:: CATALAN2 semantic presentation

REAL is non empty non trivial non finite V50() V51() V52() V56() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite V50() V51() V52() V53() V54() V55() V56() cardinal limit_cardinal Element of bool REAL
bool REAL is non empty non trivial non finite set
[:NAT,REAL:] is non empty non trivial Relation-like V35() V36() V37() non finite set
bool [:NAT,REAL:] is non empty non trivial non finite set
COMPLEX is non empty non trivial non finite V50() V56() set
RAT is non empty non trivial non finite V50() V51() V52() V53() V56() set
INT is non empty non trivial non finite V50() V51() V52() V53() V54() V56() set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{{},1} is non empty finite V49() V50() V51() V52() V53() V54() V55() set
NAT is non empty non trivial epsilon-transitive epsilon-connected ordinal non finite V50() V51() V52() V53() V54() V55() V56() 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,COMPLEX:] is non empty non trivial Relation-like V35() non finite set
bool [:COMPLEX,COMPLEX:] is non empty non trivial non finite set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial Relation-like V35() non finite set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is non empty non trivial non finite set
[:REAL,REAL:] is non empty non trivial Relation-like V35() V36() V37() non finite set
bool [:REAL,REAL:] is non empty non trivial non finite set
[:[:REAL,REAL:],REAL:] is non empty non trivial Relation-like V35() V36() V37() non finite set
bool [:[:REAL,REAL:],REAL:] is non empty non trivial non finite set
[:RAT,RAT:] is non empty non trivial Relation-like RAT -valued V35() V36() V37() non finite set
bool [:RAT,RAT:] is non empty non trivial non finite set
[:[:RAT,RAT:],RAT:] is non empty non trivial Relation-like RAT -valued V35() V36() V37() non finite set
bool [:[:RAT,RAT:],RAT:] is non empty non trivial non finite set
[:INT,INT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() non finite set
bool [:INT,INT:] is non empty non trivial non finite set
[:[:INT,INT:],INT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() non finite set
bool [:[:INT,INT:],INT:] is non empty non trivial non finite set
[:NAT,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() V38() non finite nonnegative-yielding set
[:[:NAT,NAT:],NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() V38() non finite nonnegative-yielding set
bool [:[:NAT,NAT:],NAT:] is non empty non trivial non finite set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan 1 is V11() real ext-real Element of REAL
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
- 1 is V11() real V30() ext-real non positive Element of REAL
card {} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
dom {} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
addreal is non empty Relation-like [:REAL,REAL:] -defined REAL -valued Function-like V22([:REAL,REAL:]) quasi_total V35() V36() V37() V135( REAL ) V140( REAL ) V141( REAL ) Element of bool [:[:REAL,REAL:],REAL:]
6 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
24 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{0,1} is non empty finite V49() V50() V51() V52() V53() V54() V55() Element of bool NAT
|.0.| is V11() real V31() ext-real Element of REAL
sqrt 1 is V11() real ext-real Element of REAL
K38(1) is V11() real V30() ext-real non positive set
addnat is non empty Relation-like [:NAT,NAT:] -defined NAT -valued INT -valued Function-like V22([:NAT,NAT:]) quasi_total V35() V36() V37() V38() nonnegative-yielding V135( NAT ) V140( NAT ) V141( NAT ) Element of bool [:[:NAT,NAT:],NAT:]
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
SumC ^ R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
SumC is set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r is T-Sequence-like Relation-like NAT -defined SumC -valued Function-like finite V213() set
r | R is T-Sequence-like Relation-like R -defined NAT -defined SumC -valued rng r -valued Function-like finite V213() set
rng r is finite set
Cat is T-Sequence-like Relation-like NAT -defined Function-like finite V213() set
(r | R) ^ Cat is T-Sequence-like Relation-like NAT -defined Function-like finite V213() set
rng Cat is finite set
rng r is finite Element of bool SumC
bool SumC is non empty set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
Sum (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R | (len R) is T-Sequence-like Relation-like len R -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (R | (len R)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | (len R))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
SumC . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(dom SumC) /\ 1 is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
SumC | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
(SumC | 1) . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%(SumC . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(SumC . 0)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
addnat "**" <%(SumC . 0)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (SumC | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * (SumC . 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC is set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> R is Relation-like SumC -defined RAT -valued INT -valued {R} -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() nonnegative-yielding Element of bool [:SumC,{R}:]
{R} is non empty trivial finite V49() V50() V51() V52() V53() V54() V55() 1 -element set
[:SumC,{R}:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,{R}:] is non empty set
rng (SumC --> R) is trivial finite V49() V50() V51() V52() V53() V54() V55() Element of bool {R}
bool {R} is non empty finite V49() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
{r} is non empty trivial finite V49() V50() V51() V52() V53() V54() V55() 1 -element set
R --> r is T-Sequence-like Relation-like R -defined NAT -valued RAT -valued INT -valued {r} -valued Function-like constant V22(R) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:R,{r}:]
[:R,{r}:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() finite nonnegative-yielding set
bool [:R,{r}:] is non empty finite V49() set
(R --> r) | SumC is T-Sequence-like Relation-like SumC -defined R -defined NAT -valued RAT -valued INT -valued {r} -valued rng (R --> r) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:R,{r}:]
rng (R --> r) is trivial finite V50() V51() V52() V53() V54() V55() set
SumC --> r is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued {r} -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:SumC,{r}:]
[:SumC,{r}:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() finite nonnegative-yielding set
bool [:SumC,{r}:] is non empty finite V49() set
SumC /\ R is finite V50() V51() V52() V53() V54() V55() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> 0 is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
rng (SumC --> 0) is trivial finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
{0} is non empty trivial functional finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC --> 0) | R is T-Sequence-like Relation-like R -defined SumC -defined NAT -valued RAT -valued INT -valued rng (SumC --> 0) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() set
rng (SumC --> 0) is trivial finite V50() V51() V52() V53() V54() V55() set
Sum ((SumC --> 0) | R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((SumC --> 0) | R)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC --> 0) | R is T-Sequence-like Relation-like SumC -defined R -defined SumC -defined NAT -valued RAT -valued INT -valued rng (SumC --> 0) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
R --> 0 is T-Sequence-like Relation-like R -defined NAT -valued RAT -valued INT -valued Function-like constant V22(R) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:R,NAT:]
[:R,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:R,NAT:] is non empty set
Sum (R --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 * R is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
0 --> 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding {} -defined 0 -defined NAT -valued RAT -valued INT -valued Function-like one-to-one constant functional V22( {} ) V22( 0 ) quasi_total real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of bool [:0,NAT:]
[:0,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:0,NAT:] is non empty set
1 --> 0 is non empty T-Sequence-like Relation-like 1 -defined NAT -valued RAT -valued INT -valued Function-like constant V22(1) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:1,NAT:]
[:1,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() V38() non finite nonnegative-yielding set
bool [:1,NAT:] is non empty non trivial non finite set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> 0 is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> 0 is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R --> 1 is T-Sequence-like Relation-like non-empty R -defined NAT -valued RAT -valued INT -valued Function-like constant V22(R) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:R,NAT:]
[:R,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:R,NAT:] is non empty set
((SumC --> 0),(R --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (R --> 1) is trivial finite V50() V51() V52() V53() V54() V55() V209() Element of bool RAT
bool RAT is non empty non trivial non finite set
{1} is non empty trivial finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
rng (SumC --> 0) is trivial finite V50() V51() V52() V53() V54() V55() Element of bool RAT
{0} is non empty trivial functional finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
(rng (SumC --> 0)) \/ (rng (R --> 1)) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
rng ((SumC --> 0),(R --> 1)) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
dom ((SumC --> 0),(R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((SumC --> 0),(R --> 1)) | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng ((SumC --> 0),(R --> 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng ((SumC --> 0),(R --> 1)) is finite V50() V51() V52() V53() V54() V55() set
Sum (((SumC --> 0),(R --> 1)) | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (((SumC --> 0),(R --> 1)) | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
(SumC --> 0) | Cat is T-Sequence-like Relation-like SumC -defined Cat -defined SumC -defined NAT -valued RAT -valued INT -valued rng (SumC --> 0) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
rng (SumC --> 0) is trivial finite V50() V51() V52() V53() V54() V55() set
Cat --> 0 is T-Sequence-like Relation-like Cat -defined NAT -valued RAT -valued INT -valued Function-like constant V22(Cat) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:Cat,NAT:]
[:Cat,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:Cat,NAT:] is non empty set
Sum (Cat --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 * Cat is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
Cat - (dom (SumC --> 0)) is V11() real V30() V31() ext-real Element of INT
len ((SumC --> 0),(R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((SumC --> 0),(R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (SumC --> 0)) + (len (R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat - (len (SumC --> 0)) is V11() real V30() V31() ext-real Element of INT
(len (R --> 1)) + (len (SumC --> 0)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((len (R --> 1)) + (len (SumC --> 0))) - (len (SumC --> 0)) is V11() real V30() V31() ext-real Element of INT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R --> 1) | s is T-Sequence-like Relation-like R -defined s -defined R -defined NAT -valued RAT -valued INT -valued rng (R --> 1) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:R,NAT:]
rng (R --> 1) is trivial finite V50() V51() V52() V53() V54() V55() V209() set
s --> 1 is T-Sequence-like Relation-like non-empty s -defined NAT -valued RAT -valued INT -valued Function-like constant V22(s) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:s,NAT:]
[:s,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:s,NAT:] is non empty set
s + (dom (SumC --> 0)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
c₆ | s is T-Sequence-like Relation-like s -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng c₆ is finite V50() V51() V52() V53() V54() V55() set
((SumC --> 0),(c₆ | s)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (s --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC --> 0)) + (Sum (s --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
dom (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool R
bool R is non empty finite V49() set
Cat - SumC is V11() real V30() V31() ext-real Element of INT
R + SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R + SumC) - SumC is V11() real V30() V31() ext-real Element of INT
(Cat - SumC) + (Cat - SumC) is V11() real V30() V31() ext-real Element of INT
SumC + (Cat - SumC) is V11() real V30() V31() ext-real Element of INT
SumC * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
s * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
dom (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(R | SumC) | r is T-Sequence-like Relation-like r -defined NAT -defined NAT -valued RAT -valued rng (R | SumC) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (R | SumC) is finite V50() V51() V52() V53() V54() V55() set
Sum ((R | SumC) | r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((R | SumC) | r)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(dom R) /\ SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
R | r is T-Sequence-like Relation-like r -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (R | SumC) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
rng R is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(SumC,R) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng R is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(rng SumC) \/ (rng R) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng (SumC,R) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom (SumC,R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,R) | r is T-Sequence-like Relation-like r -defined NAT -defined NAT -valued RAT -valued rng (SumC,R) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (SumC,R) is finite V50() V51() V52() V53() V54() V55() set
Sum ((SumC,R) | r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((SumC,R) | r)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC | r is T-Sequence-like Relation-like r -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
r - (dom SumC) is V11() real V30() V31() ext-real Element of INT
SumC | (dom SumC) is T-Sequence-like Relation-like dom SumC -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + (dom SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
(SumC,(R | Cat)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (R | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum SumC) + (Sum (R | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | (len SumC) is T-Sequence-like Relation-like len SumC -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | (len SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | (len SumC))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum (R | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * (Sum SumC)) + (2 * (Sum (R | Cat))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom SumC) + Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | ((2 * SumC) + 1) is T-Sequence-like Relation-like (2 * SumC) + 1 -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
Sum (R | ((2 * SumC) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | ((2 * SumC) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Sum (R | ((2 * SumC) + 1))) - SumC is V11() real V30() V31() ext-real Element of INT
2 * ((Sum (R | ((2 * SumC) + 1))) - SumC) is V11() real V30() V31() ext-real Element of INT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> 1 is T-Sequence-like Relation-like non-empty SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:SumC,NAT:]
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len R) - (2 * (Sum R)) is V11() real V30() V31() ext-real Element of INT
(R,(SumC --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (SumC --> 1) is trivial finite V50() V51() V52() V53() V54() V55() V209() Element of bool RAT
bool RAT is non empty non trivial non finite set
{1} is non empty trivial finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
rng R is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(rng R) \/ (rng (SumC --> 1)) is finite V50() V51() V52() V53() V54() V55() set
rng (R,(SumC --> 1)) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom (R,(SumC --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(R,(SumC --> 1)) | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng (R,(SumC --> 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (R,(SumC --> 1)) is finite V50() V51() V52() V53() V54() V55() set
Sum ((R,(SumC --> 1)) | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((R,(SumC --> 1)) | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
R | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Cat - (dom R) is V11() real V30() V31() ext-real Element of INT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom R) + s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s --> 1 is T-Sequence-like Relation-like non-empty s -defined NAT -valued RAT -valued INT -valued Function-like constant V22(s) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:s,NAT:]
[:s,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:s,NAT:] is non empty set
Sum (s --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
s * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R,(s --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (R,(s --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum R) + s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
len (SumC --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len R) + SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s + (dom R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + (dom R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC --> 1) | s is T-Sequence-like Relation-like SumC -defined s -defined SumC -defined NAT -valued RAT -valued INT -valued rng (SumC --> 1) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:SumC,NAT:]
rng (SumC --> 1) is trivial finite V50() V51() V52() V53() V54() V55() V209() set
(2 * (Sum R)) + Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * (Sum R)) + Cat) - (dom R) is V11() real V30() V31() ext-real Element of INT
(((2 * (Sum R)) + Cat) - (dom R)) + s is V11() real V30() V31() ext-real Element of INT
(((2 * (Sum R)) + Cat) - (dom R)) + SumC is V11() real V30() V31() ext-real Element of INT
SumC - SumC is V11() real V30() V31() ext-real Element of INT
((len R) - (2 * (Sum R))) - SumC is V11() real V30() V31() ext-real Element of INT
Cat - (((len R) - (2 * (Sum R))) - SumC) is V11() real V30() V31() ext-real Element of INT
Cat - 0 is V11() real V30() V31() ext-real non negative Element of INT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC --> 1 is T-Sequence-like Relation-like non-empty SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:SumC,NAT:]
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R --> 0 is T-Sequence-like Relation-like R -defined NAT -valued RAT -valued INT -valued Function-like constant V22(R) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:R,NAT:]
[:R,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:R,NAT:] is non empty set
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R + (len r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R + (len r)) - (2 * (Sum r)) is V11() real V30() V31() ext-real Element of INT
((R --> 0),r) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((R --> 0),r),(SumC --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom (R --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool R
bool R is non empty finite V49() set
len (R --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len ((R --> 0),r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((R --> 0),r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum (R --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
R * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
Sum ((R --> 0),r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 + (Sum r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
Sum (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R | (len R) is T-Sequence-like Relation-like len R -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(dom R) /\ SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
Sum (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((R | SumC),r) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
rng r is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng R is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng r -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng r is finite V50() V51() V52() V53() V54() V55() set
Sum (r | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (r | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len (R | SumC)) + Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R | ((len (R | SumC)) + Cat) is T-Sequence-like Relation-like (len (R | SumC)) + Cat -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((R | SumC),(r | Cat)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (R | ((len (R | SumC)) + Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (R | SumC)) + (Sum (r | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (R | ((len (R | SumC)) + Cat))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + (2 * (Sum (r | Cat))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 --> 1 is non empty T-Sequence-like Relation-like non-empty 1 -defined NAT -valued RAT -valued INT -valued Function-like constant V22(1) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:1,NAT:]
[:1,NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() V38() non finite nonnegative-yielding set
bool [:1,NAT:] is non empty non trivial non finite set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
r | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng r -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng r is finite V50() V51() V52() V53() V54() V55() set
Sum (r | SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (r | SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r | R is T-Sequence-like Relation-like R -defined NAT -defined NAT -valued RAT -valued rng r -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((r | R),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Cat . R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Sum (r | SumC)) - 1 is V11() real V30() V31() ext-real Element of INT
rng Cat is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%0%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%0%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat | R is T-Sequence-like Relation-like R -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Cat is finite V50() V51() V52() V53() V54() V55() set
Sum (Cat | R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Cat | R)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
<%(Cat . R)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((Cat | R),<%(Cat . R)%>) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (Cat | R)) + (Sum <%0%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
<%(Cat . R)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
dom <%(Cat . R)%> is non empty trivial epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal 1 -element Element of bool NAT
rng <%(Cat . R)%> is non empty trivial finite V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
{1} is non empty trivial finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
Cat | R is T-Sequence-like Relation-like R -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Cat is finite V50() V51() V52() V53() V54() V55() set
len Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((Cat | R),<%(Cat . R)%>) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
1 --> 0 is non empty T-Sequence-like Relation-like 1 -defined NAT -valued RAT -valued INT -valued Function-like constant V22(1) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:1,NAT:]
<%0%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
dom <%0%> is non empty trivial epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal 1 -element Element of bool NAT
rng <%0%> is non empty trivial finite V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
{0} is non empty trivial functional finite V49() V50() V51() V52() V53() V54() V55() 1 -element Element of bool NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Cat | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Cat | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat | r is T-Sequence-like Relation-like r -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Cat is finite V50() V51() V52() V53() V54() V55() set
s is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
min* s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Cat | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Cat | c₆)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ - 1 is V11() real V30() V31() ext-real Element of INT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 - 1 is V11() real V30() V31() ext-real Element of INT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(Cat | n) | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined NAT -valued RAT -valued rng (Cat | n) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (Cat | n) is finite V50() V51() V52() V53() V54() V55() set
