) & not ((Ke + 1),Ne,b₁,{((Ke + 1),Ne,b₁,Ke)}) = {Ke} ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) & not ((Ke + 1),Ne,b₁,{((Ke + 1),Ne,b₁,Ke)}) = {Ke} ) } is epsilon-transitive epsilon-connected ordinal cardinal set
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) ) } is set
I2 is set
P1 is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,P1,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,P1,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,P1,{((Ke + 1),Ne,P1,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
((Ke + 1),Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
card Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is Relation-like Function-like set
dom I1 is set
rng I1 is set
[:(card Ne),Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(card Ne),Ne:] is non empty finite V61() set
I2 is Relation-like card Ne -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(card Ne),Ne:]
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : S₁[b₁] } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : S₁[b₁] } is epsilon-transitive epsilon-connected ordinal cardinal set
P1 is Relation-like NAT -defined NAT -valued T-Sequence-like Function-like V40() V41() V42() V43() finite V88() V92() set
dom P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
Sum P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of COMPLEX
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 . F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
((card Ne),Ne,I2,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
rng I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ne
bool Ne is non empty finite V61() set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( S₁[b₁] & ((Ke + 1),Ne,b₁,Ke) = domF ) } is set
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( b₁ is onto & b₁ is (Ke + 1,Ne) & not ((Ke + 1),Ne,b₁,{((Ke + 1),Ne,b₁,Ke)}) = {Ke} & ((Ke + 1),Ne,b₁,Ke) = domF ) } is set
I2 is set
P1 is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
P2 is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,P2,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,P2,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,P2,{((Ke + 1),Ne,P2,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
((Ke + 1),Ne,P1,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
I2 is set
P1 is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,P1,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,P1,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,P1,{((Ke + 1),Ne,P1,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:] : ( S₁[b₁] & ((Ke + 1),Ne,b₁,Ke) = domF ) } is epsilon-transitive epsilon-connected ordinal cardinal set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 . P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
len P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(len P1) * (Ke,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is set
domF is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,domF,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,domF,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,domF,{((Ke + 1),Ne,domF,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is set
domF is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
m is Relation-like Ke + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ne:]
((Ke + 1),Ne,m,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ne
{((Ke + 1),Ne,m,Ke)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
((Ke + 1),Ne,m,{((Ke + 1),Ne,m,Ke)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 . F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ne + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ne,(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,(Ke + 1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,(Ke + 1):] : ( b₁ is onto & b₁ is (Ne,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,(Ke + 1):] : ( b₁ is onto & b₁ is (Ne,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 1) * (Ne,(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,Ke:] : ( b₁ is onto & b₁ is (Ne,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
((Ke + 1) * (Ne,(Ke + 1))) + (Ne,Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is set
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & not ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is set
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } \/ { b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & not ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is set
P1 is set
P2 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P2,{((Ne + 1),(Ke + 1),P2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P1 is set
P2 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P2,{((Ne + 1),(Ke + 1),P2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } /\ { b₁ where b₁ is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ne + 1,Ke + 1) & not ((Ne + 1),(Ke + 1),b₁,{((Ne + 1),(Ke + 1),b₁,Ne)}) = {Ne} ) } is set
P1 is set
P2 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P2,{((Ne + 1),(Ke + 1),P2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
F is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),F,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
((Ne + 1),(Ke + 1),F,{((Ne + 1),(Ke + 1),F,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
Funcs ((Ne + 1),(Ke + 1)) is non empty functional FUNCTION_DOMAIN of Ne + 1,Ke + 1
P1 is set
P2 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P2,{((Ne + 1),(Ke + 1),P2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P1 is set
P2 is Relation-like Ne + 1 -defined Ke + 1 -valued non empty Function-like V24(Ne + 1) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),(Ke + 1):]
((Ne + 1),(Ke + 1),P2,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of Ke + 1
{((Ne + 1),(Ke + 1),P2,Ne)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool (Ke + 1)
bool (Ke + 1) is non empty finite V61() set
((Ne + 1),(Ke + 1),P2,{((Ne + 1),(Ke + 1),P2,Ne)}) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
P2 is finite set
card P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,F:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,F:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined F -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,F:] : ( b₁ is onto & b₁ is (Ne,F) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined F -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,F:] : ( b₁ is onto & b₁ is (Ne,F) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
F * (Ne,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 is finite set
card P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
1 / 2 is V33() V34() V36() ext-real non negative Element of RAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,2:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,2:] : ( b₁ is onto & b₁ is (Ne,2) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,2:] : ( b₁ is onto & b₁ is (Ne,2) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 |^ Ne is V33() V34() ext-real Element of REAL
(2 |^ Ne) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 |^ Ne) - 2) is V33() V34() ext-real Element of REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,2:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,2:] : ( b₁ is onto & b₁ is (Ke,2) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,2:] : ( b₁ is onto & b₁ is (Ke,2) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 |^ Ke is V33() V34() ext-real Element of REAL
(2 |^ Ke) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 |^ Ke) - 2) is V33() V34() ext-real Element of REAL
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ke + 1),2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),2:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),2:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 1 -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),2:] : ( b₁ is onto & b₁ is (Ke + 1,2) ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),2:] : ( b₁ is onto & b₁ is (Ke + 1,2) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
(2 |^ (Ke + 1)) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 |^ (Ke + 1)) - 2) is V33() V34() ext-real Element of REAL
1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke,(1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(1 + 1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(1 + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 1 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(1 + 1):] : ( b₁ is onto & b₁ is (Ke,1 + 1) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 1 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(1 + 1):] : ( b₁ is onto & b₁ is (Ke,1 + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 * (Ke,(1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke,1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,1:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,1:] : ( b₁ is onto & b₁ is (Ke,1) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,1:] : ( b₁ is onto & b₁ is (Ke,1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(2 * (Ke,(1 + 1))) + (Ke,1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 * ((1 / 2) * ((2 |^ Ke) - 2)) is V33() V34() ext-real Element of REAL
(2 * ((1 / 2) * ((2 |^ Ke) - 2))) + 1 is V33() V34() ext-real Element of REAL
2 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
(2 * (2 |^ Ke)) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 * (2 |^ Ke)) - 2) is V33() V34() ext-real Element of REAL
2 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(2 |^ (Ke + 1)) - 2 is V33() V34() integer V36() ext-real Element of INT
(1 / 2) * ((2 |^ (Ke + 1)) - 2) is V33() V34() V36() ext-real Element of RAT
2 |^ 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(1,2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:1,2:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:1,2:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 1 -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:1,2:] : ( b₁ is onto & b₁ is (1,2) ) } is set
card { b₁ where b₁ is Relation-like 1 -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:1,2:] : ( b₁ is onto & b₁ is (1,2) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 |^ 1 is V33() V34() ext-real Element of REAL
(2 |^ 1) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 |^ 1) - 2) is V33() V34() ext-real Element of REAL
6 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
1 / 6 is V33() V34() V36() ext-real non negative Element of RAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,3:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,3:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,3:] : ( b₁ is onto & b₁ is (Ne,3) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,3:] : ( b₁ is onto & b₁ is (Ne,3) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 |^ Ne is V33() V34() ext-real Element of REAL
2 |^ Ne is V33() V34() ext-real Element of REAL
3 * (2 |^ Ne) is V33() V34() ext-real Element of REAL
(3 |^ Ne) - (3 * (2 |^ Ne)) is V33() V34() ext-real Element of REAL
((3 |^ Ne) - (3 * (2 |^ Ne))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ Ne) - (3 * (2 |^ Ne))) + 3) is V33() V34() ext-real Element of REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,3:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,3:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,3:] : ( b₁ is onto & b₁ is (Ke,3) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,3:] : ( b₁ is onto & b₁ is (Ke,3) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 |^ Ke is V33() V34() ext-real Element of REAL
2 |^ Ke is V33() V34() ext-real Element of REAL
3 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
(3 |^ Ke) - (3 * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
((3 |^ Ke) - (3 * (2 |^ Ke))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ Ke) - (3 * (2 |^ Ke))) + 3) is V33() V34() ext-real Element of REAL
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ke + 1),3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),3:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),3:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 1 -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),3:] : ( b₁ is onto & b₁ is (Ke + 1,3) ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),3:] : ( b₁ is onto & b₁ is (Ke + 1,3) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
