:: RVSUM_1 semantic presentation

REAL is non empty V53() V54() V55() V59() V60() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V53() V54() V55() V56() V57() V58() V59() V60() cardinal limit_cardinal Element of bool REAL
bool REAL is V60() set
RAT is non empty V53() V54() V55() V56() V59() V60() set
0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
COMPLEX is non empty V53() V59() V60() set
INT is non empty V53() V54() V55() V56() V57() V59() V60() set
[:COMPLEX,COMPLEX:] is Relation-like complex-valued V60() set
bool [:COMPLEX,COMPLEX:] is V60() set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like complex-valued V60() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is V60() set
[:REAL,REAL:] is Relation-like complex-valued ext-real-valued real-valued V60() set
bool [:REAL,REAL:] is V60() set
[:[:REAL,REAL:],REAL:] is Relation-like complex-valued ext-real-valued real-valued V60() set
bool [:[:REAL,REAL:],REAL:] is V60() set
[:RAT,RAT:] is Relation-like RAT -valued complex-valued ext-real-valued real-valued V60() set
bool [:RAT,RAT:] is V60() set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued complex-valued ext-real-valued real-valued V60() set
bool [:[:RAT,RAT:],RAT:] is V60() set
[:INT,INT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued V60() set
bool [:INT,INT:] is V60() set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued V60() set
bool [:[:INT,INT:],INT:] is V60() set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued V60() set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued V60() set
bool [:[:NAT,NAT:],NAT:] is V60() set
omega is non empty epsilon-transitive epsilon-connected ordinal V53() V54() V55() V56() V57() V58() V59() V60() cardinal limit_cardinal set
bool omega is V60() set
bool NAT is V60() set
K101(NAT) is V27() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
2 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT
4 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
5 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
addcomplex is Relation-like Function-like V14([:COMPLEX,COMPLEX:]) V18([:COMPLEX,COMPLEX:], COMPLEX ) commutative associative having_a_unity complex-valued Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
multcomplex is Relation-like Function-like V14([:COMPLEX,COMPLEX:]) V18([:COMPLEX,COMPLEX:], COMPLEX ) commutative associative having_a_unity complex-valued Element of bool [:[:COMPLEX,COMPLEX:],COMPLEX:]
compreal is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
addreal is Relation-like Function-like V14([:REAL,REAL:]) V18([:REAL,REAL:], REAL ) commutative associative having_a_unity complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
diffreal is Relation-like Function-like V14([:REAL,REAL:]) V18([:REAL,REAL:], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
multreal is Relation-like Function-like V14([:REAL,REAL:]) V18([:REAL,REAL:], REAL ) commutative associative having_a_unity complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
the_unity_wrt addcomplex is complex Element of COMPLEX
the_unity_wrt addreal is complex ext-real real Element of REAL
the_unity_wrt multcomplex is complex Element of COMPLEX
the_unity_wrt multreal is complex ext-real real Element of REAL
card 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
the Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F is Relation-like complex-valued ext-real-valued real-valued set
rng F is V53() V54() V55() set
F is non empty set
[:REAL,F:] is Relation-like V60() set
bool [:REAL,F:] is V60() set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like Function-like non empty V14( REAL ) V18( REAL ,F) Element of bool [:REAL,F:]
i (#) g is Relation-like NAT -defined Function-like set
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg j is V53() V54() V55() V56() V57() V58() V60() j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
dom (i (#) g) is V53() V54() V55() V56() V57() V58() set
dom g is non empty set
(i) is V53() V54() V55() Element of bool REAL
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{1} is non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
F is complex ext-real real set
g is complex ext-real real set
<*F,g*> is Relation-like NAT -defined Function-like non empty V60() 2 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
<*i,j*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() 2 -element FinSequence-like FinSubsequence-like FinSequence of REAL