Cat | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (Cat | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Cat | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Cat | 1) . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%((Cat | 1) . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((Cat | n) | 1) ^ n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),n) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),n),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Cat | (n + 1) is T-Sequence-like Relation-like n + 1 -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((Cat | n),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng ((1 --> 0),n) is non empty finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng (((1 --> 0),n),(1 --> 1)) is non empty finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
len (Cat | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Cat | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (1 --> 0)) + (len n) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len (1 --> 0)) + Fr1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + Fr1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Cat | n) | (1 + Fr1) is T-Sequence-like Relation-like 1 + Fr1 -defined NAT -defined NAT -valued RAT -valued rng (Cat | n) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Cat | (1 + Fr1) is T-Sequence-like Relation-like 1 + Fr1 -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Cat | (1 + Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Cat | (1 + Fr1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat | (Fr1 + 1) is T-Sequence-like Relation-like Fr1 + 1 -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Cat | (Fr1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Cat | (Fr1 + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((1 --> 0),(n | Fr1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (1 --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (1 --> 0)) + (Sum (n | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 * 1 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (SumC | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (SumC | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
r is set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
Sum (SumC | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
Sum (SumC | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is V50() V51() V52() V53() V54() V55() Element of bool NAT
c₆ is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
min* c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n - 1 is V11() real V30() V31() ext-real Element of INT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * n1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | (2 * n1) is T-Sequence-like Relation-like 2 * n1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | (2 * n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
SumC . (2 * n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum (SumC | n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC | n) | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng (SumC | n) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (SumC | n) is finite V50() V51() V52() V53() V54() V55() set
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | (dom SumC) is T-Sequence-like Relation-like dom SumC -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC | n) . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
rng (SumC | n) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
<%((SumC | n) . n)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((SumC | n) | n) ^ <%((SumC | n) . n)%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum <%((SumC | n) . n)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | n)) + (Sum <%((SumC | n) . n)%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum <%((SumC | n) . n)%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * (Sum (SumC | n))) + (2 * (Sum <%((SumC | n) . n)%>)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
dom (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool n
bool n is non empty finite V49() set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC | n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
<%0%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%0%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(SumC | n) | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng (SumC | n) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (SumC | n) is finite V50() V51() V52() V53() V54() V55() set
(SumC | n) . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%((SumC | n) . n)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((SumC | n) | n) ^ <%((SumC | n) . n)%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(dom SumC) /\ n is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(Sum (SumC | n)) + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (SumC | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (SumC | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * r) + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | ((2 * r) + (len R)) is T-Sequence-like Relation-like (2 * r) + (len R) -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
r --> 0 is T-Sequence-like Relation-like r -defined NAT -valued RAT -valued INT -valued Function-like constant V22(r) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:r,NAT:]
[:r,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:r,NAT:] is non empty set
((r --> 0),R) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
r --> 1 is T-Sequence-like Relation-like non-empty r -defined NAT -valued RAT -valued INT -valued Function-like constant V22(r) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:r,NAT:]
(((r --> 0),R),(r --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (r --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
r * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
s is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((r --> 0),R),s) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (((r --> 0),R),s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum ((r --> 0),R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum ((r --> 0),R)) + (Sum s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (r --> 0)) + (Sum R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
((Sum (r --> 0)) + (Sum R)) + (Sum s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
r * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum (SumC | ((2 * r) + (len R))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | ((2 * r) + (len R)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len R) + (2 * r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
min* n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R,s) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((r --> 0),(R,s)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (((r --> 0),R),s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((r --> 0),R),s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (r --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (r --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (R,s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R,s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (r --> 0)) + (len (R,s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (r --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool r
bool r is non empty finite V49() set
len s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len R) + (len s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r + ((len R) + (len s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
SumC | (min* n) is T-Sequence-like Relation-like min* n -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((r --> 0),R),s) | (min* n) is T-Sequence-like Relation-like min* n -defined NAT -defined NAT -valued RAT -valued rng (((r --> 0),R),s) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (((r --> 0),R),s) is finite V50() V51() V52() V53() V54() V55() set
(r --> 0) | (min* n) is T-Sequence-like Relation-like r -defined min* n -defined r -defined NAT -valued RAT -valued INT -valued rng (r --> 0) -valued Function-like constant V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:r,NAT:]
rng (r --> 0) is trivial finite V50() V51() V52() V53() V54() V55() set
(min* n) --> 0 is T-Sequence-like Relation-like min* n -defined NAT -valued RAT -valued INT -valued Function-like constant V22( min* n) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:(min* n),NAT:]
[:(min* n),NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:(min* n),NAT:] is non empty set
Sum ((min* n) --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(min* n) * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
Sum (SumC | (min* n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(min* n) - r is V11() real V30() V31() ext-real Element of INT
r + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 + r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((r --> 0),R) | (min* n) is T-Sequence-like Relation-like min* n -defined NAT -defined NAT -valued RAT -valued rng ((r --> 0),R) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng ((r --> 0),R) is finite V50() V51() V52() V53() V54() V55() set
R | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
((r --> 0),(R | n1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom ((r --> 0),R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(len (r --> 0)) + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum (SumC | (min* n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (R | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (r --> 0)) + (Sum (R | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(min* n) - (r + (len R)) is V11() real V30() V31() ext-real Element of INT
Sum (SumC | (min* n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | (min* n))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | Catal is T-Sequence-like Relation-like Catal -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | Catal) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (SumC | Catal)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((r --> 0),R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(len (r --> 0)) + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom ((r --> 0),R)) + Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined NAT -valued RAT -valued rng s -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng s is finite V50() V51() V52() V53() V54() V55() set
(((r --> 0),R),(s | Fr1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (s | Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum ((r --> 0),R)) + (Sum (s | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
((2 * r) + (len R)) - (r + (len R)) is V11() real V30() V31() ext-real Element of INT
Fr1 --> 1 is T-Sequence-like Relation-like non-empty Fr1 -defined NAT -valued RAT -valued INT -valued Function-like constant V22(Fr1) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:Fr1,NAT:]
[:Fr1,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:Fr1,NAT:] is non empty set
Fr1 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r + (len R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%0%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (SumC | b₁)) = b₁ & not b₁ <= 0 ) } is set
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((SumC | 1),r) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,r) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng r is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
dom (SumC | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
len (SumC | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC | 1) . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%((SumC | 1) . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
SumC . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined NAT -valued RAT -valued rng r -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng r is finite V50() V51() V52() V53() V54() V55() set
Sum (r | Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (r | Cat)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | (1 + s) is T-Sequence-like Relation-like 1 + s -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
r | s is T-Sequence-like Relation-like s -defined NAT -defined NAT -valued RAT -valued rng r -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((SumC | 1),(r | s)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | (1 + s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
<%(SumC . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(SumC . 0)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (r | s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum <%(SumC . 0)%>) + (Sum (r | s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum (r | s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
0 + (Sum (r | s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,SumC) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum ((<%0%>,SumC) | b₁)) = b₁ & not b₁ <= 0 ) } is set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%(R . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Cat is set
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(<%0%>,SumC) | s is T-Sequence-like Relation-like s -defined NAT -defined NAT -valued RAT -valued rng (<%0%>,SumC) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (<%0%>,SumC) is non empty finite V50() V51() V52() V53() V54() V55() set
Sum ((<%0%>,SumC) | s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((<%0%>,SumC) | s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s - 1 is V11() real V30() V31() ext-real Element of INT
dom <%0%> is non empty trivial epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal 1 -element Element of bool NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom <%0%>) + c₆ is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
(<%0%>,(SumC | c₆)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum <%0%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (SumC | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum <%0%>) + (Sum (SumC | c₆)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (R | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (R | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R | (2 * SumC) is T-Sequence-like Relation-like 2 * SumC -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng R is finite V50() V51() V52() V53() V54() V55() set
rng (R | (2 * SumC)) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
dom (R | (2 * SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(R | (2 * SumC)) | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng (R | (2 * SumC)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (R | (2 * SumC)) is finite V50() V51() V52() V53() V54() V55() set
Sum ((R | (2 * SumC)) | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((R | (2 * SumC)) | c₆)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R | (2 * SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (2 * SumC)
bool (2 * SumC) is non empty finite V49() set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R | (2 * SumC)) | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng (R | (2 * SumC)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
R | n is T-Sequence-like Relation-like n -defined NAT -defined NAT -valued RAT -valued rng R -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
s is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
{0,1} ^omega is non empty functional set
bool ({0,1} ^omega) is non empty set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
bool [:NAT,NAT:] is non empty non trivial non finite set
r is set
Cat is set
s is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
rng s is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Cat is functional Element of bool ({0,1} ^omega)
s is set
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
rng c₆ is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
[:(dom c₆),(rng c₆):] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() finite nonnegative-yielding set
r is functional Element of bool ({0,1} ^omega)
Cat is functional Element of bool ({0,1} ^omega)
s is set
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,R) is functional Element of bool ({0,1} ^omega)
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,R) is functional Element of bool ({0,1} ^omega)
Choose (SumC,R,1,0) is functional finite Element of bool (Funcs (SumC,{1,0}))
{1,0} is non empty finite V49() V50() V51() V52() V53() V54() V55() set
Funcs (SumC,{1,0}) is non empty functional finite FUNCTION_DOMAIN of SumC,{1,0}
bool (Funcs (SumC,{1,0})) is non empty finite V49() set
r is set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
rng Cat is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,R) is functional Element of bool ({0,1} ^omega)
Choose (SumC,R,1,0) is functional finite Element of bool (Funcs (SumC,{1,0}))
{1,0} is non empty finite V49() V50() V51() V52() V53() V54() V55() set
Funcs (SumC,{1,0}) is non empty functional finite FUNCTION_DOMAIN of SumC,{1,0}
bool (Funcs (SumC,{1,0})) is non empty finite V49() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,R) is functional finite Element of bool ({0,1} ^omega)
2 * R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R --> 1 is T-Sequence-like Relation-like non-empty R -defined NAT -valued RAT -valued INT -valued Function-like constant V22(R) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:R,NAT:]
[:R,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:R,NAT:] is non empty set
R + R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC - R is V11() real V30() V31() ext-real Element of INT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat --> 0 is T-Sequence-like Relation-like Cat -defined NAT -valued RAT -valued INT -valued Function-like constant V22(Cat) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:Cat,NAT:]
[:Cat,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:Cat,NAT:] is non empty set
(2 * R) - R is V11() real V30() V31() ext-real Element of INT
((Cat --> 0),(R --> 1)) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom ((Cat --> 0),(R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len (Cat --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Cat --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (Cat --> 0)) + (len (R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Cat --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool Cat
bool Cat is non empty finite V49() set
Cat + R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum ((Cat --> 0),(R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (Cat --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (R --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (Cat --> 0)) + (Sum (R --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 * Cat is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
1 * R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat | SumC is T-Sequence-like Relation-like SumC -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Cat is finite V50() V51() V52() V53() V54() V55() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,0) is functional finite Element of bool ({0,1} ^omega)
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
SumC --> 0 is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
{(SumC --> 0)} is non empty trivial functional finite V49() 1 -element Element of bool (bool [:SumC,NAT:])
bool (bool [:SumC,NAT:]) is non empty set
r is set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
len Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
dom (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool SumC
bool SumC is non empty finite V49() set
Sum (SumC --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
SumC * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
r is set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,0) is functional finite Element of bool ({0,1} ^omega)
card (SumC,0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
[:SumC,NAT:] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() nonnegative-yielding set
bool [:SumC,NAT:] is non empty set
SumC --> 0 is T-Sequence-like Relation-like SumC -defined NAT -valued RAT -valued INT -valued Function-like constant V22(SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Function-yielding V137() V213() Element of bool [:SumC,NAT:]
{(SumC --> 0)} is non empty trivial functional finite V49() 1 -element Element of bool (bool [:SumC,NAT:])
bool (bool [:SumC,NAT:]) is non empty set
SumC is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
{0,R} is non empty finite V49() V50() V51() V52() V53() V54() V55() set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - (SumC . Cat) is V11() real V30() V31() ext-real Element of INT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - (SumC . s) is V11() real V30() V31() ext-real Element of INT
Cat is T-Sequence-like Relation-like NAT -defined {0,R} -valued Function-like finite V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng Cat is finite V49() V50() V51() V52() V53() V54() V55() Element of bool {0,R}
bool {0,R} is non empty finite V49() set
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{0,r} is non empty finite V49() V50() V51() V52() V53() V54() V55() Element of bool NAT
s is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
Sum (SumC | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
s | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng s -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng s is finite V50() V51() V52() V53() V54() V55() set
Sum (s | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | c₆)) + (Sum (s | c₆)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
R * c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | (c₆ + 1) is T-Sequence-like Relation-like c₆ + 1 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
s | (c₆ + 1) is T-Sequence-like Relation-like c₆ + 1 -defined NAT -defined NAT -valued RAT -valued rng s -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (s | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | (c₆ + 1))) + (Sum (s | (c₆ + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
R * (c₆ + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC | (c₆ + 1)) | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng (SumC | (c₆ + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (SumC | (c₆ + 1)) is finite V50() V51() V52() V53() V54() V55() set
(s | (c₆ + 1)) | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng (s | (c₆ + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (s | (c₆ + 1)) is finite V50() V51() V52() V53() V54() V55() set
len (s | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (s | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(s | (c₆ + 1)) . c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%((s | (c₆ + 1)) . c₆)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((s | (c₆ + 1)) | c₆) ^ <%((s | (c₆ + 1)) . c₆)%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom (SumC | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (c₆ + 1)
bool (c₆ + 1) is non empty finite V49() set
(SumC | (c₆ + 1)) . c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (SumC | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (SumC | (c₆ + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
<%((SumC | (c₆ + 1)) . c₆)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((SumC | (c₆ + 1)) | c₆) ^ <%((SumC | (c₆ + 1)) . c₆)%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
<%(SumC . c₆)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(SumC . c₆)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | c₆)) + (Sum <%(SumC . c₆)%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | c₆)) + (SumC . c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s . c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - (SumC . c₆) is V11() real V30() V31() ext-real Element of INT
<%(s . c₆)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(s . c₆)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (s | c₆)) + (Sum <%(s . c₆)%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (s | c₆)) + (R - (SumC . c₆)) is V11() real V30() V31() ext-real Element of INT
len s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
rng s is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
SumC | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
rng SumC is finite V50() V51() V52() V53() V54() V55() set
Sum (SumC | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
s | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined NAT -valued RAT -valued rng s -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
rng s is finite V50() V51() V52() V53() V54() V55() set
Sum (s | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
(Sum (SumC | 0)) + (Sum (s | 0)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
R * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng SumC -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (SumC | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
s | c₆ is T-Sequence-like Relation-like c₆ -defined NAT -defined NAT -valued RAT -valued rng s -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (s | c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (SumC | c₆)) + (Sum (s | c₆)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