2 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
3 * (2 |^ (Ke + 1)) is V33() V34() ext-real Element of REAL
(3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1))) is V33() V34() ext-real Element of REAL
((3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1)))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1)))) + 3) is V33() V34() ext-real Element of REAL
(Ke,2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,2:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,2:] : ( b₁ is onto & b₁ is (Ke,2) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 2 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,2:] : ( b₁ is onto & b₁ is (Ke,2) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(2 |^ Ke) - 2 is V33() V34() ext-real Element of REAL
(1 / 2) * ((2 |^ Ke) - 2) is V33() V34() ext-real Element of REAL
2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke,(2 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(2 + 1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(2 + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 2 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(2 + 1):] : ( b₁ is onto & b₁ is (Ke,2 + 1) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 2 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(2 + 1):] : ( b₁ is onto & b₁ is (Ke,2 + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 * (Ke,(2 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * (Ke,(2 + 1))) + ((1 / 2) * ((2 |^ Ke) - 2)) is V33() V34() ext-real Element of REAL
3 * (3 |^ Ke) is V33() V34() ext-real Element of REAL
3 * 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * 2) * (2 |^ Ke) is V33() V34() ext-real Element of REAL
(3 * (3 |^ Ke)) - ((3 * 2) * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
((3 * (3 |^ Ke)) - ((3 * 2) * (2 |^ Ke))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 * (3 |^ Ke)) - ((3 * 2) * (2 |^ Ke))) + 3) is V33() V34() ext-real Element of REAL
3 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
3 * (2 * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
(3 |^ (Ke + 1)) - (3 * (2 * (2 |^ Ke))) is V33() V34() ext-real Element of REAL
((3 |^ (Ke + 1)) - (3 * (2 * (2 |^ Ke)))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ (Ke + 1)) - (3 * (2 * (2 |^ Ke)))) + 3) is V33() V34() ext-real Element of REAL
2 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * (2 |^ (Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1))) is V33() V34() integer V36() ext-real Element of INT
((3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1)))) + 3 is V33() V34() integer V36() ext-real Element of INT
(1 / 6) * (((3 |^ (Ke + 1)) - (3 * (2 |^ (Ke + 1)))) + 3) is V33() V34() V36() ext-real Element of RAT
3 |^ 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 |^ 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * (2 |^ 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 |^ 2) - (3 * (2 |^ 2)) is V33() V34() integer V36() ext-real Element of INT
((3 |^ 2) - (3 * (2 |^ 2))) + 3 is V33() V34() integer V36() ext-real Element of INT
(1 / 6) * (((3 |^ 2) - (3 * (2 |^ 2))) + 3) is V33() V34() V36() ext-real Element of RAT
3 * 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * 3) - (3 * (2 |^ 2)) is V33() V34() integer V36() ext-real Element of INT
((3 * 3) - (3 * (2 |^ 2))) + 3 is V33() V34() integer V36() ext-real Element of INT
(1 / 6) * (((3 * 3) - (3 * (2 |^ 2))) + 3) is V33() V34() V36() ext-real Element of RAT
2 * 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * (2 * 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * 3) - (3 * (2 * 2)) is V33() V34() integer V36() ext-real Element of INT
((3 * 3) - (3 * (2 * 2))) + 3 is V33() V34() integer V36() ext-real Element of INT
(1 / 6) * (((3 * 3) - (3 * (2 * 2))) + 3) is V33() V34() V36() ext-real Element of RAT
(2,3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:2,3:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:2,3:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 2 -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:2,3:] : ( b₁ is onto & b₁ is (2,3) ) } is set
card { b₁ where b₁ is Relation-like 2 -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:2,3:] : ( b₁ is onto & b₁ is (2,3) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 |^ 2 is V33() V34() ext-real Element of REAL
2 |^ 2 is V33() V34() ext-real Element of REAL
3 * (2 |^ 2) is V33() V34() ext-real Element of REAL
(3 |^ 2) - (3 * (2 |^ 2)) is V33() V34() ext-real Element of REAL
((3 |^ 2) - (3 * (2 |^ 2))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ 2) - (3 * (2 |^ 2))) + 3) is V33() V34() ext-real Element of REAL
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne |^ 3 is set
Ne * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne * Ne) * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke |^ (2 + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke |^ 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke |^ 2) * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke * Ke) * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
4 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
24 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
1 / 24 is V33() V34() V36() ext-real non negative Element of RAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ne,4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,4:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,4:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,4:] : ( b₁ is onto & b₁ is (Ne,4) ) } is set
card { b₁ where b₁ is Relation-like Ne -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ne,4:] : ( b₁ is onto & b₁ is (Ne,4) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
4 |^ Ne is V33() V34() ext-real Element of REAL
3 |^ Ne is V33() V34() ext-real Element of REAL
4 * (3 |^ Ne) is V33() V34() ext-real Element of REAL
(4 |^ Ne) - (4 * (3 |^ Ne)) is V33() V34() ext-real Element of REAL
2 |^ Ne is V33() V34() ext-real Element of REAL
6 * (2 |^ Ne) is V33() V34() ext-real Element of REAL
((4 |^ Ne) - (4 * (3 |^ Ne))) + (6 * (2 |^ Ne)) is V33() V34() ext-real Element of REAL
(((4 |^ Ne) - (4 * (3 |^ Ne))) + (6 * (2 |^ Ne))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ Ne) - (4 * (3 |^ Ne))) + (6 * (2 |^ Ne))) - 4) is V33() V34() ext-real Element of REAL
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,4:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,4:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,4:] : ( b₁ is onto & b₁ is (Ke,4) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,4:] : ( b₁ is onto & b₁ is (Ke,4) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
4 |^ Ke is V33() V34() ext-real Element of REAL
3 |^ Ke is V33() V34() ext-real Element of REAL
4 * (3 |^ Ke) is V33() V34() ext-real Element of REAL
(4 |^ Ke) - (4 * (3 |^ Ke)) is V33() V34() ext-real Element of REAL
2 |^ Ke is V33() V34() ext-real Element of REAL
6 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
((4 |^ Ke) - (4 * (3 |^ Ke))) + (6 * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
(((4 |^ Ke) - (4 * (3 |^ Ke))) + (6 * (2 |^ Ke))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ Ke) - (4 * (3 |^ Ke))) + (6 * (2 |^ Ke))) - 4) is V33() V34() ext-real Element of REAL
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ke + 1),4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),4:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),4:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 1 -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),4:] : ( b₁ is onto & b₁ is (Ke + 1,4) ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),4:] : ( b₁ is onto & b₁ is (Ke + 1,4) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
4 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
3 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
4 * (3 |^ (Ke + 1)) is V33() V34() ext-real Element of REAL
(4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1))) is V33() V34() ext-real Element of REAL
2 |^ (Ke + 1) is V33() V34() ext-real Element of REAL
6 * (2 |^ (Ke + 1)) is V33() V34() ext-real Element of REAL
((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1))) is V33() V34() ext-real Element of REAL
(((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1)))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1)))) - 4) is V33() V34() ext-real Element of REAL
(Ke,3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,3:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,3:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,3:] : ( b₁ is onto & b₁ is (Ke,3) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 3 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,3:] : ( b₁ is onto & b₁ is (Ke,3) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
3 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
(3 |^ Ke) - (3 * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
((3 |^ Ke) - (3 * (2 |^ Ke))) + 3 is V33() V34() ext-real Element of REAL
(1 / 6) * (((3 |^ Ke) - (3 * (2 |^ Ke))) + 3) is V33() V34() ext-real Element of REAL
3 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke,(3 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(3 + 1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(3 + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke -defined 3 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(3 + 1):] : ( b₁ is onto & b₁ is (Ke,3 + 1) ) } is set
card { b₁ where b₁ is Relation-like Ke -defined 3 + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(3 + 1):] : ( b₁ is onto & b₁ is (Ke,3 + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
4 * (Ke,(3 + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 * (Ke,(3 + 1))) + ((1 / 6) * (((3 |^ Ke) - (3 * (2 |^ Ke))) + 3)) is V33() V34() ext-real Element of REAL
4 * (4 |^ Ke) is V33() V34() ext-real Element of REAL
3 * (3 |^ Ke) is V33() V34() ext-real Element of REAL
4 * (3 * (3 |^ Ke)) is V33() V34() ext-real Element of REAL
(4 * (4 |^ Ke)) - (4 * (3 * (3 |^ Ke))) is V33() V34() ext-real Element of REAL
2 * (2 |^ Ke) is V33() V34() ext-real Element of REAL
6 * (2 * (2 |^ Ke)) is V33() V34() ext-real Element of REAL
((4 * (4 |^ Ke)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke))) is V33() V34() ext-real Element of REAL
(((4 * (4 |^ Ke)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke)))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 * (4 |^ Ke)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke)))) - 4) is V33() V34() ext-real Element of REAL
4 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 |^ (Ke + 1)) - (4 * (3 * (3 |^ Ke))) is V33() V34() ext-real Element of REAL
((4 |^ (Ke + 1)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke))) is V33() V34() ext-real Element of REAL
(((4 |^ (Ke + 1)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke)))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ (Ke + 1)) - (4 * (3 * (3 |^ Ke)))) + (6 * (2 * (2 |^ Ke)))) - 4) is V33() V34() ext-real Element of REAL
3 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
4 * (3 |^ (Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1))) is V33() V34() integer V36() ext-real Element of INT
((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 * (2 |^ Ke))) is V33() V34() ext-real Element of REAL
(((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 * (2 |^ Ke)))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 * (2 |^ Ke)))) - 4) is V33() V34() ext-real Element of REAL
2 |^ (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
6 * (2 |^ (Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1))) is V33() V34() integer V36() ext-real Element of INT
(((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1)))) - 4 is V33() V34() integer V36() ext-real Element of INT
(1 / 24) * ((((4 |^ (Ke + 1)) - (4 * (3 |^ (Ke + 1)))) + (6 * (2 |^ (Ke + 1)))) - 4) is V33() V34() V36() ext-real Element of RAT
4 |^ 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 |^ 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