<*i*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
<*j*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*i*> ^ <*j*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
F is complex ext-real real set
g is complex ext-real real set
i is complex ext-real real set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(1 + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
j is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
p3 is complex ext-real real Element of REAL
<*j,q2,p3*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() 3 -element FinSequence-like FinSubsequence-like FinSequence of REAL
<*j*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*q2*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,q2] is set
{1,q2} is non empty V53() V54() V55() set
{{1,q2},{1}} is non empty set
{[1,q2]} is Relation-like Function-like constant non empty trivial 1 -element set
<*j*> ^ <*q2*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*p3*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,p3] is set
{1,p3} is non empty V53() V54() V55() set
{{1,p3},{1}} is non empty set
{[1,p3]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*j*> ^ <*q2*>) ^ <*p3*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
F is complex ext-real real set
g is complex ext-real real set
i is complex ext-real real set
j is complex ext-real real set
<*F,g,i,j*> is Relation-like NAT -defined Function-like non empty V60() 4 -element FinSequence-like FinSubsequence-like set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
<*j*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F,g,i*> ^ <*j*> is Relation-like NAT -defined Function-like non empty V60() 3 + 1 -element FinSequence-like FinSubsequence-like set
3 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
q2 is complex ext-real real Element of REAL
p3 is complex ext-real real Element of REAL
f3 is complex ext-real real Element of REAL
a is complex ext-real real Element of REAL
<*q2,p3,f3,a*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() 4 -element FinSequence-like FinSubsequence-like FinSequence of REAL
<*q2,p3,f3*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 3 -element FinSequence-like FinSubsequence-like set
<*q2*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,q2] is set
{1,q2} is non empty V53() V54() V55() set
{{1,q2},{1}} is non empty set
{[1,q2]} is Relation-like Function-like constant non empty trivial 1 -element set
<*p3*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,p3] is set
{1,p3} is non empty V53() V54() V55() set
{{1,p3},{1}} is non empty set
{[1,p3]} is Relation-like Function-like constant non empty trivial 1 -element set
<*q2*> ^ <*p3*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*f3*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,f3] is set
{1,f3} is non empty V53() V54() V55() set
{{1,f3},{1}} is non empty set
{[1,f3]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*q2*> ^ <*p3*>) ^ <*f3*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
<*a*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,a] is set
{1,a} is non empty V53() V54() V55() set
{{1,a},{1}} is non empty set
{[1,a]} is Relation-like Function-like constant non empty trivial 1 -element set
<*q2,p3,f3*> ^ <*a*> is Relation-like NAT -defined Function-like non empty V60() 3 + 1 -element FinSequence-like FinSubsequence-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F ^ g is Relation-like NAT -defined Function-like V60() FinSequence-like FinSubsequence-like set
rng (F ^ g) is set
(F) is V53() V54() V55() Element of bool REAL
(g) is V53() V54() V55() Element of bool REAL
(F) \/ (g) is V53() V54() V55() set
id REAL is Relation-like REAL -defined REAL -valued Function-like one-to-one non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued V47() non-decreasing Element of bool [:REAL,REAL:]
addreal * ((id REAL),compreal) is Relation-like Function-like V14([:REAL,REAL:]) V18([:REAL,REAL:], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
F is Relation-like Function-like V14([:REAL,REAL:]) V18([:REAL,REAL:], REAL ) complex-valued ext-real-valued real-valued Element of bool [:[:REAL,REAL:],REAL:]
g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
diffreal . (g,i) is complex ext-real real Element of REAL
[g,i] is set
{g,i} is non empty V53() V54() V55() set
{g} is non empty trivial V53() V54() V55() 1 -element set