R * c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - (SumC . n) is V11() real V30() V31() ext-real Element of INT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - SumC is V11() real V30() V31() ext-real Element of INT
SumC ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC !) * (r !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC !) * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
R ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
0 * ((SumC !) * (r !)) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
(R !) / ((SumC !) * (r !)) is V11() real ext-real non negative Element of COMPLEX
{1,0} is non empty finite V49() V50() V51() V52() V53() V54() V55() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Funcs (R,{1,0}) is non empty functional finite FUNCTION_DOMAIN of R,{1,0}
Choose (R,(SumC + 1),1,0) is functional finite Element of bool (Funcs (R,{1,0}))
bool (Funcs (R,{1,0})) is non empty finite V49() set
(R,(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
(Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)) is functional finite Element of bool (Funcs (R,{1,0}))
card ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Choose (R,SumC,1,0) is functional finite Element of bool (Funcs (R,{1,0}))
card (Choose (R,SumC,1,0)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
card R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card R) choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is non empty finite set
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng n is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (n | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (n | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | (2 * n) is T-Sequence-like Relation-like 2 * n -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | (2 * n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n . (2 * n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | ((2 * n) + 1) is T-Sequence-like Relation-like (2 * n) + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((n | ((2 * n) + 1)),Fr1) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (n | ((2 * n) + 1)) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
len (n | ((2 * n) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n | ((2 * n) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
rng Catal is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(Catal,Fr1) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
CatalR is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len Catal) + (len Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng Fr1 is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(rng Catal) \/ (rng Fr1) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng CatalR is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom (n | ((2 * n) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool ((2 * n) + 1)
bool ((2 * n) + 1) is non empty finite V49() set
(n | ((2 * n) + 1)) | (dom (n | ((2 * n) + 1))) is T-Sequence-like Relation-like dom (n | ((2 * n) + 1)) -defined NAT -defined NAT -valued RAT -valued rng (n | ((2 * n) + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (n | ((2 * n) + 1)) is finite V50() V51() V52() V53() V54() V55() set
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Catal | (dom Catal) is T-Sequence-like Relation-like dom Catal -defined NAT -defined NAT -valued RAT -valued rng Catal -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Catal is finite V50() V51() V52() V53() V54() V55() set
Sum (n | ((2 * n) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n | ((2 * n) + 1))) + (Sum Catal) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
1 * (len (n | ((2 * n) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n | ((2 * n) + 1)) | (2 * n) is T-Sequence-like Relation-like 2 * n -defined NAT -defined NAT -valued RAT -valued rng (n | ((2 * n) + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(n | ((2 * n) + 1)) . (2 * n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%((n | ((2 * n) + 1)) . (2 * n))%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((n | ((2 * n) + 1)) | (2 * n)) ^ <%((n | ((2 * n) + 1)) . (2 * n))%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
<%(n . (2 * n))%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(n . (2 * n))%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n | (2 * n))) + (Sum <%(n . (2 * n))%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n | ((2 * n) + 1))) + (Sum Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum Catal) + (Sum Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(SumC + 1) - ((2 * n) + 1) is V11() real V30() V31() ext-real Element of INT
((SumC + 1) - ((2 * n) + 1)) + (2 * n) is V11() real V30() V31() ext-real Element of INT
Sum (Catal,Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Fr2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (Fr2 | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (Fr2 | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 | ((2 * k) + 1) is T-Sequence-like Relation-like (2 * k) + 1 -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Fr2 is finite V50() V51() V52() V53() V54() V55() set
len (Fr2 | ((2 * k) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Fr2 | ((2 * k) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((Fr2 | ((2 * k) + 1)),Fr1) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal . n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 . n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (Fr2 . n2) is V11() real V30() V31() ext-real Element of INT
(n | ((2 * n) + 1)) . n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - ((n | ((2 * n) + 1)) . n2) is V11() real V30() V31() ext-real Element of INT
[:((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))),r:] is Relation-like finite set
bool [:((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))),r:] is non empty finite V49() set
c₆ is Relation-like (Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)) -defined r -valued Function-like V22((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) quasi_total finite Element of bool [:((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))),r:]
rng c₆ is finite Element of bool r
bool r is non empty finite V49() set
n is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng n is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not b₁ <= 2 * (Sum (n | b₁)) } is set
n | R is T-Sequence-like Relation-like R -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | R)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is set
Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | Catal is T-Sequence-like Relation-like Catal -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | Catal) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Catal)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
min* Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(min* Fr1) - 1 is V11() real V30() V31() ext-real Element of INT
Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | Fr2 is T-Sequence-like Relation-like Fr2 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Fr2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
CatalR + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | (min* Fr1) is T-Sequence-like Relation-like min* Fr1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | (min* Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | (min* Fr1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | Fr2 is T-Sequence-like Relation-like Fr2 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Fr2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n | (min* Fr1)) | CatalR is T-Sequence-like Relation-like CatalR -defined NAT -defined NAT -valued RAT -valued rng (n | (min* Fr1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (n | (min* Fr1)) is finite V50() V51() V52() V53() V54() V55() set
n | CatalR is T-Sequence-like Relation-like CatalR -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom (n | (min* Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (min* Fr1)
bool (min* Fr1) is non empty finite V49() set
(n | (min* Fr1)) . CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n . CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum (n | CatalR) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | CatalR)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%(n . CatalR)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(n . CatalR)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
CatalR + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (n . CatalR) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * (Sum (n | CatalR))) + (2 * (n . CatalR)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * Fr2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | ((2 * Fr2) + 1) is T-Sequence-like Relation-like (2 * Fr2) + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | ((2 * Fr2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
len (n | (min* Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n | (min* Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
<%((n | (min* Fr1)) . CatalR)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
((n | (min* Fr1)) | CatalR) ^ <%((n | (min* Fr1)) . CatalR)%> is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(Sum (n | CatalR)) + (Sum <%(n . CatalR)%>) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * Catal) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | ((2 * Catal) + 1) is T-Sequence-like Relation-like (2 * Catal) + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | ((2 * Catal) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * Catal) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | ((2 * Catal) + 1) is T-Sequence-like Relation-like (2 * Catal) + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n | ((2 * Catal) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Fr2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((n | ((2 * Catal) + 1)),Fr2) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (n | ((2 * Catal) + 1)) is finite V50() V51() V52() V53() V54() V55() Element of bool RAT
bool RAT is non empty non trivial non finite set
len (n | ((2 * Catal) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n | ((2 * Catal) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
k is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
rng k is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(k,Fr2) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom (k,Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (n | ((2 * Catal) + 1))) + (len Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal + (Sum Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n | ((2 * Catal) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool ((2 * Catal) + 1)
bool ((2 * Catal) + 1) is non empty finite V49() set
(n | ((2 * Catal) + 1)) | (dom (n | ((2 * Catal) + 1))) is T-Sequence-like Relation-like dom (n | ((2 * Catal) + 1)) -defined NAT -defined NAT -valued RAT -valued rng (n | ((2 * Catal) + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (n | ((2 * Catal) + 1)) is finite V50() V51() V52() V53() V54() V55() set
dom k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
k | (dom k) is T-Sequence-like Relation-like dom k -defined NAT -defined NAT -valued RAT -valued rng k -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng k is finite V50() V51() V52() V53() V54() V55() set
Sum k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n | ((2 * Catal) + 1))) + (Sum k) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
1 * (len (n | ((2 * Catal) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
rng Fr2 is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(rng k) \/ (rng Fr2) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
rng (k,Fr2) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(k,Fr2) | ((2 * Catal) + 1) is T-Sequence-like Relation-like (2 * Catal) + 1 -defined NAT -defined NAT -valued RAT -valued rng (k,Fr2) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (k,Fr2) is finite V50() V51() V52() V53() V54() V55() set
((2 * Catal) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum k) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum ((k,Fr2) | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum ((k,Fr2) | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * n2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(k,Fr2) | (2 * n2) is T-Sequence-like Relation-like 2 * n2 -defined NAT -defined NAT -valued RAT -valued rng (k,Fr2) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum ((k,Fr2) | (2 * n2)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(k,Fr2) . (2 * n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len ((n | ((2 * Catal) + 1)),Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((n | ((2 * Catal) + 1)),Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(k,Fr2) | ((2 * n2) + 1) is T-Sequence-like Relation-like (2 * n2) + 1 -defined NAT -defined NAT -valued RAT -valued rng (k,Fr2) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (k,Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum k) + (Sum Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ . (k,Fr2) is set
len ((k,Fr2) | ((2 * n2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((k,Fr2) | ((2 * n2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2M is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
m is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(2M,m) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(((k,Fr2) | ((2 * n2) + 1)),m) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len 2M) + (len m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (2M,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (2M,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
M1 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
(n | ((2 * Catal) + 1)) | ((2 * n2) + 1) is T-Sequence-like Relation-like (2 * n2) + 1 -defined NAT -defined NAT -valued RAT -valued rng (n | ((2 * Catal) + 1)) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n | ((2 * n2) + 1) is T-Sequence-like Relation-like (2 * n2) + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum ((n | ((2 * Catal) + 1)) | ((2 * n2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
k | ((2 * n2) + 1) is T-Sequence-like Relation-like (2 * n2) + 1 -defined NAT -defined NAT -valued RAT -valued rng k -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (k | ((2 * n2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum ((n | ((2 * Catal) + 1)) | ((2 * n2) + 1))) + (Sum (k | ((2 * n2) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
((2 * n2) + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum (k | ((2 * n2) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * ((2 * n2) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum (n | ((2 * n2) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | ((2 * n2) + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * ((2 * n2) + 1)) - (2 * (Sum (n | ((2 * n2) + 1)))) is V11() real V30() V31() ext-real Element of INT
((2 * n2) + 1) - (2 * (Sum (n | ((2 * n2) + 1)))) is V11() real V30() V31() ext-real Element of INT
((2 * n2) + 1) + (((2 * n2) + 1) - (2 * (Sum (n | ((2 * n2) + 1))))) is V11() real V30() V31() ext-real Element of INT
(2 * (Sum (n | ((2 * n2) + 1)))) + (((2 * n2) + 1) - (2 * (Sum (n | ((2 * n2) + 1))))) is V11() real V30() V31() ext-real Element of INT
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(k,Fr2) | Fr is T-Sequence-like Relation-like Fr -defined NAT -defined NAT -valued RAT -valued rng (k,Fr2) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum ((k,Fr2) | Fr) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum ((k,Fr2) | Fr)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (k,Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (k,Fr2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
dom 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
2M . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(k,Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - ((k,Fr2) . Fr) is V11() real V30() V31() ext-real Element of INT
k . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n | ((2 * Catal) + 1)) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - ((n | ((2 * Catal) + 1)) . Fr) is V11() real V30() V31() ext-real Element of INT
((n | ((2 * Catal) + 1)),Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((n | ((2 * Catal) + 1)),Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr - (len k) is V11() real V30() V31() ext-real Element of INT
Fr2 . (Fr - (len k)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr - (len 2M) is V11() real V30() V31() ext-real Element of INT
m . (Fr - (len 2M)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(k,Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((n | ((2 * Catal) + 1)),Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((n | ((2 * Catal) + 1)),Fr2) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom c₆ is functional finite Element of bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)))
bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) is non empty finite V49() set
n is set
dom c₆ is finite set
c₆ . n is set
n is set
c₆ . n is set
dom c₆ is functional finite Element of bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)))
bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) is non empty finite V49() set
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng n1 is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Sum n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (n1 | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (n1 | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * Fr1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 | (2 * Fr1) is T-Sequence-like Relation-like 2 * Fr1 -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n1 is finite V50() V51() V52() V53() V54() V55() set
Sum (n1 | (2 * Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 . (2 * Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng Catal is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Sum Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (Catal | b₁)) <= b₁ } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : not 2 * (Sum (Catal | b₁)) <= b₁ } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * CatalR) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal | (2 * CatalR) is T-Sequence-like Relation-like 2 * CatalR -defined NAT -defined NAT -valued RAT -valued rng Catal -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Catal is finite V50() V51() V52() V53() V54() V55() set
Sum (Catal | (2 * CatalR)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal . (2 * CatalR) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal | ((2 * CatalR) + 1) is T-Sequence-like Relation-like (2 * CatalR) + 1 -defined NAT -defined NAT -valued RAT -valued rng Catal -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (Catal | ((2 * CatalR) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Catal | ((2 * CatalR) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
e2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(e2,n2) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((Catal | ((2 * CatalR) + 1)),n2) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (Catal | ((2 * CatalR) + 1))) + (len n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (e2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (e2,n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 | ((2 * Fr1) + 1) is T-Sequence-like Relation-like (2 * Fr1) + 1 -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (n1 | ((2 * Fr1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n1 | ((2 * Fr1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2M is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
m is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(2M,m) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((n1 | ((2 * Fr1) + 1)),m) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (n1 | ((2 * Fr1) + 1))) + (len m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (2M,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (2M,m) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2M . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
e2 . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(e2,n2) . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (n1 . M1) is V11() real V30() V31() ext-real Element of INT
1 - (Catal . M1) is V11() real V30() V31() ext-real Element of INT
(e2,n2) . M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
M1 - (len (n1 | ((2 * Fr1) + 1))) is V11() real V30() V31() ext-real Element of INT
n2 . (M1 - (len (n1 | ((2 * Fr1) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
m . (M1 - (len (n1 | ((2 * Fr1) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(e2,n2) | (len e2) is T-Sequence-like Relation-like len e2 -defined NAT -defined NAT -valued RAT -valued rng (e2,n2) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (e2,n2) is finite V50() V51() V52() V53() V54() V55() set
2M | (len e2) is T-Sequence-like Relation-like len e2 -defined NAT -defined NAT -valued RAT -valued rng 2M -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng 2M is finite V50() V51() V52() V53() V54() V55() set
n1 | (len (Catal | ((2 * CatalR) + 1))) is T-Sequence-like Relation-like len (Catal | ((2 * CatalR) + 1)) -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Catal | ((2 * CatalR) + 1)) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n1 | (len (Catal | ((2 * CatalR) + 1)))) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom Catal) /\ (len e2) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(dom n1) /\ (len e2) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
n1 . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2M . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (n1 . Fr) is V11() real V30() V31() ext-real Element of INT
dom 2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(dom 2M) /\ (len e2) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(2M | (len e2)) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
e2 . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (Catal . Fr) is V11() real V30() V31() ext-real Element of INT
Fr2 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
len (n1 | (len (Catal | ((2 * CatalR) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n1 | (len (Catal | ((2 * CatalR) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal | Fr is T-Sequence-like Relation-like Fr -defined NAT -defined NAT -valued RAT -valued rng Catal -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Catal | Fr) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Catal | Fr)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2M,m) | (len 2M) is T-Sequence-like Relation-like len 2M -defined NAT -defined NAT -valued RAT -valued rng (2M,m) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng (2M,m) is finite V50() V51() V52() V53() V54() V55() set
e2 | (len 2M) is T-Sequence-like Relation-like len 2M -defined NAT -defined NAT -valued RAT -valued rng e2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng e2 is finite V50() V51() V52() V53() V54() V55() set
Catal | (len (n1 | ((2 * Fr1) + 1))) is T-Sequence-like Relation-like len (n1 | ((2 * Fr1) + 1)) -defined NAT -defined NAT -valued RAT -valued rng Catal -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(n1 | ((2 * Fr1) + 1)) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Catal | (len (n1 | ((2 * Fr1) + 1)))) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(dom n1) /\ (len 2M) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(dom Catal) /\ (len 2M) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
Catal . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
e2 . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (Catal . Fr) is V11() real V30() V31() ext-real Element of INT
dom e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(dom e2) /\ (len 2M) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
(e2 | (len 2M)) . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2M . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 . Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 - (n1 . Fr) is V11() real V30() V31() ext-real Element of INT
n1 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
len (Catal | (len (n1 | ((2 * Fr1) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Catal | (len (n1 | ((2 * Fr1) + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Fr2 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 | Fr is T-Sequence-like Relation-like Fr -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n1 | Fr) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n1 | Fr)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom c₆ is functional finite Element of bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)))
bool ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) is non empty finite V49() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(R,(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card (R,(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R choose (SumC + 1)) - (R choose SumC) is V11() real V30() V31() ext-real Element of INT
Choose (R,(SumC + 1),1,0) is functional finite Element of bool (Funcs (R,{1,0}))
Funcs (R,{1,0}) is non empty functional finite FUNCTION_DOMAIN of R,{1,0}
bool (Funcs (R,{1,0})) is non empty finite V49() set