4 * (3 |^ 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 |^ 3) - (4 * (3 |^ 3)) is V33() V34() integer V36() ext-real Element of INT
2 |^ 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
6 * (2 |^ 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3)) is V33() V34() integer V36() ext-real Element of INT
(((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4 is V33() V34() integer V36() ext-real Element of INT
(1 / 24) * ((((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4) is V33() V34() V36() ext-real Element of RAT
4 * 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 * 4) * 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((4 * 4) * 4) - (4 * (3 |^ 3)) is V33() V34() integer V36() ext-real Element of INT
(((4 * 4) * 4) - (4 * (3 |^ 3))) + (6 * (2 |^ 3)) is V33() V34() integer V36() ext-real Element of INT
((((4 * 4) * 4) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4 is V33() V34() integer V36() ext-real Element of INT
(1 / 24) * (((((4 * 4) * 4) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4) is V33() V34() V36() ext-real Element of RAT
64 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
3 * 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * 3) * 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
4 * ((3 * 3) * 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
64 - (4 * ((3 * 3) * 3)) is V33() V34() integer V36() ext-real Element of INT
(64 - (4 * ((3 * 3) * 3))) + (6 * (2 |^ 3)) is V33() V34() integer V36() ext-real Element of INT
((64 - (4 * ((3 * 3) * 3))) + (6 * (2 |^ 3))) - 4 is V33() V34() integer V36() ext-real Element of INT
(1 / 24) * (((64 - (4 * ((3 * 3) * 3))) + (6 * (2 |^ 3))) - 4) is V33() V34() V36() ext-real Element of RAT
27 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
4 * 27 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
64 - (4 * 27) is V33() V34() integer V36() ext-real Element of INT
2 * 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(2 * 2) * 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
6 * ((2 * 2) * 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(64 - (4 * 27)) + (6 * ((2 * 2) * 2)) is V33() V34() integer V36() ext-real Element of INT
((64 - (4 * 27)) + (6 * ((2 * 2) * 2))) - 4 is V33() V34() integer V36() ext-real Element of INT
(1 / 24) * (((64 - (4 * 27)) + (6 * ((2 * 2) * 2))) - 4) is V33() V34() V36() ext-real Element of RAT
(3,4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:3,4:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:3,4:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 3 -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:3,4:] : ( b₁ is onto & b₁ is (3,4) ) } is set
card { b₁ where b₁ is Relation-like 3 -defined 4 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:3,4:] : ( b₁ is onto & b₁ is (3,4) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
4 |^ 3 is V33() V34() ext-real Element of REAL
3 |^ 3 is V33() V34() ext-real Element of REAL
4 * (3 |^ 3) is V33() V34() ext-real Element of REAL
(4 |^ 3) - (4 * (3 |^ 3)) is V33() V34() ext-real Element of REAL
2 |^ 3 is V33() V34() ext-real Element of REAL
6 * (2 |^ 3) is V33() V34() ext-real Element of REAL
((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3)) is V33() V34() ext-real Element of REAL
(((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4 is V33() V34() ext-real Element of REAL
(1 / 24) * ((((4 |^ 3) - (4 * (3 |^ 3))) + (6 * (2 |^ 3))) - 4) is V33() V34() ext-real Element of REAL
3 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
4 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(2 + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 * 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(3 + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
6 * 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne choose 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne - 1 is V33() V34() integer V36() ext-real Element of INT
Ne * (Ne - 1) is V33() V34() integer V36() ext-real Element of INT
(Ne * (Ne - 1)) / 2 is V33() V34() V36() ext-real Element of RAT
Ne choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne - 2 is V33() V34() integer V36() ext-real Element of INT
(Ne * (Ne - 1)) * (Ne - 2) is V33() V34() integer V36() ext-real Element of INT
((Ne * (Ne - 1)) * (Ne - 2)) / 6 is V33() V34() V36() ext-real Element of RAT
Ne choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne - 3 is V33() V34() integer V36() ext-real Element of INT
((Ne * (Ne - 1)) * (Ne - 2)) * (Ne - 3) is V33() V34() integer V36() ext-real Element of INT
(((Ne * (Ne - 1)) * (Ne - 2)) * (Ne - 3)) / 24 is V33() V34() V36() ext-real Element of RAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) * (F + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) / (F !) is V33() V34() V36() ext-real non negative Element of RAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke !) * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne - 1) * Ne is V33() V34() integer V36() ext-real Element of INT
(F !) * ((Ne - 1) * Ne) is V33() V34() integer V36() ext-real Element of INT
2 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) * (2 !) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((F !) * ((Ne - 1) * Ne)) / ((F !) * (2 !)) is V33() V34() V36() ext-real Element of RAT
((F !) / (F !)) * ((Ne - 1) * Ne) is V33() V34() V36() ext-real Element of RAT
(((F !) / (F !)) * ((Ne - 1) * Ne)) / 2 is V33() V34() V36() ext-real Element of RAT
((Ne - 1) * Ne) / 2 is V33() V34() V36() ext-real Element of RAT
3 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ne - 4 is V33() V34() integer V36() ext-real Element of INT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke !) * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) * (F + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) / (F !) is V33() V34() V36() ext-real non negative Element of RAT
Ke * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) * (Ke * Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F !) * (2 !) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((F !) * (Ke * Ne)) / ((F !) * (2 !)) is V33() V34() V36() ext-real non negative Element of RAT
((F !) / (F !)) * (Ke * Ne) is V33() V34() V36() ext-real non negative Element of RAT
(((F !) / (F !)) * (Ke * Ne)) / 2 is V33() V34() V36() ext-real non negative Element of RAT
Ne * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne * Ke) / 2 is V33() V34() V36() ext-real non negative Element of RAT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 !) / (I2 !) is V33() V34() V36() ext-real non negative Element of RAT
I2 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(I2 + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 !) * (I2 + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 !) / (I1 !) is V33() V34() V36() ext-real non negative Element of RAT
I1 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(I1 + 1) ! is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 !) * (I1 + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(F * Ke) * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 !) * ((F * Ke) * Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 !) * (3 !) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((I1 !) * ((F * Ke) * Ne)) / ((I1 !) * (3 !)) is V33() V34() V36() ext-real non negative Element of RAT
((I1 !) / (I1 !)) * ((F * Ke) * Ne) is V33() V34() V36() ext-real non negative Element of RAT
(((I1 !) / (I1 !)) * ((F * Ke) * Ne)) / 6 is V33() V34() V36() ext-real non negative Element of RAT
(Ne * Ke) * F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ne * Ke) * F) / 6 is V33() V34() V36() ext-real non negative Element of RAT
I1 * F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I1 * F) * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((I1 * F) * Ke) * Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 !) * (((I1 * F) * Ke) * Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(I2 !) * (4 !) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((I2 !) * (((I1 * F) * Ke) * Ne)) / ((I2 !) * (4 !)) is V33() V34() V36() ext-real non negative Element of RAT
((I2 !) / (I2 !)) * (((I1 * F) * Ke) * Ne) is V33() V34() V36() ext-real non negative Element of RAT
(((I2 !) / (I2 !)) * (((I1 * F) * Ke) * Ne)) / 24 is V33() V34() V36() ext-real non negative Element of RAT
((Ne * Ke) * F) * I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(((Ne * Ke) * F) * I1) / 24 is V33() V34() V36() ext-real non negative Element of RAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ne + 1),Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ne + 1),Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 1),Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ne:] : ( b₁ is onto & b₁ is (Ne + 1,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ne + 1 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 1),Ne:] : ( b₁ is onto & b₁ is (Ne + 1,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ne + 1) choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ke + 1),Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ke:] : ( b₁ is onto & b₁ is (Ke + 1,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),Ke:] : ( b₁ is onto & b₁ is (Ke + 1,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 1) choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(((Ke + 1) + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:((Ke + 1) + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((Ke + 1) + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like (Ke + 1) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 1,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like (Ke + 1) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 1,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
((Ke + 1) + 1) choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(Ke + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ke + 1,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like Ke + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 1),(Ke + 1):] : ( b₁ is onto & b₁ is (Ke + 1,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 1) * ((Ke + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 1) * ((Ke + 1),(Ke + 1))) + ((Ke + 1),Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 1) * 1) + ((Ke + 1) choose 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 1) - 1 is V33() V34() integer V36() ext-real Element of INT
(Ke + 1) * ((Ke + 1) - 1) is V33() V34() integer V36() ext-real Element of INT
((Ke + 1) * ((Ke + 1) - 1)) / 2 is V33() V34() V36() ext-real Element of RAT
(Ke + 1) + (((Ke + 1) * ((Ke + 1) - 1)) / 2) is V33() V34() V36() ext-real Element of RAT
((Ke + 1) + 1) - 1 is V33() V34() integer V36() ext-real Element of INT
((Ke + 1) + 1) * (((Ke + 1) + 1) - 1) is V33() V34() integer V36() ext-real Element of INT
(((Ke + 1) + 1) * (((Ke + 1) + 1) - 1)) / 2 is V33() V34() V36() ext-real Element of RAT
(1,0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:1,0:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:1,0:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 1 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:1,0:] : ( b₁ is onto & b₁ is (1, 0 ) ) } is set
card { b₁ where b₁ is Relation-like 1 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:1,0:] : ( b₁ is onto & b₁ is (1, 0 ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
0 + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((0 + 1),0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(0 + 1),0:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(0 + 1),0:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 0 + 1 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(0 + 1),0:] : ( b₁ is onto & b₁ is (0 + 1, 0 ) ) } is set
card { b₁ where b₁ is Relation-like 0 + 1 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(0 + 1),0:] : ( b₁ is onto & b₁ is (0 + 1, 0 ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(0 + 1) choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ne + 2),Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ne + 2),Ne:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ne + 2),Ne:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ne + 2 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 2),Ne:] : ( b₁ is onto & b₁ is (Ne + 2,Ne) ) } is set
card { b₁ where b₁ is Relation-like Ne + 2 -defined Ne -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ne + 2),Ne:] : ( b₁ is onto & b₁ is (Ne + 2,Ne) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ne + 2) choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * ((Ne + 2) choose 4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ne + 2) choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * ((Ne + 2) choose 4)) + ((Ne + 2) choose 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ke + 2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((Ke + 2),Ke) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke + 2),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ke + 2),Ke:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like Ke + 2 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 2),Ke:] : ( b₁ is onto & b₁ is (Ke + 2,Ke) ) } is set
card { b₁ where b₁ is Relation-like Ke + 2 -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke + 2),Ke:] : ( b₁ is onto & b₁ is (Ke + 2,Ke) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 2) choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * ((Ke + 2) choose 4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 2) choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * ((Ke + 2) choose 4)) + ((Ke + 2) choose 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke + 1) + 2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(((Ke + 1) + 2),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:((Ke + 1) + 2),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((Ke + 1) + 2),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like (Ke + 1) + 2 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 2),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 2,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like (Ke + 1) + 2 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 2),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 2,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
((Ke + 1) + 2) choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * (((Ke + 1) + 2) choose 4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 1) + 2) choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * (((Ke + 1) + 2) choose 4)) + (((Ke + 1) + 2) choose 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(((Ke + 1) + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:((Ke + 1) + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((Ke + 1) + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like (Ke + 1) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 1,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like (Ke + 1) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 1) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 1) + 1,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 1) * (((Ke + 1) + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 2) choose 2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 1) * ((Ke + 2) choose 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke + 2) - 1 is V33() V34() integer V36() ext-real Element of INT
(Ke + 2) * ((Ke + 2) - 1) is V33() V34() integer V36() ext-real Element of INT
((Ke + 2) * ((Ke + 2) - 1)) / 2 is V33() V34() V36() ext-real Element of RAT
(Ke + 1) * (((Ke + 2) * ((Ke + 2) - 1)) / 2) is V33() V34() V36() ext-real Element of RAT
12 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(Ke + 1) * 12 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 1) * 12) / 24 is V33() V34() V36() ext-real non negative Element of RAT
((Ke + 2) * ((Ke + 2) - 1)) * (((Ke + 1) * 12) / 24) is V33() V34() V36() ext-real Element of RAT
(Ke + 2) - 2 is V33() V34() integer V36() ext-real Element of INT
((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2) is V33() V34() integer V36() ext-real Element of INT
(Ke + 2) - 3 is V33() V34() integer V36() ext-real Element of INT
(((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) * ((Ke + 2) - 3) is V33() V34() integer V36() ext-real Element of INT
((((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24 is V33() V34() V36() ext-real Element of RAT
3 * (((((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24) is V33() V34() V36() ext-real Element of RAT
(3 * (((((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24)) + ((Ke + 2) choose 3) is V33() V34() V36() ext-real Element of RAT
(((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) / 6 is V33() V34() V36() ext-real Element of RAT
(3 * (((((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24)) + ((((Ke + 2) * ((Ke + 2) - 1)) * ((Ke + 2) - 2)) / 6) is V33() V34() V36() ext-real Element of RAT
3 * ((Ke + 2) - 2) is V33() V34() integer V36() ext-real Element of INT
(3 * ((Ke + 2) - 2)) * ((Ke + 2) - 3) is V33() V34() integer V36() ext-real Element of INT
((3 * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24 is V33() V34() V36() ext-real Element of RAT
4 * ((Ke + 2) - 2) is V33() V34() integer V36() ext-real Element of INT
(4 * ((Ke + 2) - 2)) / 24 is V33() V34() V36() ext-real Element of RAT
(((3 * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24) + ((4 * ((Ke + 2) - 2)) / 24) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) * ((Ke + 2) - 1)) * ((((3 * ((Ke + 2) - 2)) * ((Ke + 2) - 3)) / 24) + ((4 * ((Ke + 2) - 2)) / 24)) is V33() V34() V36() ext-real Element of RAT
(((Ke + 2) + 1),(Ke + 1)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:((Ke + 2) + 1),(Ke + 1):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((Ke + 2) + 1),(Ke + 1):] is non empty finite V61() set
{ b₁ where b₁ is Relation-like (Ke + 2) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 2) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 2) + 1,Ke + 1) ) } is set
card { b₁ where b₁ is Relation-like (Ke + 2) + 1 -defined Ke + 1 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke + 2) + 1),(Ke + 1):] : ( b₁ is onto & b₁ is ((Ke + 2) + 1,Ke + 1) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(Ke + 2) * (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((Ke + 2) * (Ke + 1)) * (((Ke + 1) * 12) / 24) is V33() V34() V36() ext-real non negative Element of RAT
3 * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * Ke) * ((Ke + 2) - 3) is V33() V34() integer V36() ext-real Element of INT
((3 * Ke) * ((Ke + 2) - 3)) / 24 is V33() V34() V36() ext-real Element of RAT
4 * Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(4 * Ke) / 24 is V33() V34() V36() ext-real non negative Element of RAT
(((3 * Ke) * ((Ke + 2) - 3)) / 24) + ((4 * Ke) / 24) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) * (Ke + 1)) * ((((3 * Ke) * ((Ke + 2) - 3)) / 24) + ((4 * Ke) / 24)) is V33() V34() V36() ext-real Element of RAT
(((Ke + 2) * (Ke + 1)) * (((Ke + 1) * 12) / 24)) + (((Ke + 2) * (Ke + 1)) * ((((3 * Ke) * ((Ke + 2) - 3)) / 24) + ((4 * Ke) / 24))) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) + 1) - 1 is V33() V34() integer V36() ext-real Element of INT
((Ke + 2) + 1) * (((Ke + 2) + 1) - 1) is V33() V34() integer V36() ext-real Element of INT
((Ke + 2) + 1) - 2 is V33() V34() integer V36() ext-real Element of INT
(((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2) is V33() V34() integer V36() ext-real Element of INT
((Ke + 2) + 1) - 3 is V33() V34() integer V36() ext-real Element of INT
((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) * (((Ke + 2) + 1) - 3) is V33() V34() integer V36() ext-real Element of INT
(((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) * (((Ke + 2) + 1) - 3)) / 24 is V33() V34() V36() ext-real Element of RAT
3 * ((((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) * (((Ke + 2) + 1) - 3)) / 24) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) + 1) * (Ke + 2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(((Ke + 2) + 1) * (Ke + 2)) * (Ke + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((((Ke + 2) + 1) * (Ke + 2)) * (Ke + 1)) / 6 is V33() V34() V36() ext-real non negative Element of RAT
(3 * ((((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) * (((Ke + 2) + 1) - 3)) / 24)) + (((((Ke + 2) + 1) * (Ke + 2)) * (Ke + 1)) / 6) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) + 1) choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * (((Ke + 2) + 1) choose 4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) / 6 is V33() V34() V36() ext-real Element of RAT
(3 * (((Ke + 2) + 1) choose 4)) + (((((Ke + 2) + 1) * (((Ke + 2) + 1) - 1)) * (((Ke + 2) + 1) - 2)) / 6) is V33() V34() V36() ext-real Element of RAT
((Ke + 2) + 1) choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * (((Ke + 2) + 1) choose 4)) + (((Ke + 2) + 1) choose 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
2 choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
0 + 2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
((0 + 2),0) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(0 + 2),0:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(0 + 2),0:] is non empty finite V61() set
{ b₁ where b₁ is Relation-like 0 + 2 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(0 + 2),0:] : ( b₁ is onto & b₁ is (0 + 2, 0 ) ) } is set
card { b₁ where b₁ is Relation-like 0 + 2 -defined 0 -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(0 + 2),0:] : ( b₁ is onto & b₁ is (0 + 2, 0 ) ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(0 + 2) choose 4 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
3 * ((0 + 2) choose 4) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(0 + 2) choose 3 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(3 * ((0 + 2) choose 4)) + ((0 + 2) choose 3) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is Relation-like Function-like set
dom Ne is set
rng Ne is set
Ke is set
{Ke} is non empty trivial finite 1 -element set
Ne " {Ke} is set
(dom Ne) \ (Ne " {Ke}) is Element of bool (dom Ne)
bool (dom Ne) is non empty set
Ne | ((dom Ne) \ (Ne " {Ke})) is Relation-like Function-like set
rng (Ne | ((dom Ne) \ (Ne " {Ke}))) is set
(rng Ne) \ {Ke} is Element of bool (rng Ne)
bool (rng Ne) is non empty set
I1 is set
dom (Ne | ((dom Ne) \ (Ne " {Ke}))) is set
I2 is set
(Ne | ((dom Ne) \ (Ne " {Ke}))) . I2 is set
(dom Ne) /\ ((dom Ne) \ (Ne " {Ke})) is Element of bool (dom Ne)
(dom Ne) /\ (dom Ne) is set
((dom Ne) /\ (dom Ne)) \ (Ne " {Ke}) is Element of bool ((dom Ne) /\ (dom Ne))
bool ((dom Ne) /\ (dom Ne)) is non empty set
Ne . I2 is set
I1 is set
I2 is set
Ne . I2 is set
(dom Ne) /\ ((dom Ne) \ (Ne " {Ke})) is Element of bool (dom Ne)
dom (Ne | ((dom Ne) \ (Ne " {Ke}))) is set
(Ne | ((dom Ne) \ (Ne " {Ke}))) . I2 is set
I1 is set
{I1} is non empty trivial finite 1 -element set
(Ne | ((dom Ne) \ (Ne " {Ke}))) " {I1} is set
Ne " {I1} is set
I2 is set
Ne . I2 is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke is set
card Ke is epsilon-transitive epsilon-connected ordinal cardinal set
F is set
{F} is non empty trivial finite 1 -element set
Ke \ {F} is Element of bool Ke
bool Ke is non empty set
card (Ke \ {F}) is epsilon-transitive epsilon-connected ordinal cardinal set
I1 is finite set
I1 \ {F} is finite Element of bool I1
bool I1 is non empty finite V61() set
{F} /\ Ke is finite set
(I1 \ {F}) \/ {F} is non empty finite set
card {F} is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
card (I1 \ {F}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(card {F}) + (card (I1 \ {F})) is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke is Relation-like Function-like set
rng Ke is set
card (rng Ke) is epsilon-transitive epsilon-connected ordinal cardinal set
dom Ke is set
F is set
{F} is non empty trivial finite 1 -element set
Ke " {F} is set
(dom Ke) \ (Ke " {F}) is Element of bool (dom Ke)
bool (dom Ke) is non empty set
Ke | ((dom Ke) \ (Ke " {F})) is Relation-like Function-like set
(rng Ke) \ {F} is Element of bool (rng Ke)
bool (rng Ke) is non empty set
card ((rng Ke) \ {F}) is epsilon-transitive epsilon-connected ordinal cardinal set
rng (Ke | ((dom Ke) \ (Ke " {F}))) is set