Choose (R,SumC,1,0) is functional finite Element of bool (Funcs (R,{1,0}))
card (Choose (R,(SumC + 1),1,0)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
card R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card R) choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)) is functional finite Element of bool (Funcs (R,{1,0}))
card ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card (Choose (R,(SumC + 1),1,0))) - (card (R,(SumC + 1))) is V11() real V30() V31() ext-real Element of INT
(card (Choose (R,(SumC + 1),1,0))) - (card ((Choose (R,(SumC + 1),1,0)) \ (R,(SumC + 1)))) is V11() real V30() V31() ext-real Element of INT
card (Choose (R,SumC,1,0)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card (Choose (R,(SumC + 1),1,0))) - (card (Choose (R,SumC,1,0))) is V11() real V30() V31() ext-real Element of INT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(R,SumC) is functional finite Element of bool ({0,1} ^omega)
card (R,SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R + 1) - (2 * SumC) is V11() real V30() V31() ext-real Element of INT
(R + 1) - SumC is V11() real V30() V31() ext-real Element of INT
((R + 1) - (2 * SumC)) / ((R + 1) - SumC) is V11() real ext-real Element of COMPLEX
R choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((R + 1) - (2 * SumC)) / ((R + 1) - SumC)) * (R choose SumC) is V11() real ext-real Element of REAL
SumC + SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - SumC is V11() real V30() V31() ext-real Element of INT
SumC - 1 is V11() real V30() V31() ext-real Element of INT
R ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r + 1) ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC !) * (r !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R !) / ((SumC !) * (r !)) is V11() real ext-real non negative Element of COMPLEX
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Cat + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Cat !) * ((r + 1) !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 / ((Cat !) * ((r + 1) !)) is V11() real ext-real non negative Element of COMPLEX
(Cat + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((Cat !) * ((r + 1) !)) * (Cat + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((Cat + 1) * 1) / (((Cat !) * ((r + 1) !)) * (Cat + 1)) is V11() real ext-real non negative Element of COMPLEX
(Cat !) * (Cat + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((r + 1) !) * ((Cat !) * (Cat + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC / (((r + 1) !) * ((Cat !) * (Cat + 1))) is V11() real ext-real non negative Element of COMPLEX
(Cat + 1) ! is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((r + 1) !) * ((Cat + 1) !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC / (((r + 1) !) * ((Cat + 1) !)) is V11() real ext-real non negative Element of COMPLEX
- SumC is V11() real V30() V31() ext-real non positive Element of INT
((r + 1) !) * (SumC !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(- SumC) / (((r + 1) !) * (SumC !)) is V11() real ext-real non positive Element of COMPLEX
- ((- SumC) / (((r + 1) !) * (SumC !))) is V11() real ext-real non negative Element of COMPLEX
1 / ((SumC !) * (r !)) is V11() real ext-real non negative Element of COMPLEX
(r + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC !) * (r !)) * (r + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((r + 1) * 1) / (((SumC !) * (r !)) * (r + 1)) is V11() real ext-real non negative Element of COMPLEX
(r !) * (r + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC !) * ((r !) * (r + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r + 1) / ((SumC !) * ((r !) * (r + 1))) is V11() real ext-real non negative Element of COMPLEX
(SumC !) * ((r + 1) !) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r + 1) / ((SumC !) * ((r + 1) !)) is V11() real ext-real non negative Element of COMPLEX
(1 / ((SumC !) * (r !))) - (1 / ((Cat !) * ((r + 1) !))) is V11() real ext-real Element of COMPLEX
(- SumC) / ((SumC !) * ((r + 1) !)) is V11() real ext-real non positive Element of COMPLEX
((r + 1) / ((SumC !) * ((r + 1) !))) + ((- SumC) / ((SumC !) * ((r + 1) !))) is V11() real ext-real Element of COMPLEX
(r + 1) + (- SumC) is V11() real V30() V31() ext-real Element of INT
((r + 1) + (- SumC)) / ((SumC !) * ((r + 1) !)) is V11() real ext-real Element of COMPLEX
((R + 1) - (2 * SumC)) / ((SumC !) * ((r !) * (r + 1))) is V11() real ext-real Element of COMPLEX
1 * ((R + 1) - (2 * SumC)) is V11() real V30() V31() ext-real Element of INT
(1 * ((R + 1) - (2 * SumC))) / (((SumC !) * (r !)) * (r + 1)) is V11() real ext-real Element of COMPLEX
((R + 1) - (2 * SumC)) / (r + 1) is V11() real ext-real Element of COMPLEX
(1 / ((SumC !) * (r !))) * (((R + 1) - (2 * SumC)) / (r + 1)) is V11() real ext-real Element of COMPLEX
1 + Cat is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(1 + Cat) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + ((1 + Cat) + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - Cat is V11() real V30() V31() ext-real Element of INT
R choose Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R !) / ((Cat !) * ((r + 1) !)) is V11() real ext-real non negative Element of COMPLEX
((R !) / ((SumC !) * (r !))) - ((R !) / ((Cat !) * ((r + 1) !))) is V11() real ext-real Element of COMPLEX
(R !) * (1 / ((SumC !) * (r !))) is V11() real ext-real non negative Element of REAL
((R !) * (1 / ((SumC !) * (r !)))) - ((R !) / ((Cat !) * ((r + 1) !))) is V11() real ext-real Element of REAL
(R !) * (1 / ((Cat !) * ((r + 1) !))) is V11() real ext-real non negative Element of REAL
((R !) * (1 / ((SumC !) * (r !)))) - ((R !) * (1 / ((Cat !) * ((r + 1) !)))) is V11() real ext-real Element of REAL
(R !) * ((1 / ((SumC !) * (r !))) - (1 / ((Cat !) * ((r + 1) !)))) is V11() real ext-real Element of REAL
(R !) * ((1 / ((SumC !) * (r !))) * (((R + 1) - (2 * SumC)) / (r + 1))) is V11() real ext-real Element of REAL
((R !) * (1 / ((SumC !) * (r !)))) * (((R + 1) - (2 * SumC)) / (r + 1)) is V11() real ext-real Element of REAL
(R !) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((R !) * 1) / ((SumC !) * (r !)) is V11() real ext-real non negative Element of COMPLEX
(((R !) * 1) / ((SumC !) * (r !))) * (((R + 1) - (2 * SumC)) / (r + 1)) is V11() real ext-real Element of COMPLEX
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 + SumC),1) is functional finite Element of bool ({0,1} ^omega)
card ((2 + SumC),1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 + SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 + SumC) + 1) - (2 * 1) is V11() real V30() V31() ext-real Element of INT
((2 + SumC) + 1) - 1 is V11() real V30() V31() ext-real Element of INT
(((2 + SumC) + 1) - (2 * 1)) / (((2 + SumC) + 1) - 1) is V11() real ext-real Element of COMPLEX
(2 + SumC) choose 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 + SumC) + 1) - (2 * 1)) / (((2 + SumC) + 1) - 1)) * ((2 + SumC) choose 1) is V11() real ext-real Element of REAL
(SumC + 1) / (2 + SumC) is V11() real ext-real non negative Element of COMPLEX
((SumC + 1) / (2 + SumC)) * (2 + SumC) is V11() real ext-real non negative Element of REAL
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
4 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((4 + SumC),2) is functional finite Element of bool ({0,1} ^omega)
card ((4 + SumC),2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC + 1) * (SumC + 4) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) * (SumC + 4)) / 2 is V11() real ext-real non negative Element of COMPLEX
(4 + SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((4 + SumC) + 1) - (2 * 2) is V11() real V30() V31() ext-real Element of INT
((4 + SumC) + 1) - 2 is V11() real V30() V31() ext-real Element of INT
(((4 + SumC) + 1) - (2 * 2)) / (((4 + SumC) + 1) - 2) is V11() real ext-real Element of COMPLEX
(4 + SumC) choose 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((4 + SumC) + 1) - (2 * 2)) / (((4 + SumC) + 1) - 2)) * ((4 + SumC) choose 2) is V11() real ext-real Element of REAL
SumC + 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC + 1) / (SumC + 3) is V11() real ext-real non negative Element of COMPLEX
(4 + SumC) - 1 is V11() real V30() V31() ext-real Element of INT
(4 + SumC) * ((4 + SumC) - 1) is V11() real V30() V31() ext-real Element of INT
((4 + SumC) * ((4 + SumC) - 1)) / 2 is V11() real ext-real Element of COMPLEX
((SumC + 1) / (SumC + 3)) * (((4 + SumC) * ((4 + SumC) - 1)) / 2) is V11() real ext-real Element of COMPLEX
3 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) / (SumC + 3)) * (3 + SumC) is V11() real ext-real non negative Element of REAL
(((SumC + 1) / (SumC + 3)) * (3 + SumC)) * (4 + SumC) is V11() real ext-real non negative Element of REAL
((((SumC + 1) / (SumC + 3)) * (3 + SumC)) * (4 + SumC)) / 2 is V11() real ext-real non negative Element of COMPLEX
(SumC + 1) * (4 + SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) * (4 + SumC)) / 2 is V11() real ext-real non negative Element of COMPLEX
5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
6 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((6 + SumC),3) is functional finite Element of bool ({0,1} ^omega)
card ((6 + SumC),3) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC + 1) * (SumC + 5) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 6 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) * (SumC + 5)) * (SumC + 6) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((SumC + 1) * (SumC + 5)) * (SumC + 6)) / 6 is V11() real ext-real non negative Element of COMPLEX
(6 + SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * 3 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((6 + SumC) + 1) - (2 * 3) is V11() real V30() V31() ext-real Element of INT
((6 + SumC) + 1) - 3 is V11() real V30() V31() ext-real Element of INT
(((6 + SumC) + 1) - (2 * 3)) / (((6 + SumC) + 1) - 3) is V11() real ext-real Element of COMPLEX
(6 + SumC) choose 3 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((6 + SumC) + 1) - (2 * 3)) / (((6 + SumC) + 1) - 3)) * ((6 + SumC) choose 3) is V11() real ext-real Element of REAL
SumC + 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC + 1) / (SumC + 4) is V11() real ext-real non negative Element of COMPLEX
(6 + SumC) - 1 is V11() real V30() V31() ext-real Element of INT
(6 + SumC) * ((6 + SumC) - 1) is V11() real V30() V31() ext-real Element of INT
(6 + SumC) - 2 is V11() real V30() V31() ext-real Element of INT
((6 + SumC) * ((6 + SumC) - 1)) * ((6 + SumC) - 2) is V11() real V30() V31() ext-real Element of INT
(((6 + SumC) * ((6 + SumC) - 1)) * ((6 + SumC) - 2)) / 6 is V11() real ext-real Element of COMPLEX
((SumC + 1) / (SumC + 4)) * ((((6 + SumC) * ((6 + SumC) - 1)) * ((6 + SumC) - 2)) / 6) is V11() real ext-real Element of COMPLEX
4 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) / (SumC + 4)) * (4 + SumC) is V11() real ext-real non negative Element of REAL
5 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((SumC + 1) / (SumC + 4)) * (4 + SumC)) * (5 + SumC) is V11() real ext-real non negative Element of REAL
((((SumC + 1) / (SumC + 4)) * (4 + SumC)) * (5 + SumC)) * (6 + SumC) is V11() real ext-real non negative Element of REAL
(((((SumC + 1) / (SumC + 4)) * (4 + SumC)) * (5 + SumC)) * (6 + SumC)) / 6 is V11() real ext-real non negative Element of COMPLEX
(SumC + 1) * (5 + SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC + 1) * (5 + SumC)) * (6 + SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((SumC + 1) * (5 + SumC)) * (6 + SumC)) / 6 is V11() real ext-real non negative Element of COMPLEX
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((2 * SumC),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) choose SumC) / (SumC + 1) is V11() real ext-real non negative Element of COMPLEX
(2 * SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) - (2 * SumC) is V11() real V30() V31() ext-real Element of INT
((2 * SumC) + 1) - SumC is V11() real V30() V31() ext-real Element of INT
(((2 * SumC) + 1) - (2 * SumC)) / (((2 * SumC) + 1) - SumC) is V11() real ext-real Element of COMPLEX
((((2 * SumC) + 1) - (2 * SumC)) / (((2 * SumC) + 1) - SumC)) * ((2 * SumC) choose SumC) is V11() real ext-real Element of REAL
1 * ((2 * SumC) choose SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(1 * ((2 * SumC) choose SumC)) / (SumC + 1) is V11() real ext-real non negative Element of COMPLEX
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((2 * SumC),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (SumC + 1) is V11() real ext-real Element of REAL
(SumC + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * (SumC + 1)) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * (SumC + 1)) -' 2) choose ((SumC + 1) -' 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * (SumC + 1)) -' 2) choose ((SumC + 1) -' 1)) / (SumC + 1) is V11() real ext-real non negative Element of COMPLEX
(2 * SumC) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) - 2 is V11() real V30() V31() ext-real Element of INT
(SumC + 1) - 1 is V11() real V30() V31() ext-real Element of INT
SumC is set
SumC ^omega is non empty functional set
R is non empty functional set
r is set
SumC is set
SumC ^omega is non empty functional set
R is set
SumC is set
R is non empty functional (SumC)
r is Relation-like Function-like Element of R
Cat is Relation-like Function-like Element of R
s is Relation-like Function-like Element of R
(NAT) is non empty functional ( NAT )
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( dom b₁ = 2 * SumC & b₁ is () ) } is set
card { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( dom b₁ = 2 * SumC & b₁ is () ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(2 * SumC) choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
({0,1}) is non empty functional ({0,1})
bool ({0,1}) is non empty set
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC),s) is functional finite Element of bool ({0,1} ^omega)
c₆ is functional Element of bool ({0,1})
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC),n) is functional finite Element of bool ({0,1} ^omega)
s is T-Sequence-like Relation-like NAT -defined bool ({0,1}) -valued Function-like finite V213() set
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng s is finite Element of bool (bool ({0,1}))
bool (bool ({0,1})) is non empty set
union (rng s) is set
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
((2 * SumC),(Sum n)) is functional finite Element of bool ({0,1} ^omega)
2 * (Sum n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 / 2 is V11() real ext-real non negative Element of COMPLEX
(1 / 2) * (2 * (Sum n)) is V11() real ext-real non negative Element of REAL
(1 / 2) * (2 * SumC) is V11() real ext-real non negative Element of REAL
s . (Sum n) is set
c₆ is set
n is set
n is set
s . n is set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),n1) is functional finite Element of bool ({0,1} ^omega)
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . c₆ is set
s . n is set
(s . c₆) /\ (s . n) is set
n is set
((2 * SumC),n) is functional finite Element of bool ({0,1} ^omega)
((2 * SumC),c₆) is functional finite Element of bool ({0,1} ^omega)
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . c₆ is set
((2 * SumC),c₆) is functional finite Element of bool ({0,1} ^omega)
card (union (rng s)) is epsilon-transitive epsilon-connected ordinal cardinal set
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ | (SumC + 1) is T-Sequence-like Relation-like SumC + 1 -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng c₆ is finite V50() V51() V52() V53() V54() V55() set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (c₆ | (0 + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(2 * SumC) choose 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s . 0 is set
((2 * SumC),0) is functional finite Element of bool ({0,1} ^omega)
card (s . 0) is epsilon-transitive epsilon-connected ordinal cardinal set
len c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
c₆ | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (c₆ | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (c₆ | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
dom (c₆ | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
(c₆ | 1) . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
<%(c₆ . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum (c₆ | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ | (n + 1) is T-Sequence-like Relation-like n + 1 -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (c₆ | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(2 * SumC) choose n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ | ((n + 1) + 1) is T-Sequence-like Relation-like (n + 1) + 1 -defined NAT -defined NAT -valued RAT -valued rng c₆ -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (c₆ | ((n + 1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(2 * SumC) choose (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ . (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Sum (c₆ | (n + 1))) + (c₆ . (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s . (n + 1) is set
card (s . (n + 1)) is epsilon-transitive epsilon-connected ordinal cardinal set
2 * (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),(n + 1)) is functional finite Element of bool ({0,1} ^omega)
((2 * SumC) choose (n + 1)) - ((2 * SumC) choose n) is V11() real V30() V31() ext-real Element of INT
((2 * SumC) choose n) + (((2 * SumC) choose (n + 1)) - ((2 * SumC) choose n)) is V11() real V30() V31() ext-real Element of INT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(r,Cat) is functional finite Element of bool ({0,1} ^omega)
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (s + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r - (2 * (s + 1)) is V11() real V30() V31() ext-real Element of INT
Cat - (s + 1) is V11() real V30() V31() ext-real Element of INT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
card { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is epsilon-transitive epsilon-connected ordinal cardinal set
2 * s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * s),s) is functional finite Element of bool ({0,1} ^omega)
card ((2 * s),s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(c₆,n) is functional finite Element of bool ({0,1} ^omega)
card (c₆,n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card ((2 * s),s)) * (card (c₆,n)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
[:((2 * s),s),(c₆,n):] is Relation-like finite set
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
Sum (1 --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 * 1 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
CatalR is set
Fr2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Fr2 | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Fr2 | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
Fr2 | (2 * (s + 1)) is T-Sequence-like Relation-like 2 * (s + 1) -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Fr2 is finite V50() V51() V52() V53() V54() V55() set
e2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((Fr2 | (2 * (s + 1))),e2) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),n2) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),n2),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (1 --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
1 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
k is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
Sum ((1 --> 0),n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum ((1 --> 0),n2)) + (Sum (1 --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Fr2 | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Fr2 | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (1 --> 0)) + (Sum n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Fr2 | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Fr2 | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (Fr2 | (2 * (s + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Fr2 | (2 * (s + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Fr2 | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Fr2 | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(s + 1) + (Sum e2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr2 | n1 is T-Sequence-like Relation-like n1 -defined NAT -defined NAT -valued RAT -valued rng Fr2 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (Fr2 | n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Fr2 | n1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
[n2,e2] is set
{n2,e2} is non empty functional finite V49() set
{n2} is non empty trivial functional finite V49() 1 -element set
{{n2,e2},{n2}} is non empty finite V49() set
dom (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
dom Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom e2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(2 * (s + 1)) + (len e2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len ((1 --> 0),n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((1 --> 0),n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len ((1 --> 0),n2)) + (len (1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (1 --> 0)) + (len n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
[: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } ,[:((2 * s),s),(c₆,n):]:] is Relation-like set
bool [: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } ,[:((2 * s),s),(c₆,n):]:] is non empty set
CatalR is Relation-like { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } -defined [:((2 * s),s),(c₆,n):] -valued Function-like quasi_total Element of bool [: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } ,[:((2 * s),s),(c₆,n):]:]
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * Cat) - (2 * (s + 1)) is V11() real V30() V31() ext-real Element of INT
Fr2 is set
k is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (k | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (k | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom CatalR is Element of bool { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) }
bool { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (r,Cat) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is non empty set
rng CatalR is Relation-like ((2 * s),s) -defined (c₆,n) -valued finite Element of bool [:((2 * s),s),(c₆,n):]
bool [:((2 * s),s),(c₆,n):] is non empty finite V49() set
Sum (1 --> 0) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
1 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
Sum (1 --> 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
1 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
Fr2 is set
k is set
e2 is set
[k,e2] is set
{k,e2} is non empty finite set
{k} is non empty trivial finite 1 -element set
{{k,e2},{k}} is non empty finite V49() set
n2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
((1 --> 0),n2) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),n2),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((((1 --> 0),n2),(1 --> 1)),n1) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom ((((1 --> 0),n2),(1 --> 1)),n1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len (((1 --> 0),n2),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((1 --> 0),n2),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (((1 --> 0),n2),(1 --> 1))) + (len n1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((1 --> 0),n2),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len ((1 --> 0),n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom ((1 --> 0),n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len ((1 --> 0),n2)) + (len (1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
len (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (1 --> 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (1 --> 0)) + (len n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((len (1 --> 0)) + (len n2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * 1) + (len n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((1 --> 0),n2),(1 --> 1)),n1) | ((2 * 1) + (len n2)) is T-Sequence-like Relation-like (2 * 1) + (len n2) -defined NAT -defined NAT -valued RAT -valued rng ((((1 --> 0),n2),(1 --> 1)),n1) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng ((((1 --> 0),n2),(1 --> 1)),n1) is non empty finite V50() V51() V52() V53() V54() V55() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (((((1 --> 0),n2),(1 --> 1)),n1) | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (((((1 --> 0),n2),(1 --> 1)),n1) | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + (len n2) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Sum n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(1 + (len n2)) - (2 * (Sum n2)) is V11() real V30() V31() ext-real Element of INT
(n2,(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),(n2,(1 --> 1))) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (((1 --> 0),n2),(1 --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (n2,(1 --> 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (1 --> 0)) + (Sum (n2,(1 --> 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum n2) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
0 + ((Sum n2) + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum ((((1 --> 0),n2),(1 --> 1)),n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(s + 1) + n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
CatalR . ((((1 --> 0),n2),(1 --> 1)),n1) is set