card (rng (Ke | ((dom Ke) \ (Ke " {F})))) is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is Relation-like Function-like set
rng Ne is set
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
card (rng Ne) is epsilon-transitive epsilon-connected ordinal cardinal set
F is Relation-like Function-like set
rng F is set
card (rng F) is epsilon-transitive epsilon-connected ordinal cardinal set
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F is Relation-like Function-like set
dom F is set
rng F is set
I1 is Relation-like NAT -defined T-Sequence-like Function-like finite V88() set
I2 is Relation-like NAT -defined NAT -valued T-Sequence-like Function-like V40() V41() V42() V43() finite V88() V92() set
Sum I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of COMPLEX
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
len I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
F is set
I2 . F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne is set
Ke is set
[:Ne,Ke:] is Relation-like set
bool [:Ne,Ke:] is non empty set
F is set
{F} is non empty trivial finite 1 -element set
Ne \/ {F} is non empty set
I1 is set
{I1} is non empty trivial finite 1 -element set
Ke \/ {I1} is non empty set
[:(Ne \/ {F}),(Ke \/ {I1}):] is Relation-like non empty set
bool [:(Ne \/ {F}),(Ke \/ {I1}):] is non empty set
P2 is Relation-like Ne -defined Ke -valued Function-like quasi_total Element of bool [:Ne,Ke:]
(Ne \/ {F}) \ Ne is Element of bool (Ne \/ {F})
bool (Ne \/ {F}) is non empty set
F is set
F is Relation-like Ne \/ {F} -defined Ke \/ {I1} -valued non empty Function-like V24(Ne \/ {F}) quasi_total Element of bool [:(Ne \/ {F}),(Ke \/ {I1}):]
F | Ne is Relation-like Ne -defined Ne \/ {F} -defined Ke \/ {I1} -valued Function-like Element of bool [:(Ne \/ {F}),(Ke \/ {I1}):]
F . F is set
Ne is set
Ke is set
[:Ne,Ke:] is Relation-like set
bool [:Ne,Ke:] is non empty set
F is set
{F} is non empty trivial finite 1 -element set
Ne \/ {F} is non empty set
I1 is set
{I1} is non empty trivial finite 1 -element set
Ke \/ {I1} is non empty set
[:(Ne \/ {F}),(Ke \/ {I1}):] is Relation-like non empty set
bool [:(Ne \/ {F}),(Ke \/ {I1}):] is non empty set
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total Element of bool [:Ne,Ke:]
P1 is Relation-like Ne \/ {F} -defined Ke \/ {I1} -valued non empty Function-like V24(Ne \/ {F}) quasi_total Element of bool [:(Ne \/ {F}),(Ke \/ {I1}):]
P1 | Ne is Relation-like Ne -defined Ne \/ {F} -defined Ke \/ {I1} -valued Function-like Element of bool [:(Ne \/ {F}),(Ke \/ {I1}):]
P1 . F is set
rng P1 is non empty Element of bool (Ke \/ {I1})
bool (Ke \/ {I1}) is non empty set
P2 is set
rng I2 is Element of bool Ke
bool Ke is non empty set
dom I2 is Element of bool Ne
bool Ne is non empty set
F is set
I2 . F is set
dom P1 is non empty Element of bool (Ne \/ {F})
bool (Ne \/ {F}) is non empty set
P1 . F is set
dom P1 is non empty Element of bool (Ne \/ {F})
bool (Ne \/ {F}) is non empty set
P2 is set
dom P1 is non empty set
F is set
P1 . P2 is set
P1 . F is set
dom P1 is non empty Element of bool (Ne \/ {F})
bool (Ne \/ {F}) is non empty set
dom I2 is Element of bool Ne
bool Ne is non empty set
domF is set
I2 . domF is set
P1 . domF is set
rng I2 is Element of bool Ke
bool Ke is non empty set
I2 . P2 is set
I2 . F is set
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
Ne + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(card Ke):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(card Ke):] is non empty finite V61() set
F is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
Ke \ {I1} is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card (Ke \ {I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:(Ke \ {I1}),(card (Ke \ {I1})):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(Ke \ {I1}),(card (Ke \ {I1})):] is non empty finite V61() set
P1 is Relation-like Ke \ {I1} -defined card (Ke \ {I1}) -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(Ke \ {I1}),(card (Ke \ {I1})):]
dom P1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (Ke \ {I1})
bool (Ke \ {I1}) is non empty finite V61() set
{Ne} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(card (Ke \ {I1})) \/ {Ne} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
(Ke \ {I1}) \/ {I1} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
[:((Ke \ {I1}) \/ {I1}),((card (Ke \ {I1})) \/ {Ne}):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((Ke \ {I1}) \/ {I1}),((card (Ke \ {I1})) \/ {Ne}):] is non empty finite V61() set
P2 is Relation-like (Ke \ {I1}) \/ {I1} -defined (card (Ke \ {I1})) \/ {Ne} -valued non empty Function-like V24((Ke \ {I1}) \/ {I1}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((Ke \ {I1}) \/ {I1}),((card (Ke \ {I1})) \/ {Ne}):]
P2 | (Ke \ {I1}) is Relation-like Ke \ {I1} -defined (Ke \ {I1}) \/ {I1} -defined RAT -valued (card (Ke \ {I1})) \/ {Ne} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:((Ke \ {I1}) \/ {I1}),((card (Ke \ {I1})) \/ {Ne}):]
P2 . I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
F is Relation-like Ke -defined card Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(card Ke):]
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
((Ke \ {I1}),(card (Ke \ {I1})),P1,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card (Ke \ {I1})
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,m) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
((Ke \ {I1}),(card (Ke \ {I1})),P1,m) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card (Ke \ {I1})
((Ke \ {I1}),(card (Ke \ {I1})),P1,domF) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card (Ke \ {I1})
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
bool RAT is non empty set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(card Ke):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(card Ke):] is non empty finite V61() set
F is Relation-like Ke -defined card Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(card Ke):]
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (card Ke)
bool (card Ke) is non empty finite V61() set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
Ne is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ne,(card Ne):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ne,(card Ne):] is non empty finite V61() set
Ne is finite set
card Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is set
{Ke} is non empty trivial finite 1 -element set
Ne \ {Ke} is finite Element of bool Ne
bool Ne is non empty finite V61() set
card (Ne \ {Ke}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(card Ne) - 1 is V33() V34() integer V36() ext-real Element of INT
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
Ne is finite set
Ke is finite set
[:Ne,Ke:] is Relation-like finite set
bool [:Ne,Ke:] is non empty finite V61() set
card Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Relation-like Ne -defined Ke -valued Function-like quasi_total finite Element of bool [:Ne,Ke:]
dom F is finite Element of bool Ne
bool Ne is non empty finite V61() set
I1 is set
I2 is set
F . I1 is set
F . I2 is set
{I1} is non empty trivial finite 1 -element set
Ne \ {I1} is finite Element of bool Ne
P1 is finite set
F .: P1 is finite Element of bool Ke
bool Ke is non empty finite V61() set
P2 is set
rng F is finite Element of bool Ke
F is set
F . F is set
card P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom F is finite Element of bool Ne
bool Ne is non empty finite V61() set
F .: (dom F) is finite Element of bool Ke
bool Ke is non empty finite V61() set
card (dom F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
card (F .: (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng F is finite Element of bool Ke
I1 is set
card (rng F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{I1} is non empty trivial finite 1 -element set
Ke \ {I1} is finite Element of bool Ke
card (Ke \ {I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ke is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool NAT
card Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
[:Ke,(card Ke):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,(card Ke):] is non empty finite V61() set
[:Ke,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:Ke,Ke:] is non empty finite V61() set
F is Relation-like Ke -defined card Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,(card Ke):]
dom F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
bool Ke is non empty finite V61() set
F " is Relation-like Function-like set
(F ") . 0 is set
rng F is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (card Ke)
bool (card Ke) is non empty finite V61() set
[:(card Ke),Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(card Ke),Ke:] is non empty finite V61() set
I1 is Relation-like card Ke -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(card Ke),Ke:]
dom I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (card Ke)
I2 is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(Ke,(card Ke),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
I1 . ((Ke,(card Ke),F,P1) + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
(F ") . ((Ke,(card Ke),F,P1) + 1) is set
F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,F) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F ") . ((Ke,(card Ke),F,F) + 1) is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F ") . ((Ke,(card Ke),F,P2) + 1) is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F ") . ((Ke,(card Ke),F,P2) + 1) is set
P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is set
I2 is Relation-like Ke -defined Ke -valued Function-like V24(Ke) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ke:]
rng I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
P1 is set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng I1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
F is set
I1 . F is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
I2 . Ne is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
domF - 1 is V33() V34() integer V36() ext-real Element of INT
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
m + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
I1 is set
(Ke,(card Ke),F,I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
(Ke,(card Ke),F,Ne) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,I2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F ") . ((Ke,(card Ke),F,I2) + 1) is set
I2 . I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom I2 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool Ke
I2 . P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 is Relation-like Ke -defined Ke -valued Function-like one-to-one V24(Ke) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:Ke,Ke:]
P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 . P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(Ke,(card Ke),F,P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card Ke
(Ke,(card Ke),F,P2) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(F ") . ((Ke,(card Ke),F,P2) + 1) is set
Ne is Relation-like Function-like set
Ke is Relation-like Function-like set
Ne * Ke is Relation-like Function-like set
rng (Ne * Ke) is set
dom Ke is set
rng Ne is set
F is set
{F} is non empty trivial finite 1 -element set
Ke " {F} is set
(Ne * Ke) " {F} is set
dom (Ne * Ke) is set
I1 is set
(Ne * Ke) . I1 is set
Ne . I1 is set
Ke . (Ne . I1) is set
{(Ne . I1)} is non empty trivial finite 1 -element set
Ne " {(Ne . I1)} is set
I2 is set
dom Ne is set
Ne . I2 is set
Ke . (Ne . I2) is set
(Ne * Ke) . I2 is set
rng Ke is set
I2 is set
{I2} is non empty trivial finite 1 -element set
dom Ne is set
P1 is set
(Ne * Ke) . P1 is set
Ne . P1 is set
Ke . (Ne . P1) is set
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
bool Ke is non empty set
min* (rng F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
dom F is V50() V51() V52() V53() V54() V55() V68() Element of bool Ne
bool Ne is non empty set
min* (dom F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F . (min* (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I2 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
P1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* P1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F . (min* P1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
domF is set
F . domF is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{(F . (min* P1))} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
{(min* I1)} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
F " {(min* I1)} is V50() V51() V52() V53() V54() V55() V68() Element of bool Ne
F " {(F . (min* P1))} is V50() V51() V52() V53() V54() V55() V68() Element of bool Ne
m is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* (F " {(F . (min* P1))}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* (F " {(min* I1)}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
F is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:F,I1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:F,I1:] is non empty set
I2 is Relation-like F -defined I1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:F,I1:]
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
bool I1 is non empty set
[:(rng I2),(rng I2):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng I2),(rng I2):] is non empty set
rng {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
bool RAT is non empty set
dom {} is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty proper Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool NAT
P1 is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() set
[:P1,P1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:P1,P1:] is non empty finite V61() set
rng P1 is Relation-like non-empty empty-yielding NAT -defined RAT -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty trivial Function-like one-to-one constant functional V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V44() V45() V46() V47() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V84() V88() V92() Element of bool RAT
F is Relation-like non-empty empty-yielding P1 -defined P1 -valued epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural empty Function-like one-to-one constant functional V24(P1) quasi_total V33() V34() integer ext-real non positive non negative V40() V41() V42() V43() V50() V51() V52() V53() V54() V55() V56() finite finite-yielding V61() V68() V69() V70() V71() cardinal {} -element V88() V92() Element of bool [:P1,P1:]
domF is Relation-like rng I2 -defined rng I2 -valued Function-like one-to-one V24( rng I2) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng I2),(rng I2):]
domF * I2 is Relation-like F -defined RAT -valued rng I2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:F,(rng I2):]
[:F,(rng I2):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:F,(rng I2):] is non empty set
m is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
I2 " {I1} is V50() V51() V52() V53() V54() V55() V68() Element of bool F
bool F is non empty set
min* (I2 " {I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
{m} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
I2 " {m} is V50() V51() V52() V53() V54() V55() V68() Element of bool F
min* (I2 " {m}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F is Relation-like Function-like set
rng F is set
dom F is set
min* (dom F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
F . (min* (dom F)) is set
I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I1,I2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,I2:] is non empty set
P1 is Relation-like I1 -defined I2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
rng P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
bool I2 is non empty set
[:(rng P1),(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng P1),(rng P1):] is non empty set
dom P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
bool I1 is non empty set
P2 is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
min* P2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P1 . (min* P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{(P1 . (min* P2))} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
P1 " {(P1 . (min* P2))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
(dom P1) \ (P1 " {(P1 . (min* P2))}) is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))})) is Relation-like I1 -defined (dom P1) \ (P1 " {(P1 . (min* P2))}) -defined I1 -defined RAT -valued I2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
rng (P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))}))) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(rng P1) \ {(P1 . (min* P2))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
I1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
P1 " {I1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
min* (P1 " {I1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{I2} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
P1 " {I2} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
min* (P1 " {I2}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
id (rng P1) is Relation-like rng P1 -defined rng P1 -valued RAT -valued INT -valued Function-like one-to-one V24( rng P1) quasi_total V40() V41() V42() V43() V44() V46() V92() Element of bool [:(rng P1),(rng P1):]
rng (id (rng P1)) is V50() V51() V52() V53() V54() V55() V68() Element of bool (rng P1)
bool (rng P1) is non empty set
[:(dom P1),(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(dom P1),(rng P1):] is non empty set
I2 is Relation-like rng P1 -defined rng P1 -valued Function-like one-to-one V24( rng P1) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng P1),(rng P1):]
I2 * P1 is Relation-like I1 -defined RAT -valued rng P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,(rng P1):]
[:I1,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,(rng P1):] is non empty set
P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))})) is Relation-like I1 -defined (dom P1) \ (P1 " {(P1 . (min* P2))}) -defined I1 -defined RAT -valued I2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
rng (P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))}))) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
dom (P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))}))) is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I1 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool NAT
[:I2,I1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,I1:] is non empty set
F is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
P1 is Relation-like I2 -defined I1 -valued Function-like V24(I2) quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,I1:]
rng P1 is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool I1
bool I1 is non empty finite V61() set
[:(rng P1),(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() finite V92() set
bool [:(rng P1),(rng P1):] is non empty finite V61() set
D is Relation-like I2 -defined I1 -valued Function-like V24(I2) quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,I1:]
I is Relation-like rng P1 -defined rng P1 -valued Function-like one-to-one V24( rng P1) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:(rng P1),(rng P1):]
I * D is Relation-like I2 -defined RAT -valued rng P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,(rng P1):]
[:I2,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,(rng P1):] is non empty set
rng D is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool I1
I1 \ I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I1D is set
[:I1,F:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,F:] is non empty set
I1D is Relation-like I1 -defined F -valued Function-like V24(I1) quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,F:]
I1D | I2 is Relation-like I1 -defined I2 -defined I1 -defined RAT -valued F -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,F:]
rng I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool F
bool F is non empty set
I2D is set
dom I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
rFD is set
I1D . rFD is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(dom I1D) /\ I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
((dom I1D) /\ I2) \/ (I1 \ I2) is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
dom D is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
bool I2 is non empty set
D . rFD is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(rng P1) \ {(P1 . (min* P2))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(rng P1) \ {(P1 . (min* P2))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
dom P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
bool I2 is non empty set
(dom P1) /\ ((dom P1) \ (P1 " {(P1 . (min* P2))})) is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
I1D " {(P1 . (min* P2))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
I2D is set
I1D . I2D is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
(rng P1) \/ {(P1 . (min* P2))} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
I2D is set
rng (I1D | I2) is V50() V51() V52() V53() V54() V55() V68() Element of bool F
dom I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
I1D . (min* P2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(rng P1) \/ {(P1 . (min* P2))} is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() set
[:((rng P1) \/ {(P1 . (min* P2))}),((rng P1) \/ {(P1 . (min* P2))}):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:((rng P1) \/ {(P1 . (min* P2))}),((rng P1) \/ {(P1 . (min* P2))}):] is non empty finite V61() set
I2D is Relation-like (rng P1) \/ {(P1 . (min* P2))} -defined (rng P1) \/ {(P1 . (min* P2))} -valued non empty Function-like V24((rng P1) \/ {(P1 . (min* P2))}) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:((rng P1) \/ {(P1 . (min* P2))}),((rng P1) \/ {(P1 . (min* P2))}):]
I2D | (rng P1) is Relation-like rng P1 -defined (rng P1) \/ {(P1 . (min* P2))} -defined RAT -valued (rng P1) \/ {(P1 . (min* P2))} -valued Function-like V40() V41() V42() V43() finite V92() Element of bool [:((rng P1) \/ {(P1 . (min* P2))}),((rng P1) \/ {(P1 . (min* P2))}):]
I2D . (P1 . (min* P2)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool NAT
card P2 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
[:P2,(card P2):] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:P2,(card P2):] is non empty finite V61() set
FD is Relation-like P2 -defined card P2 -valued non empty Function-like V24(P2) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:P2,(card P2):]
dom FD is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool P2
bool P2 is non empty finite V61() set
rng FD is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (card P2)
bool (card P2) is non empty finite V61() set
[:(card P2),P2:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:(card P2),P2:] is non empty finite V61() set
FD " is Relation-like Function-like set
[:P2,P2:] is Relation-like RAT -valued INT -valued non empty V40() V41() V42() V43() finite V92() set
bool [:P2,P2:] is non empty finite V61() set
(FD ") . 0 is set
l is Relation-like P2 -defined P2 -valued non empty Function-like one-to-one V24(P2) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:P2,P2:]
dom I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
[:I1,P2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,P2:] is non empty set
l " is Relation-like P2 -defined P2 -valued non empty Function-like one-to-one V24(P2) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:P2,P2:]
rFD is Relation-like rng P1 -defined rng P1 -valued Function-like one-to-one V24( rng P1) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng P1),(rng P1):]
rFD * (l ") is Relation-like P2 -defined RAT -valued rng P1 -valued Function-like one-to-one V40() V41() V42() V43() finite V92() Element of bool [:P2,(rng P1):]
[:P2,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:P2,(rng P1):] is non empty set
n is Relation-like P2 -defined P2 -valued non empty Function-like V24(P2) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:P2,P2:]
dom l is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool P2
(l ") * l is Relation-like P2 -defined RAT -valued P2 -valued non empty Function-like one-to-one V24(P2) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:P2,P2:]