2M is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),2M) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),2M),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
m is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((((1 --> 0),2M),(1 --> 1)),m) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (((1 --> 0),2M),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((1 --> 0),2M),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
[2M,m] is set
{2M,m} is non empty functional finite V49() set
{2M} is non empty trivial functional finite V49() 1 -element set
{{2M,m},{2M}} is non empty finite V49() set
((((1 --> 0),n2),(1 --> 1)),n1) | (2 * (s + 1)) is T-Sequence-like Relation-like 2 * (s + 1) -defined NAT -defined NAT -valued RAT -valued rng ((((1 --> 0),n2),(1 --> 1)),n1) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((((1 --> 0),2M),(1 --> 1)),m) | (2 * (s + 1)) is T-Sequence-like Relation-like 2 * (s + 1) -defined NAT -defined NAT -valued RAT -valued rng ((((1 --> 0),2M),(1 --> 1)),m) -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng ((((1 --> 0),2M),(1 --> 1)),m) is non empty finite V50() V51() V52() V53() V54() V55() set
Fr2 is set
CatalR . Fr2 is set
k is set
CatalR . k is set
e2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),e2) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),e2),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n2 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((((1 --> 0),e2),(1 --> 1)),n2) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (((1 --> 0),e2),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((1 --> 0),e2),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
[e2,n2] is set
{e2,n2} is non empty functional finite V49() set
{e2} is non empty trivial functional finite V49() 1 -element set
{{e2,n2},{e2}} is non empty finite V49() set
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((1 --> 0),n1) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(((1 --> 0),n1),(1 --> 1)) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
M is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((((1 --> 0),n1),(1 --> 1)),M) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len (((1 --> 0),n1),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (((1 --> 0),n1),(1 --> 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal set
[n1,M] is set
{n1,M} is non empty functional finite V49() set
{n1} is non empty trivial functional finite V49() 1 -element set
{{n1,M},{n1}} is non empty finite V49() set
card [:((2 * s),s),(c₆,n):] is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC,R) is functional finite Element of bool ({0,1} ^omega)
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
card { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is epsilon-transitive epsilon-connected ordinal cardinal set
bool (SumC,R) is non empty finite V49() set
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (s + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (s + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
n is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is functional finite Element of bool (SumC,R)
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (n + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
s is T-Sequence-like Relation-like NAT -defined bool (SumC,R) -valued Function-like finite V213() set
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng s is finite V49() Element of bool (bool (SumC,R))
bool (bool (SumC,R)) is non empty finite V49() set
union (rng s) is finite set
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n | b₁)) = b₁ & not b₁ <= 0 ) } is set
n1 is set
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is non empty V50() V51() V52() V53() V54() V55() Element of bool NAT
min* n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | Fr1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Sum (n | Fr1)) - 1 is V11() real V30() V31() ext-real Element of INT
CatalR is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
((n | Fr1),CatalR) is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n | Fr1)) + (Sum CatalR) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s . Catal is set
2 * (Catal + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (Catal + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . c₆ is set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . n is set
(s . c₆) /\ (s . n) is set
n is set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (n + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (c₆ + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (c₆ + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n1 | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n1 | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Fr1 | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Fr1 | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . c₆ is set
card (union (rng s)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
n is set
n is set
n1 is set
s . n1 is set
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (Fr1 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (Fr1 + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Catal | b₁)) = b₁ & not b₁ <= 0 ) } is set
min* { b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Catal | b₁)) = b₁ & not b₁ <= 0 ) } is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
c₆ . n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * n),n) is functional finite Element of bool ({0,1} ^omega)
card ((2 * n),n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC -' (2 * (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R -' (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC -' (2 * (n + 1))),(R -' (n + 1))) is functional finite Element of bool ({0,1} ^omega)
card ((SumC -' (2 * (n + 1))),(R -' (n + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card ((2 * n),n)) * (card ((SumC -' (2 * (n + 1))),(R -' (n + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R - (n + 1) is V11() real V30() V31() ext-real Element of INT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & 2 * (n + 1) = min* { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } ) } is set
s . n is set
SumC - (2 * (n + 1)) is V11() real V30() V31() ext-real Element of INT
card (s . n) is epsilon-transitive epsilon-connected ordinal cardinal set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),SumC) is functional finite Element of bool ({0,1} ^omega)
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((2 * SumC),SumC) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
SumC + SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
0 + 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
r is set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat | (2 * SumC) is T-Sequence-like Relation-like 2 * SumC -defined NAT -defined NAT -valued RAT -valued rng Cat -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng Cat is finite V50() V51() V52() V53() V54() V55() set
Sum (Cat | (2 * SumC)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (Cat | (2 * SumC))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Cat | b₁)) = b₁ & not b₁ <= 0 ) } is set
r is set
Cat is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Cat | b₁)) = b₁ & not b₁ <= 0 ) } is set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (SumC + 1) is V11() real ext-real Element of REAL
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC),SumC) is functional finite Element of bool ({0,1} ^omega)
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((2 * SumC),SumC) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
card { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((2 * SumC),SumC) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is epsilon-transitive epsilon-connected ordinal cardinal set
R is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
card ((2 * SumC),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R . r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (r + 1) is V11() real ext-real Element of REAL
SumC -' r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (SumC -' r) is V11() real ext-real Element of REAL
(Catalan (r + 1)) * (Catalan (SumC -' r)) is V11() real ext-real Element of REAL
SumC - r is V11() real V30() V31() ext-real Element of INT
r - r is V11() real V30() V31() ext-real Element of INT
(SumC -' r) - 1 is V11() real V30() V31() ext-real Element of INT
2 * (r + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) -' (2 * (r + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) - (2 * (r + 1)) is V11() real V30() V31() ext-real Element of INT
SumC -' (r + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC - (r + 1) is V11() real V30() V31() ext-real Element of INT
2 * r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * r),r) is functional finite Element of bool ({0,1} ^omega)
card ((2 * r),r) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) -' (2 * (r + 1))),(SumC -' (r + 1))) is functional finite Element of bool ({0,1} ^omega)
card (((2 * SumC) -' (2 * (r + 1))),(SumC -' (r + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * Cat),Cat) is functional finite Element of bool ({0,1} ^omega)
card ((2 * Cat),Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (Cat + 1) is V11() real ext-real Element of REAL
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((SumC + 1),R) is functional finite Element of bool ({0,1} ^omega)
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
card { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is epsilon-transitive epsilon-connected ordinal cardinal set
(SumC,R) is functional finite Element of bool ({0,1} ^omega)
card (SumC,R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len <%0%> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom <%0%> is non empty trivial epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal 1 -element set
s is set
Sum <%0%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (c₆ | b₁)) = b₁ & not b₁ <= 0 ) } is set
len c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
dom c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,n) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len <%0%>) + (len n) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum <%0%>) + (Sum n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
[: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } ,(SumC,R):] is Relation-like set
bool [: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } ,(SumC,R):] is non empty set
s is Relation-like { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } -defined (SumC,R) -valued Function-like quasi_total Function-yielding V137() Element of bool [: { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } ,(SumC,R):]
2 * R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n | b₁)) = b₁ & not b₁ <= 0 ) } is set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
n | (SumC + 1) is T-Sequence-like Relation-like SumC + 1 -defined NAT -defined NAT -valued RAT -valued rng n -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n is finite V50() V51() V52() V53() V54() V55() set
Sum (n | (SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (Sum (n | (SumC + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom s is Element of bool { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) }
bool { b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in ((SumC + 1),R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is non empty set
rng s is functional finite Element of bool (SumC,R)
bool (SumC,R) is non empty finite V49() set
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(<%0%>,n) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum ((<%0%>,n) | b₁)) = b₁ & not b₁ <= 0 ) } is set
Sum (<%0%>,n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum <%0%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum <%0%>) + (Sum n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
0 + R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (<%0%>,n) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len <%0%> is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom <%0%> is non empty trivial epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal 1 -element set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len <%0%>) + (len n) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + SumC is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s . (<%0%>,n) is Relation-like Function-like set
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,n1) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
c₆ is set
s . c₆ is Relation-like Function-like set
n is set
s . n is Relation-like Function-like set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,n) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
(<%0%>,n1) is non empty T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC,R) is functional finite Element of bool ({0,1} ^omega)
card (SumC,R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC -' 1),R) is functional finite Element of bool ({0,1} ^omega)
card ((SumC -' 1),R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & not { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
s is set
c₆ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (c₆ | b₁)) = b₁ & not b₁ <= 0 ) } is set
{ b₁ where b₁ is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT) : ( b₁ in (SumC,R) & { b₂ where b₂ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (b₁ | b₂)) = b₂ & not b₂ <= 0 ) } = {} ) } is set
c₆ is set
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (n | b₁)) = b₁ & not b₁ <= 0 ) } is set
c₆ is finite set
card c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(Sum n) + (card ((SumC -' 1),R)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is finite set
n1 is set
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Fr1 | b₁)) = b₁ & not b₁ <= 0 ) } is set
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Catal | b₁)) = b₁ & not b₁ <= 0 ) } is set
n \/ c₆ is finite set
n1 is set
Fr1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() Element of (NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT : ( 2 * (Sum (Catal | b₁)) = b₁ & not b₁ <= 0 ) } is set
1 - 1 is V11() real V30() V31() ext-real Element of INT
SumC - 1 is V11() real V30() V31() ext-real Element of INT
SumC - 1 is V11() real V30() V31() ext-real Element of INT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
card n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n1,R) is functional finite Element of bool ({0,1} ^omega)
card (n1,R) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n . n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * n1),n1) is functional finite Element of bool ({0,1} ^omega)
card ((2 * n1),n1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2 * (n1 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC -' (2 * (n1 + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R -' (n1 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((SumC -' (2 * (n1 + 1))),(R -' (n1 + 1))) is functional finite Element of bool ({0,1} ^omega)
card ((SumC -' (2 * (n1 + 1))),(R -' (n1 + 1))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(card ((2 * n1),n1)) * (card ((SumC -' (2 * (n1 + 1))),(R -' (n1 + 1)))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
2 * SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC) + 2) + R is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + R),(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 2) + R),(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC) + 1) + r is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + r),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + r),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC) + 1) + Cat is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + Cat),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + Cat),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r . Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + Cat is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + Cat),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + Cat),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is set
r . Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + s),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + s),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R + 1) --> 1 is non empty T-Sequence-like Relation-like non-empty R + 1 -defined NAT -valued RAT -valued INT -valued Function-like constant V22(R + 1) quasi_total V35() V36() V37() V38() finite nonnegative-yielding V213() Element of bool [:(R + 1),NAT:]
[:(R + 1),NAT:] is non empty non trivial Relation-like RAT -valued INT -valued V35() V36() V37() V38() non finite nonnegative-yielding set
bool [:(R + 1),NAT:] is non empty non trivial non finite set
(R + 1) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC - 1 is V11() real V30() V31() ext-real Element of INT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) + s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + s),(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 2) + s),(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(s + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) + (s + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + (s + 1)),(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 2) + (s + 1)),(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 2) + s) choose (Cat + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 2) + s) choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
2 * (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * (SumC + 1)) + (s + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 | (s + 1) is T-Sequence-like Relation-like s + 1 -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
rng n1 is finite V50() V51() V52() V53() V54() V55() set
dom (n1 | (s + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (s + 1)
bool (s + 1) is non empty finite V49() set
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(n1 | (s + 1)) . Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + Fr1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + Fr1),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + Fr1),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 . Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + (s + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 1) + (s + 1)) choose Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 1) + (s + 1)) choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + (s + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(2 * SumC) + (1 + (s + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 . (s + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + (s + 1)),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + (s + 1)),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + (s + 1)) choose SumC) - ((((2 * SumC) + 1) + (s + 1)) choose Cat) is V11() real V30() V31() ext-real Element of INT
n1 | ((s + 1) + 1) is T-Sequence-like Relation-like (s + 1) + 1 -defined NAT -defined NAT -valued RAT -valued rng n1 -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum (n1 | ((s + 1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Sum (n1 | (s + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
(Sum (n1 | (s + 1))) + (n1 . (s + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + s) choose (SumC + 1)) - ((((2 * SumC) + 2) + s) choose (Cat + 1)) is V11() real V30() V31() ext-real Element of INT
((((2 * SumC) + 2) + s) choose (SumC + 1)) + ((((2 * SumC) + 2) + s) choose (Cat + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + (s + 1)) choose SumC) + ((((2 * SumC) + 1) + (s + 1)) choose Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((((2 * SumC) + 2) + s) choose (SumC + 1)) + ((((2 * SumC) + 2) + s) choose (Cat + 1))) - (((((2 * SumC) + 1) + (s + 1)) choose SumC) + ((((2 * SumC) + 1) + (s + 1)) choose Cat)) is V11() real V30() V31() ext-real Element of INT
(((2 * SumC) + 2) + s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + s) + 1) choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((((2 * SumC) + 2) + s) + 1) choose (SumC + 1)) - (((((2 * SumC) + 1) + (s + 1)) choose SumC) + ((((2 * SumC) + 1) + (s + 1)) choose Cat)) is V11() real V30() V31() ext-real Element of INT
(((2 * SumC) + 2) + (s + 1)) choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 2) + (s + 1)) choose (Cat + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + (s + 1)) choose (SumC + 1)) - ((((2 * SumC) + 2) + (s + 1)) choose (Cat + 1)) is V11() real V30() V31() ext-real Element of INT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 2) + 0),(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 2) + 0),(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 2) choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s choose (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s choose Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s choose SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Catal . 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + 0),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + 0),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((2 * SumC) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(s choose (SumC + 1)) + (s choose SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(s choose SumC) + (s choose Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC + (SumC + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) - SumC is V11() real V30() V31() ext-real Element of INT
2 * (SumC + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 2),(SumC + 1)) is functional finite Element of bool ({0,1} ^omega)
card (((2 * SumC) + 2),(SumC + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(((2 * SumC) + 2) choose (SumC + 1)) - (((2 * SumC) + 2) choose SumC) is V11() real V30() V31() ext-real Element of INT
(s,(Cat + 1)) is functional finite Element of bool ({0,1} ^omega)
card (s,(Cat + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(s choose SumC) - (s choose Cat) is V11() real V30() V31() ext-real Element of INT
<%(Catal . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined NAT -valued Function-like constant V35() V36() V37() V38() V39() V40() V41() V42() finite nonnegative-yielding 1 -element V213() set
Sum <%(Catal . 0)%> is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
r . Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((2 * SumC) + 1) + Cat is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((((2 * SumC) + 1) + Cat),SumC) is functional finite Element of bool ({0,1} ^omega)
card ((((2 * SumC) + 1) + Cat),SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum SumC is V11() real ext-real Element of COMPLEX
SumC . 0 is V11() real ext-real Element of REAL
<%(SumC . 0)%> is non empty trivial T-Sequence-like Relation-like NAT -defined REAL -valued Function-like constant V35() V36() V37() V39() V40() V41() V42() finite 1 -element V213() set
SumC is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum SumC is V11() real ext-real Element of COMPLEX
R is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum R is V11() real ext-real Element of COMPLEX
card (len SumC) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + Cat is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) -' (1 + Cat) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) - (1 + Cat) is V11() real V30() V31() ext-real Element of INT
(len SumC) + (1 + Cat) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
((len SumC) + (1 + Cat)) - (1 + Cat) is V11() real V30() V31() ext-real Element of INT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
1 + s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) -' (1 + s) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
[:(len SumC),(len SumC):] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() finite nonnegative-yielding set
bool [:(len SumC),(len SumC):] is non empty finite V49() set
r is Relation-like len SumC -defined len SumC -valued Function-like V22( len SumC) quasi_total V35() V36() V37() V38() finite nonnegative-yielding Element of bool [:(len SumC),(len SumC):]
Cat is set
r . Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of len SumC
s is set
r . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of len SumC
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) -' (1 + n) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) - (1 + n) is V11() real V30() V31() ext-real Element of INT
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 + c₆ is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) -' (1 + c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) - (1 + c₆) is V11() real V30() V31() ext-real Element of INT
[:(dom SumC),(dom SumC):] is Relation-like RAT -valued INT -valued V35() V36() V37() V38() finite nonnegative-yielding set
bool [:(dom SumC),(dom SumC):] is non empty finite V49() set
s is set
Cat is Relation-like dom SumC -defined dom SumC -valued Function-like one-to-one V22( dom SumC) quasi_total onto bijective V35() V36() V37() V38() finite nonnegative-yielding Element of bool [:(dom SumC),(dom SumC):]
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat . c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of dom SumC
1 + c₆ is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len SumC) -' (1 + c₆) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . s is V11() real ext-real Element of REAL
Cat . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of dom SumC
R . (Cat . s) is V11() real ext-real Element of REAL
dom Cat is finite V50() V51() V52() V53() V54() V55() Element of bool (dom SumC)
bool (dom SumC) is non empty finite V49() set