id P2 is Relation-like P2 -defined P2 -valued RAT -valued INT -valued non empty Function-like one-to-one V24(P2) quasi_total V40() V41() V42() V43() V44() V46() finite V92() Element of bool [:P2,P2:]
l * I1D is Relation-like I1 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,P2:]
rng (l * I1D) is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool P2
(id P2) * I1D is Relation-like I1 -defined RAT -valued INT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,P2:]
(l ") * (l * I1D) is Relation-like I1 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,P2:]
x is set
dom D is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(dom I1D) \ (I1D " {(P1 . (min* P2))}) is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{x} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
D " {x} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
I1D " {x} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
PG is Relation-like I1 -defined F -valued Function-like V24(I1) quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,F:]
rng PG is V50() V51() V52() V53() V54() V55() V68() Element of bool F
(P2,(card P2),FD,(P1 . (min* P2))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(P2,(card P2),FD,x) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
(P2,(card P2),FD,x) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(P2,(card P2),FD,x) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
j is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(P2,(card P2),FD,j) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
x is Relation-like card P2 -defined P2 -valued non empty Function-like V24( card P2) quasi_total V40() V41() V42() V43() finite V92() Element of bool [:(card P2),P2:]
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
j is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x . j is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(P2,(card P2),FD,(x . x)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
rng x is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool P2
(P2,(card P2),FD,(x . j)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
dom x is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (card P2)
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{x} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
PG " {x} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
min* (PG " {x}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
j is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{j} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
PG " {j} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
min* (PG " {j}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
l " {x} is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool P2
i1 is set
{i1} is non empty trivial finite 1 -element set
I1D " {i1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
l " {j} is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool P2
j1 is set
{j1} is non empty trivial finite 1 -element set
I1D " {j1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
i1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
l . i1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
j1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
l . j1 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{i1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {i1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(P2,(card P2),FD,i1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
(P2,(card P2),FD,j1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
(P2,(card P2),FD,i1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
(P2,(card P2),FD,j1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
x . ((P2,(card P2),FD,j1) + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x . ((P2,(card P2),FD,i1) + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{j1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {j1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
min* (D " {j1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* (D " {i1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
x is set
I1D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{j1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {j1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(P2,(card P2),FD,i1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
(P2,(card P2),FD,i1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
x . ((P2,(card P2),FD,i1) + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{i1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {i1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
{j1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {j1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
min* (D " {j1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* (D " {i1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
rng (FD ") is set
dom x is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool (card P2)
x is set
x . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x . 0 is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
x . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{i1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {i1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
{j1} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool NAT
D " {j1} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
min* (D " {j1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
min* (D " {i1}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
(P2,(card P2),FD,j1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of card P2
(P2,(card P2),FD,j1) + 1 is epsilon-transitive epsilon-connected ordinal natural non empty V33() V34() integer V36() ext-real positive non negative V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() cardinal Element of NAT
x . (P2,(card P2),FD,(P1 . (min* P2))) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of P2
x . ((P2,(card P2),FD,j1) + 1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x is set
P1 . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
rFD . (I1D . x) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P1 . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I . (D . x) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
dom I is V50() V51() V52() V53() V54() V55() finite V68() V69() V70() Element of bool (rng P1)
bool (rng P1) is non empty finite V61() set
dom D is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
dom rFD is V50() V51() V52() V53() V54() V55() V68() Element of bool (rng P1)
bool (rng P1) is non empty set
x is set
I1D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
rFD * I1D is Relation-like I1 -defined RAT -valued rng P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,(rng P1):]
[:I1,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,(rng P1):] is non empty set
P21 is Relation-like P2 -defined P2 -valued non empty Function-like one-to-one V24(P2) quasi_total onto bijective V40() V41() V42() V43() finite V92() Element of bool [:P2,P2:]
P21 * PG is Relation-like I1 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,P2:]
rng l is non empty V50() V51() V52() V53() V54() V55() finite V66() V67() V68() V69() V70() Element of bool P2
P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))})) is Relation-like I1 -defined (dom P1) \ (P1 " {(P1 . (min* P2))}) -defined I1 -defined RAT -valued I2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
rng (P1 | ((dom P1) \ (P1 " {(P1 . (min* P2))}))) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
I2 is Relation-like I1 -defined I2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
I1 is Relation-like rng P1 -defined rng P1 -valued Function-like one-to-one V24( rng P1) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng P1),(rng P1):]
I1 * I2 is Relation-like I1 -defined RAT -valued rng P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,(rng P1):]
[:I1,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,(rng P1):] is non empty set
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
F is Relation-like I1 -defined I2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
P2 is Relation-like rng P1 -defined rng P1 -valued Function-like one-to-one V24( rng P1) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng P1),(rng P1):]
P2 * F is Relation-like I1 -defined RAT -valued rng P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I1,(rng P1):]
[:I1,(rng P1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,(rng P1):] is non empty set
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
bool Ke is non empty set
[:(rng F),(rng F):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng F),(rng F):] is non empty set
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
I1 is Relation-like rng F -defined rng F -valued Function-like one-to-one V24( rng F) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng F),(rng F):]
I1 * I2 is Relation-like Ne -defined RAT -valued rng F -valued Function-like V40() V41() V42() V43() V92() Element of bool [:Ne,(rng F):]
[:Ne,(rng F):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,(rng F):] is non empty set
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
F is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,F:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,F:] is non empty set
I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I1,I2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,I2:] is non empty set
P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I1,P1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I1,P1:] is non empty set
P2 is Relation-like I1 -defined I2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,I2:]
F is Relation-like I1 -defined P1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,P1:]
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool P1
bool P1 is non empty set
domF is Relation-like I1 -defined P1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I1,P1:]
rng domF is V50() V51() V52() V53() V54() V55() V68() Element of bool P1
m is Relation-like Function-like set
I1 is Relation-like Function-like set
dom m is set
dom I1 is set
F * m is Relation-like I1 -defined Function-like set
domF * I1 is Relation-like I1 -defined Function-like set
dom F is V50() V51() V52() V53() V54() V55() V68() Element of bool I1
bool I1 is non empty set
rng m is set
I1 is Relation-like Function-like set
rng I1 is set
dom I1 is set
min* (dom I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 . (min* (dom I1)) is set
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P1:] is non empty set
P2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P2:] is non empty set
F is Relation-like I2 -defined P1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P1:]
I1 is Relation-like Function-like set
I2 is Relation-like Function-like set
domF is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng domF is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
bool P2 is non empty set
m is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng m is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
dom I1 is set
dom I2 is set
domF * I1 is Relation-like I2 -defined Function-like set
m * I2 is Relation-like I2 -defined Function-like set
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P1:] is non empty set
F is Relation-like I2 -defined P1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P1:]
dom F is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
bool I2 is non empty set
min* (dom F) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
P2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P2:] is non empty set
P1 is Relation-like Function-like set
P2 is Relation-like Function-like set
I1 is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
bool P2 is non empty set
I2 is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
dom P1 is set
dom P2 is set
I1 * P1 is Relation-like I2 -defined Function-like set
I2 * P2 is Relation-like I2 -defined Function-like set
dom I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
min* (rng I1) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1 . (min* (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{(I1 . (min* (dom F)))} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(rng I1) \ {(I1 . (min* (dom F)))} is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