s is set
Cat . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of dom SumC
s is set
Cat . s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of dom SumC
Cat (#) R is Relation-like dom SumC -defined REAL -valued Function-like V35() V36() V37() finite set
addreal "**" SumC is V11() real ext-real Element of REAL
addreal "**" R is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
r is set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . s is V11() real ext-real Element of REAL
Cat -' s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R . (Cat -' s) is V11() real ext-real Element of REAL
(SumC . s) * (R . (Cat -' s)) is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . c₆ is V11() real ext-real Element of REAL
Cat -' c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R . (Cat -' c₆) is V11() real ext-real Element of REAL
(SumC . c₆) * (R . (Cat -' c₆)) is V11() real ext-real Element of REAL
s is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum s is V11() real ext-real Element of COMPLEX
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . c₆ is V11() real ext-real Element of REAL
SumC . c₆ is V11() real ext-real Element of REAL
Cat -' c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R . (Cat -' c₆) is V11() real ext-real Element of REAL
(SumC . c₆) * (R . (Cat -' c₆)) is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r . Cat is V11() real ext-real Element of REAL
r is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
s is set
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r . c₆ is V11() real ext-real Element of REAL
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is V11() real ext-real Element of COMPLEX
Cat . c₆ is V11() real ext-real Element of REAL
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is V11() real ext-real Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n . n1 is V11() real ext-real Element of REAL
SumC . n1 is V11() real ext-real Element of REAL
c₆ -' n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R . (c₆ -' n1) is V11() real ext-real Element of REAL
(SumC . n1) * (R . (c₆ -' n1)) is V11() real ext-real Element of REAL
n . n1 is V11() real ext-real Element of REAL
r . s is V11() real ext-real Element of REAL
Cat . s is V11() real ext-real Element of REAL
r is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
s is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r . c₆ is V11() real ext-real Element of REAL
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is V11() real ext-real Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . n1 is V11() real ext-real Element of REAL
c₆ -' n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat . (c₆ -' n1) is V11() real ext-real Element of REAL
(s . n1) * (Cat . (c₆ -' n1)) is V11() real ext-real Element of REAL
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s . Fr1 is V11() real ext-real Element of REAL
c₆ -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat . (c₆ -' Fr1) is V11() real ext-real Element of REAL
(s . Fr1) * (Cat . (c₆ -' Fr1)) is V11() real ext-real Element of REAL
n1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is V11() real ext-real Element of COMPLEX
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 . Fr1 is V11() real ext-real Element of REAL
s . Fr1 is V11() real ext-real Element of REAL
c₆ -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat . (c₆ -' Fr1) is V11() real ext-real Element of REAL
(s . Fr1) * (Cat . (c₆ -' Fr1)) is V11() real ext-real Element of REAL
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
c₆ -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ - Fr1 is V11() real V30() V31() ext-real Element of INT
(c₆ -' Fr1) + Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ -' (c₆ -' Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
c₆ - (c₆ -' Fr1) is V11() real V30() V31() ext-real Element of INT
Fr1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len n1) -' (Fr1 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(c₆ + 1) - (Fr1 + 1) is V11() real V30() V31() ext-real Element of INT
n1 . ((len n1) -' (Fr1 + 1)) is V11() real ext-real Element of REAL
s . (c₆ -' Fr1) is V11() real ext-real Element of REAL
Cat . Fr1 is V11() real ext-real Element of REAL
(s . (c₆ -' Fr1)) * (Cat . Fr1) is V11() real ext-real Element of REAL
n . Fr1 is V11() real ext-real Element of REAL
1 + Fr1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(len n) -' (1 + Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 . ((len n) -' (1 + Fr1)) is V11() real ext-real Element of REAL
SumC is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
R is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum SumC is V11() real ext-real Element of COMPLEX
Sum R is V11() real ext-real Element of COMPLEX
SumC is V11() real ext-real set
R is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
len R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Sum R is V11() real ext-real Element of COMPLEX
r is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum r is V11() real ext-real Element of COMPLEX
SumC * (Sum r) is V11() real ext-real Element of REAL
R | (dom R) is T-Sequence-like Relation-like dom R -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
rng R is finite V50() V51() V52() set
r | (dom R) is T-Sequence-like Relation-like dom R -defined NAT -defined REAL -valued rng r -valued Function-like V35() V36() V37() finite V213() set
rng r is finite V50() V51() V52() set
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
Sum (R | Cat) is V11() real ext-real Element of COMPLEX
r | Cat is T-Sequence-like Relation-like Cat -defined NAT -defined REAL -valued rng r -valued Function-like V35() V36() V37() finite V213() set
Sum (r | Cat) is V11() real ext-real Element of COMPLEX
SumC * (Sum (r | Cat)) is V11() real ext-real Element of REAL
Cat + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R | (Cat + 1) is T-Sequence-like Relation-like Cat + 1 -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
Sum (R | (Cat + 1)) is V11() real ext-real Element of COMPLEX
r | (Cat + 1) is T-Sequence-like Relation-like Cat + 1 -defined NAT -defined REAL -valued rng r -valued Function-like V35() V36() V37() finite V213() set
Sum (r | (Cat + 1)) is V11() real ext-real Element of COMPLEX
SumC * (Sum (r | (Cat + 1))) is V11() real ext-real Element of REAL
R . Cat is V11() real ext-real Element of REAL
r . Cat is V11() real ext-real Element of REAL
SumC * (r . Cat) is V11() real ext-real Element of REAL
(R . Cat) + (Sum (R | Cat)) is V11() real ext-real Element of REAL
(r . Cat) + (Sum (r | Cat)) is V11() real ext-real Element of REAL
R | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng R -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (R | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
r | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng r -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (r | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
SumC * (Sum (r | 0)) is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
r is V11() real ext-real set
r (#) R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,(r (#) R)) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
r (#) (SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
c₆ is set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC,(r (#) R)) . n is V11() real ext-real Element of REAL
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n is V11() real ext-real Element of COMPLEX
(SumC,R) . n is V11() real ext-real Element of REAL
n1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is V11() real ext-real Element of COMPLEX
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n . Fr1 is V11() real ext-real Element of REAL
SumC . Fr1 is V11() real ext-real Element of REAL
n -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r (#) R) . (n -' Fr1) is V11() real ext-real Element of REAL
(SumC . Fr1) * ((r (#) R) . (n -' Fr1)) is V11() real ext-real Element of REAL
n1 . Fr1 is V11() real ext-real Element of REAL
R . (n -' Fr1) is V11() real ext-real Element of REAL
(SumC . Fr1) * (R . (n -' Fr1)) is V11() real ext-real Element of REAL
r * (R . (n -' Fr1)) is V11() real ext-real Element of REAL
r * (n1 . Fr1) is V11() real ext-real Element of REAL
r * (Sum n1) is V11() real ext-real Element of REAL
(SumC,(r (#) R)) . c₆ is V11() real ext-real Element of REAL
(r (#) (SumC,R)) . c₆ is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
r is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R + r is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,(R + r)) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,r) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) + (SumC,r) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
n is set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(SumC,(R + r)) . n is V11() real ext-real Element of REAL
n1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum n1 is V11() real ext-real Element of COMPLEX
(SumC,R) . n is V11() real ext-real Element of REAL
Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Fr1 is V11() real ext-real Element of COMPLEX
len Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(SumC,r) . n is V11() real ext-real Element of REAL
Catal is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Catal is V11() real ext-real Element of COMPLEX
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 . CatalR is V11() real ext-real Element of REAL
Fr1 . CatalR is V11() real ext-real Element of REAL
Catal . CatalR is V11() real ext-real Element of REAL
addreal . ((Fr1 . CatalR),(Catal . CatalR)) is V11() real ext-real Element of REAL
SumC . CatalR is V11() real ext-real Element of REAL
n -' CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R + r) . (n -' CatalR) is V11() real ext-real Element of REAL
(SumC . CatalR) * ((R + r) . (n -' CatalR)) is V11() real ext-real Element of REAL
R . (n -' CatalR) is V11() real ext-real Element of REAL
r . (n -' CatalR) is V11() real ext-real Element of REAL
(R . (n -' CatalR)) + (r . (n -' CatalR)) is V11() real ext-real Element of REAL
(SumC . CatalR) * (R . (n -' CatalR)) is V11() real ext-real Element of REAL
(SumC . CatalR) * (r . (n -' CatalR)) is V11() real ext-real Element of REAL
(Fr1 . CatalR) + (Catal . CatalR) is V11() real ext-real Element of REAL
len Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Fr1 ^ Catal is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
addreal "**" (Fr1 ^ Catal) is V11() real ext-real Element of REAL
addreal "**" n1 is V11() real ext-real Element of REAL
Sum (Fr1 ^ Catal) is V11() real ext-real Element of COMPLEX
(Sum Fr1) + (Sum Catal) is V11() real ext-real Element of COMPLEX
(SumC,(R + r)) . n is V11() real ext-real Element of REAL
((SumC,R) + (SumC,r)) . n is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
SumC . 0 is V11() real ext-real Element of REAL
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) . 0 is V11() real ext-real Element of REAL
R . 0 is V11() real ext-real Element of REAL
(SumC . 0) * (R . 0) is V11() real ext-real Element of REAL
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Cat is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Cat is V11() real ext-real Element of COMPLEX
0 -' 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat . 0 is V11() real ext-real Element of REAL
R . (0 -' 0) is V11() real ext-real Element of REAL
(SumC . 0) * (R . (0 -' 0)) is V11() real ext-real Element of REAL
<%((SumC . 0) * (R . 0))%> is non empty trivial T-Sequence-like Relation-like NAT -defined REAL -valued Function-like constant V35() V36() V37() V39() V40() V41() V42() finite 1 -element V213() set
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums (SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Partial_Sums (SumC,R)) . r is V11() real ext-real Element of REAL
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Partial_Sums (SumC,R)) . n is V11() real ext-real Element of REAL
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums (SumC,R)) . (n + 1) is V11() real ext-real Element of REAL
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n + 1) -' (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . 0 is V11() real ext-real Element of REAL
R . 0 is V11() real ext-real Element of REAL
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . n1 is V11() real ext-real Element of REAL
(n + 1) -' n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . ((n + 1) -' n1) is V11() real ext-real Element of REAL
(SumC . n1) * ((Partial_Sums R) . ((n + 1) -' n1)) is V11() real ext-real Element of REAL
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . Fr1 is V11() real ext-real Element of REAL
(n + 1) -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . ((n + 1) -' Fr1) is V11() real ext-real Element of REAL
(SumC . Fr1) * ((Partial_Sums R) . ((n + 1) -' Fr1)) is V11() real ext-real Element of REAL
n1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
Sum Fr1 is V11() real ext-real Element of COMPLEX
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
Sum Fr1 is V11() real ext-real Element of COMPLEX
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
(SumC,R) . (n + 1) is V11() real ext-real Element of REAL
Catal is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Catal is V11() real ext-real Element of COMPLEX
Catal | ((n + 1) + 1) is T-Sequence-like Relation-like (n + 1) + 1 -defined NAT -defined REAL -valued rng Catal -valued Function-like V35() V36() V37() finite V213() set
rng Catal is finite V50() V51() V52() set
n1 | (n + 1) is T-Sequence-like Relation-like n + 1 -defined NAT -defined REAL -valued rng n1 -valued Function-like V35() V36() V37() finite V213() set
rng n1 is finite V50() V51() V52() set
dom (n1 | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (n + 1)
bool (n + 1) is non empty finite V49() set
Catal | (n + 1) is T-Sequence-like Relation-like n + 1 -defined NAT -defined REAL -valued rng Catal -valued Function-like V35() V36() V37() finite V213() set
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(n1 | (n + 1)) . CatalR is V11() real ext-real Element of REAL
Fr1 . CatalR is V11() real ext-real Element of REAL
(Catal | (n + 1)) . CatalR is V11() real ext-real Element of REAL
addreal . ((Fr1 . CatalR),((Catal | (n + 1)) . CatalR)) is V11() real ext-real Element of REAL
(dom n1) /\ (n + 1) is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
dom (Catal | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool (n + 1)
Catal . CatalR is V11() real ext-real Element of REAL
n -' CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n - CatalR is V11() real V30() V31() ext-real Element of INT
SumC . CatalR is V11() real ext-real Element of REAL
(n + 1) -' CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R . ((n + 1) -' CatalR) is V11() real ext-real Element of REAL
(SumC . CatalR) * (R . ((n + 1) -' CatalR)) is V11() real ext-real Element of REAL
n1 . CatalR is V11() real ext-real Element of REAL
(Partial_Sums R) . ((n + 1) -' CatalR) is V11() real ext-real Element of REAL
(SumC . CatalR) * ((Partial_Sums R) . ((n + 1) -' CatalR)) is V11() real ext-real Element of REAL
(n + 1) - CatalR is V11() real V30() V31() ext-real Element of INT
(n -' CatalR) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . (n -' CatalR) is V11() real ext-real Element of REAL
((Partial_Sums R) . (n -' CatalR)) + (R . ((n + 1) -' CatalR)) is V11() real ext-real Element of REAL
(SumC . CatalR) * ((Partial_Sums R) . (n -' CatalR)) is V11() real ext-real Element of REAL
(Fr1 . CatalR) + (Catal . CatalR) is V11() real ext-real Element of REAL
len (Catal | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (Catal | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
len Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal . (n + 1) is V11() real ext-real Element of REAL
SumC . (n + 1) is V11() real ext-real Element of REAL
R . ((n + 1) -' (n + 1)) is V11() real ext-real Element of REAL
(SumC . (n + 1)) * (R . ((n + 1) -' (n + 1))) is V11() real ext-real Element of REAL
Sum (Catal | ((n + 1) + 1)) is V11() real ext-real Element of COMPLEX
Sum (Catal | (n + 1)) is V11() real ext-real Element of COMPLEX
(Catal . (n + 1)) + (Sum (Catal | (n + 1))) is V11() real ext-real Element of REAL
len (n1 | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (n1 | (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
addreal "**" (n1 | (n + 1)) is V11() real ext-real Element of REAL
Fr1 ^ (Catal | (n + 1)) is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
addreal "**" (Fr1 ^ (Catal | (n + 1))) is V11() real ext-real Element of REAL
Sum (Fr1 ^ (Catal | (n + 1))) is V11() real ext-real Element of COMPLEX
(Sum Fr1) + (Sum (Catal | (n + 1))) is V11() real ext-real Element of COMPLEX
Sum (n1 | (n + 1)) is V11() real ext-real Element of COMPLEX
Sum n1 is V11() real ext-real Element of COMPLEX
n1 . (n + 1) is V11() real ext-real Element of REAL
(Partial_Sums R) . ((n + 1) -' (n + 1)) is V11() real ext-real Element of REAL
(SumC . (n + 1)) * ((Partial_Sums R) . ((n + 1) -' (n + 1))) is V11() real ext-real Element of REAL
n1 | ((n + 1) + 1) is T-Sequence-like Relation-like (n + 1) + 1 -defined NAT -defined REAL -valued rng n1 -valued Function-like V35() V36() V37() finite V213() set
Sum (n1 | ((n + 1) + 1)) is V11() real ext-real Element of COMPLEX
(n1 . (n + 1)) + (Sum (n1 | (n + 1))) is V11() real ext-real Element of REAL
((Partial_Sums (SumC,R)) . n) + ((SumC,R) . (n + 1)) is V11() real ext-real Element of REAL
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 . CatalR is V11() real ext-real Element of REAL
SumC . CatalR is V11() real ext-real Element of REAL
(n + 1) -' CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . ((n + 1) -' CatalR) is V11() real ext-real Element of REAL
(SumC . CatalR) * ((Partial_Sums R) . ((n + 1) -' CatalR)) is V11() real ext-real Element of REAL
(Partial_Sums (SumC,R)) . 0 is V11() real ext-real Element of REAL
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . 0 is V11() real ext-real Element of REAL
R . 0 is V11() real ext-real Element of REAL
(SumC . 0) * (R . 0) is V11() real ext-real Element of REAL
1 --> ((SumC . 0) * (R . 0)) is non empty T-Sequence-like Relation-like 1 -defined REAL -valued Function-like constant V22(1) quasi_total V35() V36() V37() finite V213() Element of bool [:1,REAL:]
[:1,REAL:] is non empty non trivial Relation-like V35() V36() V37() non finite set
bool [:1,REAL:] is non empty non trivial non finite set
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
Sum n is V11() real ext-real Element of COMPLEX
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
n | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng n -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
rng n is finite V50() V51() V52() set
dom (n | 0) is empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of bool NAT
n | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
n . 0 is V11() real ext-real Element of REAL
Sum (n | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
(Sum (n | 0)) + (n . 0) is V11() real ext-real Element of REAL
n | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | (0 + 1)) is V11() real ext-real Element of COMPLEX
(SumC,R) . 0 is V11() real ext-real Element of REAL
(Partial_Sums (SumC,R)) . 0 is V11() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n . n is V11() real ext-real Element of REAL
SumC . n is V11() real ext-real Element of REAL
0 -' n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . (0 -' n) is V11() real ext-real Element of REAL
(SumC . n) * ((Partial_Sums R) . (0 -' n)) is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums (SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum R is V11() real ext-real Element of REAL
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Partial_Sums (SumC,R)) . r is V11() real ext-real Element of REAL
(Partial_Sums SumC) . r is V11() real ext-real Element of REAL
(Sum R) * ((Partial_Sums SumC) . r) is V11() real ext-real Element of REAL
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Partial_Sums R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . n is V11() real ext-real Element of REAL
r -' n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r -' n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((r -' n) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((r -' n) + 1)) is V11() real ext-real Element of REAL
(SumC . n) * (Sum (R ^\ ((r -' n) + 1))) is V11() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . n is V11() real ext-real Element of REAL
r -' n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r -' n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((r -' n) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((r -' n) + 1)) is V11() real ext-real Element of REAL
(SumC . n) * (Sum (R ^\ ((r -' n) + 1))) is V11() real ext-real Element of REAL
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
n is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
Sum n is V11() real ext-real Element of COMPLEX
dom n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
n . 0 is V11() real ext-real Element of REAL
SumC . 0 is V11() real ext-real Element of REAL
r -' 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . (r -' 0) is V11() real ext-real Element of REAL
(SumC . 0) * ((Partial_Sums R) . (r -' 0)) is V11() real ext-real Element of REAL
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
rng n is finite V50() V51() V52() set
Sum (n | (0 + 1)) is V11() real ext-real Element of COMPLEX
n | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng n -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (n | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
(n . 0) + (Sum (n | 0)) is V11() real ext-real Element of REAL
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | (n1 + 1) is T-Sequence-like Relation-like n1 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | (n1 + 1)) is V11() real ext-real Element of COMPLEX
n | (n1 + 1) is T-Sequence-like Relation-like n1 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
rng n is finite V50() V51() V52() set
Sum (n | (n1 + 1)) is V11() real ext-real Element of COMPLEX
(Sum (n | (n1 + 1))) + (Sum (n | (n1 + 1))) is V11() real ext-real Element of COMPLEX
(Partial_Sums SumC) . n1 is V11() real ext-real Element of REAL
(Sum R) * ((Partial_Sums SumC) . n1) is V11() real ext-real Element of REAL
(n1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | ((n1 + 1) + 1) is T-Sequence-like Relation-like (n1 + 1) + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | ((n1 + 1) + 1)) is V11() real ext-real Element of COMPLEX
n | ((n1 + 1) + 1) is T-Sequence-like Relation-like (n1 + 1) + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | ((n1 + 1) + 1)) is V11() real ext-real Element of COMPLEX
(Sum (n | ((n1 + 1) + 1))) + (Sum (n | ((n1 + 1) + 1))) is V11() real ext-real Element of COMPLEX
(Partial_Sums SumC) . (n1 + 1) is V11() real ext-real Element of REAL
(Sum R) * ((Partial_Sums SumC) . (n1 + 1)) is V11() real ext-real Element of REAL
Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n . Fr1 is V11() real ext-real Element of REAL
SumC . Fr1 is V11() real ext-real Element of REAL
r -' Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r -' Fr1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((r -' Fr1) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((r -' Fr1) + 1)) is V11() real ext-real Element of REAL
(SumC . Fr1) * (Sum (R ^\ ((r -' Fr1) + 1))) is V11() real ext-real Element of REAL
Fr1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n | (Fr1 + 1) is T-Sequence-like Relation-like Fr1 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | (Fr1 + 1)) is V11() real ext-real Element of COMPLEX
n . Fr1 is V11() real ext-real Element of REAL
n | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | Fr1) is V11() real ext-real Element of COMPLEX
(n . Fr1) + (Sum (n | Fr1)) is V11() real ext-real Element of REAL
n | Fr1 is T-Sequence-like Relation-like Fr1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | Fr1) is V11() real ext-real Element of COMPLEX
(Sum (n | Fr1)) + (Sum (n | Fr1)) is V11() real ext-real Element of COMPLEX
n | (Fr1 + 1) is T-Sequence-like Relation-like Fr1 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
Sum (n | (Fr1 + 1)) is V11() real ext-real Element of COMPLEX
(n . Fr1) + (Sum (n | Fr1)) is V11() real ext-real Element of REAL
(Partial_Sums R) . (r -' Fr1) is V11() real ext-real Element of REAL
(SumC . Fr1) * ((Partial_Sums R) . (r -' Fr1)) is V11() real ext-real Element of REAL
(Sum (n | (Fr1 + 1))) + (Sum (n | (Fr1 + 1))) is V11() real ext-real Element of COMPLEX
(Sum (R ^\ ((r -' Fr1) + 1))) + ((Partial_Sums R) . (r -' Fr1)) is V11() real ext-real Element of REAL
(SumC . Fr1) * ((Sum (R ^\ ((r -' Fr1) + 1))) + ((Partial_Sums R) . (r -' Fr1))) is V11() real ext-real Element of REAL
((SumC . Fr1) * ((Sum (R ^\ ((r -' Fr1) + 1))) + ((Partial_Sums R) . (r -' Fr1)))) + ((Sum R) * ((Partial_Sums SumC) . n1)) is V11() real ext-real Element of REAL
(SumC . Fr1) * (Sum R) is V11() real ext-real Element of REAL
((SumC . Fr1) * (Sum R)) + ((Sum R) * ((Partial_Sums SumC) . n1)) is V11() real ext-real Element of REAL
((Partial_Sums SumC) . n1) + (SumC . Fr1) is V11() real ext-real Element of REAL
(Sum R) * (((Partial_Sums SumC) . n1) + (SumC . Fr1)) is V11() real ext-real Element of REAL
(Partial_Sums SumC) . Fr1 is V11() real ext-real Element of REAL
((Partial_Sums SumC) . Fr1) * (Sum R) is V11() real ext-real Element of REAL
n | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
rng n is finite V50() V51() V52() set
Sum (n | (0 + 1)) is V11() real ext-real Element of COMPLEX
n . 0 is V11() real ext-real Element of REAL
n | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng n -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (n | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
(n . 0) + (Sum (n | 0)) is V11() real ext-real Element of REAL
(r -' 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((r -' 0) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((r -' 0) + 1)) is V11() real ext-real Element of REAL
(SumC . 0) * (Sum (R ^\ ((r -' 0) + 1))) is V11() real ext-real Element of REAL
(Sum (n | (0 + 1))) + (Sum (n | (0 + 1))) is V11() real ext-real Element of COMPLEX
(Sum (R ^\ ((r -' 0) + 1))) + ((Partial_Sums R) . (r -' 0)) is V11() real ext-real Element of REAL
(SumC . 0) * ((Sum (R ^\ ((r -' 0) + 1))) + ((Partial_Sums R) . (r -' 0))) is V11() real ext-real Element of REAL
(SumC . 0) * (Sum R) is V11() real ext-real Element of REAL
(Sum (n | (0 + 1))) + (Sum (n | (0 + 1))) is V11() real ext-real Element of COMPLEX
(Partial_Sums SumC) . 0 is V11() real ext-real Element of REAL
(Sum R) * ((Partial_Sums SumC) . 0) is V11() real ext-real Element of REAL
Sum n is V11() real ext-real Element of COMPLEX
((Sum R) * ((Partial_Sums SumC) . r)) - (Sum n) is V11() real ext-real Element of REAL
n | (r + 1) is T-Sequence-like Relation-like r + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
n | (r + 1) is T-Sequence-like Relation-like r + 1 -defined NAT -defined REAL -valued rng n -valued Function-like V35() V36() V37() finite V213() set
(Sum n) + (Sum n) is V11() real ext-real Element of COMPLEX
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
n . n1 is V11() real ext-real Element of REAL
SumC . n1 is V11() real ext-real Element of REAL
r -' n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(r -' n1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((r -' n1) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((r -' n1) + 1)) is V11() real ext-real Element of REAL
(SumC . n1) * (Sum (R ^\ ((r -' n1) + 1))) is V11() real ext-real Element of REAL
SumC is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum SumC is V11() real ext-real Element of COMPLEX
abs (Sum SumC) is V11() real ext-real Element of REAL
SumC | (dom SumC) is T-Sequence-like Relation-like dom SumC -defined NAT -defined REAL -valued rng SumC -valued Function-like V35() V36() V37() finite V213() set
rng SumC is finite V50() V51() V52() set
len SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom SumC is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . R is V11() real ext-real Element of REAL
abs (SumC . R) is V11() real ext-real Element of REAL
R is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC | r is T-Sequence-like Relation-like r -defined NAT -defined REAL -valued rng SumC -valued Function-like V35() V36() V37() finite V213() set
Sum (SumC | r) is V11() real ext-real Element of COMPLEX
abs (Sum (SumC | r)) is V11() real ext-real Element of REAL
R | r is T-Sequence-like Relation-like r -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
rng R is finite V50() V51() V52() set
Sum (R | r) is V11() real ext-real Element of COMPLEX
r + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC | (r + 1) is T-Sequence-like Relation-like r + 1 -defined NAT -defined REAL -valued rng SumC -valued Function-like V35() V36() V37() finite V213() set
Sum (SumC | (r + 1)) is V11() real ext-real Element of COMPLEX
abs (Sum (SumC | (r + 1))) is V11() real ext-real Element of REAL
R | (r + 1) is T-Sequence-like Relation-like r + 1 -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
Sum (R | (r + 1)) is V11() real ext-real Element of COMPLEX
SumC . r is V11() real ext-real Element of REAL
(SumC . r) + (Sum (SumC | r)) is V11() real ext-real Element of REAL
R . r is V11() real ext-real Element of REAL
abs (SumC . r) is V11() real ext-real Element of REAL
(R . r) + (abs (Sum (SumC | r))) is V11() real ext-real Element of REAL
(R . r) + (Sum (R | r)) is V11() real ext-real Element of REAL
Sum R is V11() real ext-real Element of COMPLEX
SumC | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng SumC -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (SumC | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
abs (Sum (SumC | 0)) is V11() real V31() ext-real Element of REAL
R | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng R -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
rng R is finite V50() V51() V52() set
Sum (R | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
SumC | (len SumC) is T-Sequence-like Relation-like len SumC -defined NAT -defined REAL -valued rng SumC -valued Function-like V35() V36() V37() finite V213() set
Sum (SumC | (len SumC)) is V11() real ext-real Element of COMPLEX
abs (Sum (SumC | (len SumC))) is V11() real ext-real Element of REAL
R | (len SumC) is T-Sequence-like Relation-like len SumC -defined NAT -defined REAL -valued rng R -valued Function-like V35() V36() V37() finite V213() set
Sum (R | (len SumC)) is V11() real ext-real Element of COMPLEX
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R . r is V11() real ext-real Element of REAL
SumC . r is V11() real ext-real Element of REAL
abs (SumC . r) is V11() real ext-real Element of REAL
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r is V11() real ext-real set
r is V11() real ext-real set
SumC ^\ (R + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC ^\ (R + 1)) is V11() real ext-real Element of REAL
abs (Sum (SumC ^\ (R + 1))) is V11() real ext-real Element of REAL
max (r,(abs (Sum (SumC ^\ (R + 1))))) is V11() real ext-real set
Cat is V11() real ext-real set
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC ^\ s is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC ^\ s) is V11() real ext-real Element of REAL
abs (Sum (SumC ^\ s)) is V11() real ext-real Element of REAL
Partial_Sums SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
lim (Partial_Sums SumC) is V11() real ext-real Element of REAL
Sum SumC is V11() real ext-real Element of REAL
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
abs (Sum SumC) is V11() real ext-real Element of REAL
Cat is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC ^\ Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC ^\ Cat) is V11() real ext-real Element of REAL
abs (Sum (SumC ^\ Cat)) is V11() real ext-real Element of REAL
Cat is V11() real ext-real set
Cat + 1 is V11() real ext-real Element of REAL
s is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC ^\ c₆ is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC ^\ c₆) is V11() real ext-real Element of REAL
abs (Sum (SumC ^\ c₆)) is V11() real ext-real Element of REAL
0 + Cat is V11() real ext-real Element of REAL
c₆ - 1 is V11() real V30() V31() ext-real Element of INT
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums SumC) . n is V11() real ext-real Element of REAL
((Partial_Sums SumC) . n) - (Sum SumC) is V11() real ext-real Element of REAL
abs (((Partial_Sums SumC) . n) - (Sum SumC)) is V11() real ext-real Element of REAL
SumC ^\ (n + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC ^\ (n + 1)) is V11() real ext-real Element of REAL
((Partial_Sums SumC) . n) + (Sum (SumC ^\ (n + 1))) is V11() real ext-real Element of REAL
- (Sum (SumC ^\ (n + 1))) is V11() real ext-real Element of REAL
abs (- (Sum (SumC ^\ (n + 1)))) is V11() real ext-real Element of REAL
abs (Sum (SumC ^\ (n + 1))) is V11() real ext-real Element of REAL
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Partial_Sums SumC) . R is V11() real ext-real Element of REAL
r is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(Partial_Sums SumC) . r is V11() real ext-real Element of REAL
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
R + s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums SumC) . (R + s) is V11() real ext-real Element of REAL
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R + (s + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums SumC) . (R + (s + 1)) is V11() real ext-real Element of REAL
(R + s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums SumC) . ((R + s) + 1) is V11() real ext-real Element of REAL
SumC . ((R + s) + 1) is V11() real ext-real Element of REAL
((Partial_Sums SumC) . (R + s)) + (SumC . ((R + s) + 1)) is V11() real ext-real Element of REAL
((Partial_Sums SumC) . (R + s)) + 0 is V11() real ext-real Element of REAL
R + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums SumC) . (R + 0) is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
s - c₆ is V11() real V30() V31() ext-real Element of INT
c₆ + (s - c₆) is V11() real V30() V31() ext-real Element of INT
SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum SumC is V11() real ext-real Element of REAL
R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (SumC,R) is V11() real ext-real Element of REAL
Sum R is V11() real ext-real Element of REAL
(Sum SumC) * (Sum R) is V11() real ext-real Element of REAL
abs SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums (abs SumC) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums R is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums SumC is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Partial_Sums (SumC,R) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Fr1 is V11() real ext-real set
abs (Sum R) is V11() real ext-real Element of REAL
(abs (Sum R)) + 1 is V11() real ext-real Element of REAL
3 * ((abs (Sum R)) + 1) is V11() real ext-real Element of REAL
Fr1 / (3 * ((abs (Sum R)) + 1)) is V11() real ext-real Element of COMPLEX
0 + 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
3 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
lim (Partial_Sums SumC) is V11() real ext-real Element of REAL
CatalR is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Sum (abs SumC) is V11() real ext-real Element of REAL
(Sum (abs SumC)) + 1 is V11() real ext-real Element of REAL
3 * ((Sum (abs SumC)) + 1) is V11() real ext-real Element of REAL
Fr1 / (3 * ((Sum (abs SumC)) + 1)) is V11() real ext-real Element of COMPLEX
max (1,CatalR) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of REAL
(Fr1 / (3 * ((abs (Sum R)) + 1))) * ((abs (Sum R)) + 1) is V11() real ext-real Element of REAL
Fr1 / 3 is V11() real ext-real Element of COMPLEX
lim (Partial_Sums R) is V11() real ext-real Element of REAL
k is V11() real ext-real set
3 * k is V11() real ext-real Element of REAL
Fr1 / (3 * k) is V11() real ext-real Element of COMPLEX
(abs (Sum R)) + 0 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
SumC . n2 is V11() real ext-real Element of REAL
abs (SumC . n2) is V11() real ext-real Element of REAL
(abs SumC) . n2 is V11() real ext-real Element of REAL
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(abs SumC) . n2 is V11() real ext-real Element of REAL
((Sum (abs SumC)) + 1) * (Fr1 / (3 * ((Sum (abs SumC)) + 1))) is V11() real ext-real Element of REAL
0 * 3 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
n2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums (abs SumC)) . n1 is V11() real ext-real Element of REAL
n1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
max ((n1 + 1),n2) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of REAL
max ((max (1,CatalR)),(max ((n1 + 1),n2))) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of REAL
M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
M * 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
2M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums (SumC,R)) . m is V11() real ext-real Element of REAL
((Partial_Sums (SumC,R)) . m) - ((Sum SumC) * (Sum R)) is V11() real ext-real Element of REAL
abs (((Partial_Sums (SumC,R)) . m) - ((Sum SumC) * (Sum R))) is V11() real ext-real Element of REAL
M - 1 is V11() real V30() V31() ext-real Element of INT
M1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
M1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums (abs SumC)) . M1 is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . m is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . m) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . m) - ((Partial_Sums (abs SumC)) . n1) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . m) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . m) - ((Partial_Sums (abs SumC)) . n1)) is V11() real ext-real Element of REAL
(Partial_Sums SumC) . m is V11() real ext-real Element of REAL
(Sum R) * ((Partial_Sums SumC) . m) is V11() real ext-real Element of REAL
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
Sum Fr is V11() real ext-real Element of COMPLEX
((Sum R) * ((Partial_Sums SumC) . m)) - (Sum Fr) is V11() real ext-real Element of REAL
dom Fr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
abs (Sum Fr) is V11() real ext-real Element of REAL
absFr is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom absFr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum absFr is V11() real ext-real Element of COMPLEX
M + M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
len absFr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom absFr is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
absFr | M is T-Sequence-like Relation-like M -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
rng absFr is finite V50() V51() V52() set
len (absFr | M) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom (absFr | M) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
((Partial_Sums (abs SumC)) . n1) - ((Partial_Sums (abs SumC)) . n1) is V11() real ext-real Element of REAL
abs (((Partial_Sums (abs SumC)) . m) - ((Partial_Sums (abs SumC)) . n1)) is V11() real ext-real Element of REAL
Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
(absFr | M) ^ Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
len Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(len (absFr | M)) + (len Fr1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
m - M is V11() real V30() V31() ext-real Element of INT
(m - M) + 1 is V11() real V30() V31() ext-real Element of INT
Fr1 | ((m - M) + 1) is Relation-like (m - M) + 1 -defined NAT -defined REAL -valued Function-like V35() V36() V37() finite set
(Partial_Sums R) . m is V11() real ext-real Element of REAL
((Partial_Sums R) . m) - (Sum R) is V11() real ext-real Element of REAL
abs (((Partial_Sums R) . m) - (Sum R)) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
M + k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(M + k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 | (k + 1) is T-Sequence-like Relation-like k + 1 -defined NAT -defined REAL -valued rng Fr1 -valued Function-like V35() V36() V37() finite V213() set
rng Fr1 is finite V50() V51() V52() set
Sum (Fr1 | (k + 1)) is V11() real ext-real Element of COMPLEX
(Partial_Sums (abs SumC)) . (M + k) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . (M + k)) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . (M + k)) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
M + (k + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(M + (k + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(k + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 | ((k + 1) + 1) is T-Sequence-like Relation-like (k + 1) + 1 -defined NAT -defined REAL -valued rng Fr1 -valued Function-like V35() V36() V37() finite V213() set
Sum (Fr1 | ((k + 1) + 1)) is V11() real ext-real Element of COMPLEX
(Partial_Sums (abs SumC)) . (M + (k + 1)) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . (M + (k + 1))) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . (M + (k + 1))) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
SumC . (M + (k + 1)) is V11() real ext-real Element of REAL
abs (SumC . (M + (k + 1))) is V11() real ext-real Element of REAL
(abs SumC) . (M + (k + 1)) is V11() real ext-real Element of REAL
Fr . (M + (k + 1)) is V11() real ext-real Element of REAL
m -' (M + (k + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(m -' (M + (k + 1))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((m -' (M + (k + 1))) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((m -' (M + (k + 1))) + 1)) is V11() real ext-real Element of REAL
(SumC . (M + (k + 1))) * (Sum (R ^\ ((m -' (M + (k + 1))) + 1))) is V11() real ext-real Element of REAL
abs (Fr . (M + (k + 1))) is V11() real ext-real Element of REAL
abs (Sum (R ^\ ((m -' (M + (k + 1))) + 1))) is V11() real ext-real Element of REAL
(abs (SumC . (M + (k + 1)))) * (abs (Sum (R ^\ ((m -' (M + (k + 1))) + 1)))) is V11() real ext-real Element of REAL
Fr1 . (k + 1) is V11() real ext-real Element of REAL
(Fr1 . (k + 1)) + (Sum (Fr1 | (k + 1))) is V11() real ext-real Element of REAL
absFr . (M + (k + 1)) is V11() real ext-real Element of REAL
(M + (k + 1)) - M is V11() real V30() V31() ext-real Element of INT
Fr1 . ((M + (k + 1)) - M) is V11() real ext-real Element of REAL
k * (abs (SumC . (M + (k + 1)))) is V11() real ext-real Element of REAL
k * ((abs SumC) . (M + (k + 1))) is V11() real ext-real Element of REAL
(k * ((abs SumC) . (M + (k + 1)))) + (k * (((Partial_Sums (abs SumC)) . (M + k)) - ((Partial_Sums (abs SumC)) . M1))) is V11() real ext-real Element of REAL
((abs SumC) . (M + (k + 1))) + ((Partial_Sums (abs SumC)) . (M + k)) is V11() real ext-real Element of REAL
(((abs SumC) . (M + (k + 1))) + ((Partial_Sums (abs SumC)) . (M + k))) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
k * ((((abs SumC) . (M + (k + 1))) + ((Partial_Sums (abs SumC)) . (M + k))) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . ((M + k) + 1) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . ((M + k) + 1)) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . ((M + k) + 1)) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
k * (Fr1 / (3 * k)) is V11() real ext-real Element of REAL
M + (m - M) is V11() real V30() V31() ext-real Element of INT
m -' M is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
M + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(M + 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined REAL -valued rng Fr1 -valued Function-like V35() V36() V37() finite V213() set
rng Fr1 is finite V50() V51() V52() set
Sum (Fr1 | (0 + 1)) is V11() real ext-real Element of COMPLEX
(Partial_Sums (abs SumC)) . (M + 0) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . (M + 0)) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
k * (((Partial_Sums (abs SumC)) . (M + 0)) - ((Partial_Sums (abs SumC)) . M1)) is V11() real ext-real Element of REAL
Fr . M is V11() real ext-real Element of REAL
SumC . M is V11() real ext-real Element of REAL
(m -' M) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((m -' M) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((m -' M) + 1)) is V11() real ext-real Element of REAL
(SumC . M) * (Sum (R ^\ ((m -' M) + 1))) is V11() real ext-real Element of REAL
M + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(M + 1) - M is V11() real V30() V31() ext-real Element of INT
(m + 1) - M is V11() real V30() V31() ext-real Element of INT
Fr1 | 1 is T-Sequence-like Relation-like 1 -defined NAT -defined REAL -valued rng Fr1 -valued Function-like V35() V36() V37() finite V213() set
dom (Fr1 | 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool 1
bool 1 is non empty finite V49() set
absFr . M is V11() real ext-real Element of REAL
M - M is V11() real V30() V31() ext-real Element of INT
Fr1 . (M - M) is V11() real ext-real Element of REAL
Fr1 . 0 is V11() real ext-real Element of REAL
abs (Fr . M) is V11() real ext-real Element of REAL
abs (SumC . M) is V11() real ext-real Element of REAL
abs (Sum (R ^\ ((m -' M) + 1))) is V11() real ext-real Element of REAL
(abs (SumC . M)) * (abs (Sum (R ^\ ((m -' M) + 1)))) is V11() real ext-real Element of REAL
(Fr1 | 1) . 0 is V11() real ext-real Element of REAL
(abs SumC) . (M1 + 1) is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . M1) + ((abs SumC) . (M1 + 1)) is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . (M1 + 1) is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . M is V11() real ext-real Element of REAL
((Partial_Sums (abs SumC)) . M) - ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
Sum (Fr1 | 1) is V11() real ext-real Element of COMPLEX
Sum Fr1 is V11() real ext-real Element of COMPLEX
(abs SumC) . 0 is V11() real ext-real Element of REAL
((abs SumC) . 0) * (abs (((Partial_Sums R) . m) - (Sum R))) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((abs SumC) . 0) is V11() real ext-real Element of REAL
Fr . 0 is V11() real ext-real Element of REAL
SumC . 0 is V11() real ext-real Element of REAL
m -' 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(m -' 0) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((m -' 0) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((m -' 0) + 1)) is V11() real ext-real Element of REAL
(SumC . 0) * (Sum (R ^\ ((m -' 0) + 1))) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . M1) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * (Sum (abs SumC)) is V11() real ext-real Element of REAL
(Partial_Sums R) . (m -' 0) is V11() real ext-real Element of REAL
((Partial_Sums R) . (m -' 0)) + (Sum (R ^\ ((m -' 0) + 1))) is V11() real ext-real Element of REAL
(Sum R) - ((Partial_Sums R) . m) is V11() real ext-real Element of REAL
((Partial_Sums SumC) . m) - (Sum SumC) is V11() real ext-real Element of REAL
abs (((Partial_Sums SumC) . m) - (Sum SumC)) is V11() real ext-real Element of REAL
(Sum R) * (((Partial_Sums SumC) . m) - (Sum SumC)) is V11() real ext-real Element of REAL
abs ((Sum R) * (((Partial_Sums SumC) . m) - (Sum SumC))) is V11() real ext-real Element of REAL
(abs (Sum R)) * (abs (((Partial_Sums SumC) . m) - (Sum SumC))) is V11() real ext-real Element of REAL
(abs (Sum R)) * (Fr1 / (3 * ((abs (Sum R)) + 1))) is V11() real ext-real Element of REAL
Sum (absFr | M) is V11() real ext-real Element of COMPLEX
(Sum (absFr | M)) + (Sum Fr1) is V11() real ext-real Element of COMPLEX
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
absFr | (k + 1) is T-Sequence-like Relation-like k + 1 -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
Sum (absFr | (k + 1)) is V11() real ext-real Element of COMPLEX
(Partial_Sums (abs SumC)) . k is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . k) is V11() real ext-real Element of REAL
(k + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
absFr | ((k + 1) + 1) is T-Sequence-like Relation-like (k + 1) + 1 -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
Sum (absFr | ((k + 1) + 1)) is V11() real ext-real Element of COMPLEX
(Partial_Sums (abs SumC)) . (k + 1) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . (k + 1)) is V11() real ext-real Element of REAL
k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
SumC . k1 is V11() real ext-real Element of REAL
abs (SumC . k1) is V11() real ext-real Element of REAL
(abs SumC) . k1 is V11() real ext-real Element of REAL
2M - M is V11() real V30() V31() ext-real Element of INT
m - k1 is V11() real V30() V31() ext-real Element of INT
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * (abs (SumC . k1)) is V11() real ext-real Element of REAL
absFr | k1 is T-Sequence-like Relation-like k1 -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
Sum (absFr | k1) is V11() real ext-real Element of COMPLEX
((Fr1 / (3 * ((Sum (abs SumC)) + 1))) * (abs (SumC . k1))) + (Sum (absFr | k1)) is V11() real ext-real Element of REAL
((Fr1 / (3 * ((Sum (abs SumC)) + 1))) * (abs (SumC . k1))) + ((Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . k)) is V11() real ext-real Element of REAL
((abs SumC) . k1) + ((Partial_Sums (abs SumC)) . k) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * (((abs SumC) . k1) + ((Partial_Sums (abs SumC)) . k)) is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . k1 is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . k1) is V11() real ext-real Element of REAL
k1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
absFr | (k1 + 1) is T-Sequence-like Relation-like k1 + 1 -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
Sum (absFr | (k1 + 1)) is V11() real ext-real Element of COMPLEX
absFr . k1 is V11() real ext-real Element of REAL
(absFr . k1) + (Sum (absFr | k1)) is V11() real ext-real Element of REAL
m -' k1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Partial_Sums R) . (m -' k1) is V11() real ext-real Element of REAL
((Partial_Sums R) . (m -' k1)) - (Sum R) is V11() real ext-real Element of REAL
abs (((Partial_Sums R) . (m -' k1)) - (Sum R)) is V11() real ext-real Element of REAL
(Sum R) - ((Partial_Sums R) . (m -' k1)) is V11() real ext-real Element of REAL
abs ((Sum R) - ((Partial_Sums R) . (m -' k1))) is V11() real ext-real Element of REAL
(m -' k1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
R ^\ ((m -' k1) + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (R ^\ ((m -' k1) + 1)) is V11() real ext-real Element of REAL
((Partial_Sums R) . (m -' k1)) + (Sum (R ^\ ((m -' k1) + 1))) is V11() real ext-real Element of REAL
(abs ((Sum R) - ((Partial_Sums R) . (m -' k1)))) * (abs (SumC . k1)) is V11() real ext-real Element of REAL
(SumC . k1) * (Sum (R ^\ ((m -' k1) + 1))) is V11() real ext-real Element of REAL
abs ((SumC . k1) * (Sum (R ^\ ((m -' k1) + 1)))) is V11() real ext-real Element of REAL
Fr . k1 is V11() real ext-real Element of REAL
abs (Fr . k1) is V11() real ext-real Element of REAL