F . (min* (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{(F . (min* (dom F)))} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
F " {(F . (min* (dom F)))} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(dom F) \ (F " {(F . (min* (dom F)))}) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
D is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
F | D is Relation-like I2 -defined D -defined I2 -defined RAT -valued P1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,P1:]
I1D is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
I1D | D is Relation-like I2 -defined D -defined I2 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
dom (I1D | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
rng (I1D | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
I1D . (min* (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{(I1D . (min* (dom F)))} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
(rng I1D) \ {(I1D . (min* (dom F)))} is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
I2D is Relation-like Function-like set
dom I2D is set
I1D * I2D is Relation-like I2 -defined Function-like set
I2D | ((rng I1D) \ {(I1D . (min* (dom F)))}) is Relation-like Function-like set
dom (I2D | ((rng I1D) \ {(I1D . (min* (dom F)))})) is set
(I1D | D) * (I2D | ((rng I1D) \ {(I1D . (min* (dom F)))})) is Relation-like I2 -defined Function-like set
(dom I2D) /\ ((rng I1D) \ {(I1D . (min* (dom F)))}) is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
domF is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool P1
bool P1 is non empty set
I2D " {(F . (min* (dom F)))} is set
rFD is set
{rFD} is non empty trivial finite 1 -element set
I1D " {rFD} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
dom I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
(dom I1D) /\ D is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
FD is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:D,FD:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:D,FD:] is non empty set
x is Relation-like D -defined FD -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:D,FD:]
rng x is V50() V51() V52() V53() V54() V55() V68() Element of bool FD
bool FD is non empty set
l is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{l} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
x " {l} is V50() V51() V52() V53() V54() V55() V68() Element of bool D
bool D is non empty set
min* (x " {l}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
{n} is non empty trivial V50() V51() V52() V53() V54() V55() finite V61() V66() V67() V68() V69() V70() 1 -element Element of bool REAL
x " {n} is V50() V51() V52() V53() V54() V55() V68() Element of bool D
min* (x " {n}) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I1D " {n} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
I1D " {l} is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
dom (F | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
x is set
(F | D) . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(I1D | D) . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(I2D | ((rng I1D) \ {(I1D . (min* (dom F)))})) . ((I1D | D) . x) is set
(dom F) /\ D is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
I2D . ((I1D | D) . x) is set
F . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
I1D . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
(dom F) /\ D is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
x is set
(I1D | D) . x is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
l is set
(I1D | D) . l is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
x is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:D,x:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:D,x:] is non empty set
l is Relation-like D -defined x -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:D,x:]
I is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
P1 | I is Relation-like Function-like set
dom I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
min* (rng I2) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer V36() ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of NAT
I2 . (min* (dom F)) is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal set
P2 | I is Relation-like Function-like set
I2 | D is Relation-like I2 -defined D -defined I2 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
dom (I2 | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
I1 | D is Relation-like I2 -defined D -defined I2 -defined RAT -valued P2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
dom (I1 | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
rng (I1 | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
rng (I2 | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
[:D,I:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:D,I:] is non empty set
I2D is Relation-like D -defined I -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:D,I:]
I1D is Relation-like D -defined I -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:D,I:]
rng I1D is V50() V51() V52() V53() V54() V55() V68() Element of bool I
bool I is non empty set
dom (P1 | I) is set
rng (F | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool P1
bool P1 is non empty set
(dom F) /\ D is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
dom (F | D) is V50() V51() V52() V53() V54() V55() V68() Element of bool I2
rFD is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:D,rFD:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:D,rFD:] is non empty set
FD is Relation-like D -defined rFD -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:D,rFD:]
I1D * (P1 | I) is Relation-like D -defined Function-like set
I2D * (P2 | I) is Relation-like D -defined Function-like set
domF is non empty V50() V51() V52() V53() V54() V55() V66() V68() Element of bool NAT
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool P1
dom (P2 | I) is set
rng I2D is V50() V51() V52() V53() V54() V55() V68() Element of bool I
I \/ {(I1 . (min* (dom F)))} is non empty V50() V51() V52() V53() V54() V55() V66() V68() set
x is set
P1 . x is set
P2 . x is set
(dom P1) /\ I is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
(P1 | I) . x is set
(dom P2) /\ I is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
(P2 | I) . x is set
[:(dom I2),(rng I2):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(dom I2),(rng I2):] is non empty set
id (rng I2) is Relation-like rng I2 -defined rng I2 -valued RAT -valued INT -valued Function-like one-to-one V24( rng I2) quasi_total V40() V41() V42() V43() V44() V46() V92() Element of bool [:(rng I2),(rng I2):]
[:(rng I2),(rng I2):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng I2),(rng I2):] is non empty set
(id (rng I2)) * I2 is Relation-like I2 -defined RAT -valued INT -valued rng I2 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,(rng I2):]
[:I2,(rng I2):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,(rng I2):] is non empty set
[:(dom I1),(rng I1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(dom I1),(rng I1):] is non empty set
id (rng I1) is Relation-like rng I1 -defined rng I1 -valued RAT -valued INT -valued Function-like one-to-one V24( rng I1) quasi_total V40() V41() V42() V43() V44() V46() V92() Element of bool [:(rng I1),(rng I1):]
[:(rng I1),(rng I1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng I1),(rng I1):] is non empty set
(id (rng I1)) * I1 is Relation-like I2 -defined RAT -valued INT -valued rng I1 -valued Function-like V40() V41() V42() V43() V92() Element of bool [:I2,(rng I1):]
[:I2,(rng I1):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,(rng I1):] is non empty set
P1 " is Relation-like Function-like set
P1 * (P1 ") is Relation-like Function-like set
id (dom P1) is Relation-like dom P1 -defined dom P1 -valued Function-like one-to-one V24( dom P1) quasi_total Element of bool [:(dom P1),(dom P1):]
[:(dom P1),(dom P1):] is Relation-like set
bool [:(dom P1),(dom P1):] is non empty set
(I1 * P1) * (P1 ") is Relation-like I2 -defined Function-like set
P2 " is Relation-like Function-like set
P2 * (P2 ") is Relation-like Function-like set
id (dom P2) is Relation-like dom P2 -defined dom P2 -valued Function-like one-to-one V24( dom P2) quasi_total Element of bool [:(dom P2),(dom P2):]
[:(dom P2),(dom P2):] is Relation-like set
bool [:(dom P2),(dom P2):] is non empty set
I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P1:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P1:] is non empty set
P2 is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:I2,P2:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:I2,P2:] is non empty set
F is Relation-like I2 -defined P1 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P1:]
I1 is Relation-like Function-like set
I2 is Relation-like Function-like set
domF is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng domF is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
bool P2 is non empty set
m is Relation-like I2 -defined P2 -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:I2,P2:]
rng m is V50() V51() V52() V53() V54() V55() V68() Element of bool P2
dom I1 is set
dom I2 is set
domF * I1 is Relation-like I2 -defined Function-like set
m * I2 is Relation-like I2 -defined Function-like set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
rng I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
bool Ke is non empty set
P2 is Relation-like Function-like set
F is Relation-like Function-like set
I2 is Relation-like Ne -defined F -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,F:]
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool F
bool F is non empty set
P1 is Relation-like Ne -defined F -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,F:]
rng P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool F
dom P2 is set
dom F is set
I2 * P2 is Relation-like Ne -defined Function-like set
P1 * F is Relation-like Ne -defined Function-like set
Ne is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
Ke is V50() V51() V52() V53() V54() V55() V68() Element of bool NAT
[:Ne,Ke:] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,Ke:] is non empty set
F is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
rng F is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
bool Ke is non empty set
[:(rng F),(rng F):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:(rng F),(rng F):] is non empty set
I1 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
I2 is Relation-like Ne -defined Ke -valued Function-like quasi_total V40() V41() V42() V43() V92() Element of bool [:Ne,Ke:]
rng I1 is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
rng I2 is V50() V51() V52() V53() V54() V55() V68() Element of bool Ke
P1 is Relation-like rng F -defined rng F -valued Function-like one-to-one V24( rng F) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng F),(rng F):]
P1 * I1 is Relation-like Ne -defined RAT -valued rng F -valued Function-like V40() V41() V42() V43() V92() Element of bool [:Ne,(rng F):]
[:Ne,(rng F):] is Relation-like RAT -valued INT -valued V40() V41() V42() V43() V92() set
bool [:Ne,(rng F):] is non empty set
P2 is Relation-like rng F -defined rng F -valued Function-like one-to-one V24( rng F) quasi_total onto bijective V40() V41() V42() V43() V92() Element of bool [:(rng F),(rng F):]
P2 * I2 is Relation-like Ne -defined RAT -valued rng F -valued Function-like V40() V41() V42() V43() V92() Element of bool [:Ne,(rng F):]
dom P2 is V50() V51() V52() V53() V54() V55() V68() Element of bool (rng F)
bool (rng F) is non empty set
dom P1 is V50() V51() V52() V53() V54() V55() V68() Element of bool (rng F)
Ne is non empty set
Ke is Relation-like NAT -defined Ne -valued T-Sequence-like Function-like finite V88() set
dom Ke is epsilon-transitive epsilon-connected ordinal natural V33() V34() integer ext-real non negative V50() V51() V52() V53() V54() V55() finite V68() V69() V70() cardinal Element of bool NAT
rng Ke is finite Element of bool Ne
bool Ne is non empty set
union (rng Ke) is set
card (union (rng Ke)) is epsilon-transitive epsilon-connected ordinal cardinal set