absFr | (0 + 1) is T-Sequence-like Relation-like 0 + 1 -defined NAT -defined REAL -valued rng absFr -valued Function-like V35() V36() V37() finite V213() set
Sum (absFr | (0 + 1)) is V11() real ext-real Element of COMPLEX
absFr . 0 is V11() real ext-real Element of REAL
absFr | 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined 0 -defined NAT -defined REAL -valued RAT -valued rng absFr -valued Function-like one-to-one constant functional real V30() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() set
Sum (absFr | 0) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of COMPLEX
(absFr . 0) + (Sum (absFr | 0)) is V11() real ext-real Element of REAL
abs (Fr . 0) is V11() real ext-real Element of REAL
abs (SumC . 0) is V11() real ext-real Element of REAL
abs (Sum (R ^\ ((m -' 0) + 1))) is V11() real ext-real Element of REAL
(abs (SumC . 0)) * (abs (Sum (R ^\ ((m -' 0) + 1)))) is V11() real ext-real Element of REAL
((abs SumC) . 0) * (abs (Sum (R ^\ ((m -' 0) + 1)))) is V11() real ext-real Element of REAL
(Partial_Sums (abs SumC)) . 0 is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Partial_Sums (abs SumC)) . 0) is V11() real ext-real Element of REAL
(Sum (abs SumC)) + 0 is V11() real ext-real Element of REAL
(Fr1 / (3 * ((Sum (abs SumC)) + 1))) * ((Sum (abs SumC)) + 1) is V11() real ext-real Element of REAL
(Fr1 / 3) + (Fr1 / 3) is V11() real ext-real Element of COMPLEX
((Sum R) * (((Partial_Sums SumC) . m) - (Sum SumC))) - (Sum Fr) is V11() real ext-real Element of REAL
(abs ((Sum R) * (((Partial_Sums SumC) . m) - (Sum SumC)))) + (abs (Sum Fr)) is V11() real ext-real Element of REAL
(Fr1 / (3 * ((abs (Sum R)) + 1))) * (abs (Sum R)) is V11() real ext-real Element of REAL
(Fr1 / 3) + ((Fr1 / 3) + (Fr1 / 3)) is V11() real ext-real Element of COMPLEX
lim (Partial_Sums (SumC,R)) is V11() real ext-real Element of REAL
1 / 4 is V11() real ext-real non negative Element of COMPLEX
SumC is set
abs 1 is V11() real V31() ext-real Element of REAL
R is V11() real ext-real Element of REAL
abs R is V11() real ext-real Element of REAL
4 * (abs R) is V11() real ext-real Element of REAL
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(4 * (abs R)) GeoSeq is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
abs Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(abs Cat) . c₆ is V11() real ext-real Element of REAL
((4 * (abs R)) GeoSeq) . c₆ is V11() real ext-real Element of REAL
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(abs Cat) . (c₆ + 1) is V11() real ext-real Element of REAL
((4 * (abs R)) GeoSeq) . (c₆ + 1) is V11() real ext-real Element of REAL
(4 * (abs R)) * ((abs Cat) . c₆) is V11() real ext-real Element of REAL
(4 * (abs R)) * (((4 * (abs R)) GeoSeq) . c₆) is V11() real ext-real Element of REAL
R |^ (c₆ + 1) is V11() real ext-real Element of REAL
abs (R |^ (c₆ + 1)) is V11() real ext-real Element of REAL
R |^ c₆ is V11() real ext-real Element of REAL
R * (R |^ c₆) is V11() real ext-real Element of REAL
(c₆ + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan ((c₆ + 1) + 1) is V11() real ext-real Element of REAL
abs (Catalan ((c₆ + 1) + 1)) is V11() real ext-real Element of REAL
Catalan (c₆ + 1) is V11() real ext-real Element of REAL
abs (Catalan (c₆ + 1)) is V11() real ext-real Element of REAL
4 * (abs (Catalan (c₆ + 1))) is V11() real ext-real Element of REAL
(abs (R |^ (c₆ + 1))) * (abs (Catalan ((c₆ + 1) + 1))) is V11() real ext-real Element of REAL
abs (R * (R |^ c₆)) is V11() real ext-real Element of REAL
(4 * (abs (Catalan (c₆ + 1)))) * (abs (R * (R |^ c₆))) is V11() real ext-real Element of REAL
abs (R |^ c₆) is V11() real ext-real Element of REAL
(abs R) * (abs (R |^ c₆)) is V11() real ext-real Element of REAL
(R |^ (c₆ + 1)) * (Catalan ((c₆ + 1) + 1)) is V11() real ext-real Element of REAL
abs ((R |^ (c₆ + 1)) * (Catalan ((c₆ + 1) + 1))) is V11() real ext-real Element of REAL
(abs (Catalan (c₆ + 1))) * (abs (R |^ c₆)) is V11() real ext-real Element of REAL
(4 * (abs R)) * ((abs (Catalan (c₆ + 1))) * (abs (R |^ c₆))) is V11() real ext-real Element of REAL
Cat . (c₆ + 1) is V11() real ext-real Element of REAL
abs (Cat . (c₆ + 1)) is V11() real ext-real Element of REAL
(Catalan (c₆ + 1)) * (R |^ c₆) is V11() real ext-real Element of REAL
abs ((Catalan (c₆ + 1)) * (R |^ c₆)) is V11() real ext-real Element of REAL
(4 * (abs R)) * (abs ((Catalan (c₆ + 1)) * (R |^ c₆))) is V11() real ext-real Element of REAL
Cat . c₆ is V11() real ext-real Element of REAL
abs (Cat . c₆) is V11() real ext-real Element of REAL
(4 * (abs R)) * (abs (Cat . c₆)) is V11() real ext-real Element of REAL
(abs Cat) . (c₆ + 1) is V11() real ext-real Element of REAL
Cat . 0 is V11() real ext-real Element of REAL
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (0 + 1) is V11() real ext-real Element of REAL
R |^ 0 is V11() real ext-real Element of REAL
(Catalan (0 + 1)) * (R |^ 0) is V11() real ext-real Element of REAL
(abs Cat) . 0 is V11() real ext-real Element of REAL
abs (R |^ 0) is V11() real ext-real Element of REAL
(4 * (abs R)) |^ 0 is V11() real ext-real Element of REAL
(abs Cat) . 0 is V11() real ext-real Element of REAL
((4 * (abs R)) GeoSeq) . 0 is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(abs Cat) . c₆ is V11() real ext-real Element of REAL
((4 * (abs R)) GeoSeq) . c₆ is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(abs Cat) . c₆ is V11() real ext-real Element of REAL
Cat . c₆ is V11() real ext-real Element of REAL
abs (Cat . c₆) is V11() real ext-real Element of REAL
Sum Cat is V11() real ext-real Element of REAL
c₆ is V11() real ext-real set
abs c₆ is V11() real ext-real Element of REAL
Cat ^\ 1 is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
R (#) Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(Cat,(R (#) Cat)) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
n is set
(Cat ^\ 1) . n is V11() real ext-real Element of REAL
(Cat,(R (#) Cat)) . n is V11() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Cat,(R (#) Cat)) . n is V11() real ext-real Element of REAL
Fr1 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Fr1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
Sum Fr1 is V11() real ext-real Element of COMPLEX
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan ((n + 1) + 1) is V11() real ext-real Element of REAL
Catal is T-Sequence-like Relation-like NAT -defined NAT -valued Function-like V35() V36() V37() V38() finite nonnegative-yielding V213() set
Sum Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of COMPLEX
dom Catal is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
rng Catal is finite V50() V51() V52() V53() V54() V55() Element of bool NAT
R |^ (n + 1) is V11() real ext-real Element of REAL
Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal . Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R |^ (n + 1)) * (Catal . Fr2) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Catal . k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(R |^ (n + 1)) * (Catal . k) is V11() real ext-real Element of REAL
Fr2 is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
dom Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of bool NAT
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(n + 1) -' k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(n + 1) - k is V11() real V30() V31() ext-real Element of INT
n - k is V11() real V30() V31() ext-real Element of INT
k + (n - k) is V11() real V30() V31() ext-real Element of INT
n -' k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Fr1 . k is V11() real ext-real Element of REAL
Cat . k is V11() real ext-real Element of REAL
(R (#) Cat) . (n - k) is V11() real ext-real Element of REAL
(Cat . k) * ((R (#) Cat) . (n - k)) is V11() real ext-real Element of REAL
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (k + 1) is V11() real ext-real Element of REAL
R |^ k is V11() real ext-real Element of REAL
(Catalan (k + 1)) * (R |^ k) is V11() real ext-real Element of REAL
((Catalan (k + 1)) * (R |^ k)) * ((R (#) Cat) . (n - k)) is V11() real ext-real Element of REAL
Cat . (n - k) is V11() real ext-real Element of REAL
R * (Cat . (n - k)) is V11() real ext-real Element of REAL
((Catalan (k + 1)) * (R |^ k)) * (R * (Cat . (n - k))) is V11() real ext-real Element of REAL
(n -' k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan ((n -' k) + 1) is V11() real ext-real Element of REAL
R |^ (n -' k) is V11() real ext-real Element of REAL
(Catalan ((n -' k) + 1)) * (R |^ (n -' k)) is V11() real ext-real Element of REAL
R * ((Catalan ((n -' k) + 1)) * (R |^ (n -' k))) is V11() real ext-real Element of REAL
((Catalan (k + 1)) * (R |^ k)) * (R * ((Catalan ((n -' k) + 1)) * (R |^ (n -' k)))) is V11() real ext-real Element of REAL
Catalan ((n + 1) -' k) is V11() real ext-real Element of REAL
(Catalan (k + 1)) * (Catalan ((n + 1) -' k)) is V11() real ext-real Element of REAL
((Catalan (k + 1)) * (Catalan ((n + 1) -' k))) * R is V11() real ext-real Element of REAL
(R |^ k) * (R |^ (n -' k)) is V11() real ext-real Element of REAL
(((Catalan (k + 1)) * (Catalan ((n + 1) -' k))) * R) * ((R |^ k) * (R |^ (n -' k))) is V11() real ext-real Element of REAL
R |^ n is V11() real ext-real Element of REAL
(((Catalan (k + 1)) * (Catalan ((n + 1) -' k))) * R) * (R |^ n) is V11() real ext-real Element of REAL
Catal . k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(Catal . k) * R is V11() real ext-real Element of REAL
((Catal . k) * R) * (R |^ n) is V11() real ext-real Element of REAL
R * (R |^ n) is V11() real ext-real Element of REAL
(Catal . k) * (R * (R |^ n)) is V11() real ext-real Element of REAL
(Catal . k) * (R |^ (n + 1)) is V11() real ext-real Element of REAL
Fr2 . k is V11() real ext-real Element of REAL
len Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
dom Fr2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
CatalR is T-Sequence-like Relation-like NAT -defined REAL -valued Function-like V35() V36() V37() finite V213() set
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Fr2 . k is V11() real ext-real Element of REAL
CatalR . k is V11() real ext-real Element of REAL
(R |^ (n + 1)) * (CatalR . k) is V11() real ext-real Element of REAL
Sum Fr2 is V11() real ext-real Element of COMPLEX
Sum CatalR is V11() real ext-real Element of COMPLEX
(R |^ (n + 1)) * (Sum CatalR) is V11() real ext-real Element of REAL
Cat . (n + 1) is V11() real ext-real Element of REAL
(Cat ^\ 1) . n is V11() real ext-real Element of REAL
abs (4 * (abs R)) is V11() real ext-real Element of REAL
(Sum Cat) |^ 2 is V11() real ext-real Element of REAL
c₆ * ((Sum Cat) |^ 2) is V11() real ext-real Element of REAL
1 + (c₆ * ((Sum Cat) |^ 2)) is V11() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat . n is V11() real ext-real Element of REAL
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (n + 1) is V11() real ext-real Element of REAL
c₆ |^ n is V11() real ext-real set
(Catalan (n + 1)) * (c₆ |^ n) is V11() real ext-real Element of REAL
Partial_Sums Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(Partial_Sums Cat) . 0 is V11() real ext-real Element of REAL
4 * (1 / 4) is V11() real ext-real non negative Element of REAL
Sum (R (#) Cat) is V11() real ext-real Element of REAL
R * (Sum Cat) is V11() real ext-real Element of REAL
Cat ^\ (0 + 1) is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum (Cat ^\ (0 + 1)) is V11() real ext-real Element of REAL
(Sum Cat) * (R * (Sum Cat)) is V11() real ext-real Element of REAL
(Sum Cat) * (Sum Cat) is V11() real ext-real Element of REAL
R * ((Sum Cat) * (Sum Cat)) is V11() real ext-real Element of REAL
1 + (R * ((Sum Cat) * (Sum Cat))) is V11() real ext-real Element of REAL
SumC is non empty Relation-like REAL -defined REAL -valued Function-like V22( REAL ) quasi_total V35() V36() V37() Element of bool [:REAL,REAL:]
R is V11() real ext-real set
SumC . R is V11() real ext-real Element of REAL
r is V11() real ext-real set
SumC . r is V11() real ext-real Element of REAL
abs R is V11() real ext-real Element of REAL
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum Cat is V11() real ext-real Element of REAL
(Sum Cat) |^ 2 is V11() real ext-real Element of REAL
R * ((Sum Cat) |^ 2) is V11() real ext-real Element of REAL
1 + (R * ((Sum Cat) |^ 2)) is V11() real ext-real Element of REAL
abs r is V11() real ext-real Element of REAL
s is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum s is V11() real ext-real Element of REAL
(Sum s) |^ 2 is V11() real ext-real Element of REAL
r * ((Sum s) |^ 2) is V11() real ext-real Element of REAL
1 + (r * ((Sum s) |^ 2)) is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
r |^ c₆ is V11() real ext-real set
R |^ c₆ is V11() real ext-real set
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (c₆ + 1) is V11() real ext-real Element of REAL
(Catalan (c₆ + 1)) * (r |^ c₆) is V11() real ext-real Element of REAL
(Catalan (c₆ + 1)) * (R |^ c₆) is V11() real ext-real Element of REAL
Cat . c₆ is V11() real ext-real Element of REAL
s . c₆ is V11() real ext-real Element of REAL
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= 0 & not 1 / 4 <= b₁ & SumC . b₁ = (1 + (sqrt (1 - (4 * b₁)))) / (2 * b₁) ) } is set
r is V11() real ext-real set
abs r is V11() real ext-real Element of REAL
SumC . r is V11() real ext-real Element of REAL
4 * r is V11() real ext-real Element of REAL
1 - (4 * r) is V11() real ext-real Element of REAL
sqrt (1 - (4 * r)) is V11() real ext-real Element of REAL
1 - (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
1 + (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
(1 / 4) * 4 is V11() real ext-real non negative Element of REAL
(4 * r) - (4 * r) is V11() real ext-real Element of REAL
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum Cat is V11() real ext-real Element of REAL
(Sum Cat) |^ 2 is V11() real ext-real Element of REAL
r * ((Sum Cat) |^ 2) is V11() real ext-real Element of REAL
1 + (r * ((Sum Cat) |^ 2)) is V11() real ext-real Element of REAL
(Sum Cat) ^2 is V11() real ext-real Element of REAL
K37((Sum Cat),(Sum Cat)) is V11() real ext-real set
r * ((Sum Cat) ^2) is V11() real ext-real Element of REAL
1 + (r * ((Sum Cat) ^2)) is V11() real ext-real Element of REAL
- 1 is V11() real V30() V31() ext-real non positive Element of INT
(- 1) * (Sum Cat) is V11() real ext-real Element of REAL
(r * ((Sum Cat) ^2)) + ((- 1) * (Sum Cat)) is V11() real ext-real Element of REAL
((r * ((Sum Cat) ^2)) + ((- 1) * (Sum Cat))) + 1 is V11() real ext-real Element of REAL
delta (r,(- 1),1) is set
(- 1) ^2 is set
K37((- 1),(- 1)) is V11() real V30() ext-real non negative set
K37(4,r) is V11() real ext-real set
K37(K37(4,r),1) is V11() real ext-real set
K40(((- 1) ^2),K37(K37(4,r),1)) is set
- (- 1) is V11() real V30() V31() ext-real non negative Element of INT
r is V11() real ext-real set
4 * r is V11() real ext-real Element of REAL
1 - (4 * r) is V11() real ext-real Element of REAL
sqrt (1 - (4 * r)) is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
Cat is V11() real ext-real set
4 * Cat is V11() real ext-real Element of REAL
1 - (4 * Cat) is V11() real ext-real Element of REAL
sqrt (1 - (4 * Cat)) is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * Cat))) is V11() real ext-real Element of REAL
2 * Cat is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * Cat)))) / (2 * Cat) is V11() real ext-real Element of COMPLEX
4 * (1 / 4) is V11() real ext-real non negative Element of REAL
(4 * Cat) - (4 * Cat) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * Cat)))) / (2 * r) is V11() real ext-real Element of COMPLEX
2 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
r is set
Cat is V11() real ext-real Element of REAL
SumC . Cat is V11() real ext-real Element of REAL
4 * Cat is V11() real ext-real Element of REAL
1 - (4 * Cat) is V11() real ext-real Element of REAL
sqrt (1 - (4 * Cat)) is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * Cat))) is V11() real ext-real Element of REAL
2 * Cat is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * Cat)))) / (2 * Cat) is V11() real ext-real Element of COMPLEX
s is V11() real ext-real set
abs s is V11() real ext-real Element of REAL
4 * (1 / 4) is V11() real ext-real non negative Element of REAL
4 * s is V11() real ext-real Element of REAL
1 - (4 * s) is V11() real ext-real Element of REAL
(4 * s) - (4 * s) is V11() real ext-real Element of REAL
sqrt (1 - (4 * s)) is V11() real ext-real Element of REAL
1 - (sqrt (1 - (4 * s))) is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real V30() V31() ext-real positive non negative Element of INT
2 * s is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * s)))) / (2 * s) is V11() real ext-real Element of COMPLEX
1 / (2 * s) is V11() real ext-real Element of COMPLEX
2 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
{Cat} is non empty trivial finite V50() V51() V52() 1 -element Element of bool REAL
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= 0 & not 1 / 4 <= b₁ & SumC . b₁ = (1 + (sqrt (1 - (4 * b₁)))) / (2 * b₁) ) } \ {Cat} is Element of bool { b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= 0 & not 1 / 4 <= b₁ & SumC . b₁ = (1 + (sqrt (1 - (4 * b₁)))) / (2 * b₁) ) }
bool { b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= 0 & not 1 / 4 <= b₁ & SumC . b₁ = (1 + (sqrt (1 - (4 * b₁)))) / (2 * b₁) ) } is non empty set
c₆ is set
n is V11() real ext-real Element of REAL
SumC . n is V11() real ext-real Element of REAL
4 * n is V11() real ext-real Element of REAL
1 - (4 * n) is V11() real ext-real Element of REAL
sqrt (1 - (4 * n)) is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * n))) is V11() real ext-real Element of REAL
2 * n is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * n)))) / (2 * n) is V11() real ext-real Element of COMPLEX
SumC . s is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * s))) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * s)))) / (2 * s) is V11() real ext-real Element of COMPLEX
(4 * Cat) - (4 * Cat) is V11() real ext-real Element of REAL
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
1 / (2 * Cat) is V11() real ext-real Element of COMPLEX
r is V11() real ext-real set
abs r is V11() real ext-real Element of REAL
SumC . r is V11() real ext-real Element of REAL
4 * r is V11() real ext-real Element of REAL
1 - (4 * r) is V11() real ext-real Element of REAL
sqrt (1 - (4 * r)) is V11() real ext-real Element of REAL
1 - (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
1 + (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
r is V11() real ext-real set
abs r is V11() real ext-real Element of REAL
SumC . r is V11() real ext-real Element of REAL
4 * r is V11() real ext-real Element of REAL
1 - (4 * r) is V11() real ext-real Element of REAL
sqrt (1 - (4 * r)) is V11() real ext-real Element of REAL
1 - (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
2 * 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of NAT
abs (2 * r) is V11() real ext-real Element of REAL
- (2 * r) is V11() real ext-real Element of REAL
0 - (2 * r) is V11() real ext-real Element of REAL
0 - 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional real V30() V31() ext-real non positive non negative V35() V36() V37() V38() finite finite-yielding V49() V50() V51() V52() V53() V54() V55() V56() nonnegative-yielding cardinal {} -element Function-yielding V137() V213() Element of INT
- r is V11() real ext-real Element of REAL
abs (- r) is V11() real ext-real Element of REAL
4 * (- r) is V11() real ext-real Element of REAL
4 * (1 / 4) is V11() real ext-real non negative Element of REAL
(4 * (- r)) - (4 * (- r)) is V11() real ext-real Element of REAL
1 - (4 * (- r)) is V11() real ext-real Element of REAL
sqrt (1 - (4 * (- r))) is V11() real ext-real Element of REAL
1 - (sqrt (1 - (4 * (- r)))) is V11() real ext-real Element of REAL
1 - 0 is non empty V11() real V30() V31() ext-real positive non negative Element of INT
1 + (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
abs (1 + (sqrt (1 - (4 * r)))) is V11() real ext-real Element of REAL
(abs (1 + (sqrt (1 - (4 * r))))) / (abs (2 * r)) is V11() real ext-real Element of COMPLEX
2 * (- r) is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * (- r))))) / (2 * (- r)) is V11() real ext-real Element of COMPLEX
SumC . (- r) is V11() real ext-real Element of REAL
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum Cat is V11() real ext-real Element of REAL
(Sum Cat) |^ 2 is V11() real ext-real Element of REAL
(- r) * ((Sum Cat) |^ 2) is V11() real ext-real Element of REAL
1 + ((- r) * ((Sum Cat) |^ 2)) is V11() real ext-real Element of REAL
s is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum s is V11() real ext-real Element of REAL
(Sum s) |^ 2 is V11() real ext-real Element of REAL
r * ((Sum s) |^ 2) is V11() real ext-real Element of REAL
1 + (r * ((Sum s) |^ 2)) is V11() real ext-real Element of REAL
c₆ is set
n is epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
(- r) |^ n is V11() real ext-real Element of REAL
- 1 is V11() real V30() V31() ext-real non positive Element of INT
(- 1) * r is V11() real ext-real Element of REAL
((- 1) * r) |^ n is V11() real ext-real Element of REAL
(- 1) |^ n is V11() real ext-real set
r |^ n is V11() real ext-real set
((- 1) |^ n) * (r |^ n) is V11() real ext-real Element of REAL
abs ((- r) |^ n) is V11() real ext-real Element of REAL
abs ((- 1) |^ n) is V11() real ext-real Element of REAL
abs (r |^ n) is V11() real ext-real Element of REAL
(abs ((- 1) |^ n)) * (abs (r |^ n)) is V11() real ext-real Element of REAL
1 * (abs (r |^ n)) is V11() real ext-real Element of REAL
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (n + 1) is V11() real ext-real Element of REAL
abs (Catalan (n + 1)) is V11() real ext-real Element of REAL
Cat . n is V11() real ext-real Element of REAL
(abs (r |^ n)) * (abs (Catalan (n + 1))) is V11() real ext-real Element of REAL
(r |^ n) * (Catalan (n + 1)) is V11() real ext-real Element of REAL
abs ((r |^ n) * (Catalan (n + 1))) is V11() real ext-real Element of REAL
s . n is V11() real ext-real Element of REAL
abs (s . n) is V11() real ext-real Element of REAL
abs s is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
(abs s) . n is V11() real ext-real Element of REAL
(abs s) . c₆ is V11() real ext-real Element of REAL
Cat . c₆ is V11() real ext-real Element of REAL
0 - r is V11() real ext-real Element of REAL
abs (Sum s) is V11() real ext-real Element of REAL
Sum (abs s) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
abs ((1 + (sqrt (1 - (4 * r)))) / (2 * r)) is V11() real ext-real Element of REAL
r is V11() real ext-real set
abs r is V11() real ext-real Element of REAL
4 * r is V11() real ext-real Element of REAL
1 - (4 * r) is V11() real ext-real Element of REAL
sqrt (1 - (4 * r)) is V11() real ext-real Element of REAL
1 + (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 / (1 + (sqrt (1 - (4 * r)))) is V11() real ext-real Element of COMPLEX
1 - (sqrt (1 - (4 * r))) is V11() real ext-real Element of REAL
2 * r is V11() real ext-real Element of REAL
(1 - (sqrt (1 - (4 * r)))) / (2 * r) is V11() real ext-real Element of COMPLEX
SumC . r is V11() real ext-real Element of REAL
Cat is non empty Relation-like NAT -defined REAL -valued Function-like V22( NAT ) quasi_total V35() V36() V37() Element of bool [:NAT,REAL:]
Sum Cat is V11() real ext-real Element of REAL
(Sum Cat) |^ 2 is V11() real ext-real Element of REAL
r * ((Sum Cat) |^ 2) is V11() real ext-real Element of REAL
1 + (r * ((Sum Cat) |^ 2)) is V11() real ext-real Element of REAL
c₆ is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
Cat . c₆ is V11() real ext-real Element of REAL
c₆ + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() V31() ext-real positive non negative finite V50() V51() V52() V53() V54() V55() cardinal Element of NAT
Catalan (c₆ + 1) is V11() real ext-real Element of REAL
r |^ c₆ is V11() real ext-real set
(Catalan (c₆ + 1)) * (r |^ c₆) is V11() real ext-real Element of REAL
4 * (1 / 4) is V11() real ext-real non negative Element of REAL
(4 * r) - (4 * r) is V11() real ext-real Element of REAL
(1 + (sqrt (1 - (4 * r)))) / (1 + (sqrt (1 - (4 * r)))) is V11() real ext-real Element of COMPLEX
((1 - (sqrt (1 - (4 * r)))) / (2 * r)) * ((1 + (sqrt (1 - (4 * r)))) / (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
(1 - (sqrt (1 - (4 * r)))) * (1 + (sqrt (1 - (4 * r)))) is V11() real ext-real Element of REAL
(2 * r) * (1 + (sqrt (1 - (4 * r)))) is V11() real ext-real Element of REAL
((1 - (sqrt (1 - (4 * r)))) * (1 + (sqrt (1 - (4 * r))))) / ((2 * r) * (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
1 ^2 is V11() real ext-real Element of REAL
K37(1,1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative finite V50() V51() V52() V53() V54() V55() cardinal set
(sqrt (1 - (4 * r))) ^2 is V11() real ext-real Element of REAL
K37((sqrt (1 - (4 * r))),(sqrt (1 - (4 * r)))) is V11() real ext-real set
(1 ^2) - ((sqrt (1 - (4 * r))) ^2) is V11() real ext-real Element of REAL
((1 ^2) - ((sqrt (1 - (4 * r))) ^2)) / ((2 * r) * (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
1 - (1 - (4 * r)) is V11() real ext-real Element of REAL
(1 - (1 - (4 * r))) / ((2 * r) * (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
(2 * r) * 2 is V11() real ext-real Element of REAL
((2 * r) * 2) / ((2 * r) * (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
(2 * r) / (2 * r) is V11() real ext-real Element of COMPLEX
((2 * r) / (2 * r)) * (2 / (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of COMPLEX
1 * (2 / (1 + (sqrt (1 - (4 * r))))) is V11() real ext-real Element of REAL