{{g,i},{g}} is non empty set
diffreal . [g,i] is complex ext-real real set
g - i is complex ext-real real Element of REAL
- i is complex ext-real real Element of REAL
g + (- i) is complex ext-real real Element of REAL
addreal . (g,(- i)) is complex ext-real real Element of REAL
[g,(- i)] is set
{g,(- i)} is non empty V53() V54() V55() set
{{g,(- i)},{g}} is non empty set
addreal . [g,(- i)] is complex ext-real real set
compreal . i is complex ext-real real Element of REAL
addreal . (g,(compreal . i)) is complex ext-real real Element of REAL
[g,(compreal . i)] is set
{g,(compreal . i)} is non empty V53() V54() V55() set
{{g,(compreal . i)},{g}} is non empty set
addreal . [g,(compreal . i)] is complex ext-real real set
(addreal * ((id REAL),compreal)) . (g,i) is complex ext-real real Element of REAL
(addreal * ((id REAL),compreal)) . [g,i] is complex ext-real real set
F is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
g is complex ext-real real set
F . g is complex ext-real real Element of REAL
g ^2 is complex ext-real real set
g * g is complex ext-real real set
F is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
g is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
i is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
i ^2 is complex ext-real real Element of REAL
i * i is complex ext-real real set
g . i is complex ext-real real Element of REAL
() is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
F is complex ext-real real Element of REAL
g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
addreal . (g,i) is complex ext-real real Element of REAL
[g,i] is set
{g,i} is non empty V53() V54() V55() set
{g} is non empty trivial V53() V54() V55() 1 -element set
{{g,i},{g}} is non empty set
addreal . [g,i] is complex ext-real real set
multreal . (F,(addreal . (g,i))) is complex ext-real real Element of REAL
[F,(addreal . (g,i))] is set
{F,(addreal . (g,i))} is non empty V53() V54() V55() set
{F} is non empty trivial V53() V54() V55() 1 -element set
{{F,(addreal . (g,i))},{F}} is non empty set
multreal . [F,(addreal . (g,i))] is complex ext-real real set
g + i is complex ext-real real Element of REAL
multreal . (F,(g + i)) is complex ext-real real Element of REAL
[F,(g + i)] is set
{F,(g + i)} is non empty V53() V54() V55() set
{{F,(g + i)},{F}} is non empty set
multreal . [F,(g + i)] is complex ext-real real set
F * (g + i) is complex ext-real real Element of REAL
F * g is complex ext-real real Element of REAL
F * i is complex ext-real real Element of REAL
(F * g) + (F * i) is complex ext-real real Element of REAL
addreal . ((F * g),(F * i)) is complex ext-real real Element of REAL
[(F * g),(F * i)] is set
{(F * g),(F * i)} is non empty V53() V54() V55() set
{(F * g)} is non empty trivial V53() V54() V55() 1 -element set
{{(F * g),(F * i)},{(F * g)}} is non empty set
addreal . [(F * g),(F * i)] is complex ext-real real set
multreal . (F,g) is complex ext-real real Element of REAL
[F,g] is set
{F,g} is non empty V53() V54() V55() set
{{F,g},{F}} is non empty set
multreal . [F,g] is complex ext-real real set
addreal . ((multreal . (F,g)),(F * i)) is complex ext-real real Element of REAL
[(multreal . (F,g)),(F * i)] is set
{(multreal . (F,g)),(F * i)} is non empty V53() V54() V55() set
{(multreal . (F,g))} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal . (F,g)),(F * i)},{(multreal . (F,g))}} is non empty set
addreal . [(multreal . (F,g)),(F * i)] is complex ext-real real set
multreal . (F,i) is complex ext-real real Element of REAL
[F,i] is set
{F,i} is non empty V53() V54() V55() set
{{F,i},{F}} is non empty set
multreal . [F,i] is complex ext-real real set
addreal . ((multreal . (F,g)),(multreal . (F,i))) is complex ext-real real Element of REAL
[(multreal . (F,g)),(multreal . (F,i))] is set
{(multreal . (F,g)),(multreal . (F,i))} is non empty V53() V54() V55() set
{{(multreal . (F,g)),(multreal . (F,i))},{(multreal . (F,g))}} is non empty set
addreal . [(multreal . (F,g)),(multreal . (F,i))] is complex ext-real real set
addreal . (F,g) is complex ext-real real Element of REAL
addreal . [F,g] is complex ext-real real set
multreal . ((addreal . (F,g)),i) is complex ext-real real Element of REAL
[(addreal . (F,g)),i] is set
{(addreal . (F,g)),i} is non empty V53() V54() V55() set
{(addreal . (F,g))} is non empty trivial V53() V54() V55() 1 -element set
{{(addreal . (F,g)),i},{(addreal . (F,g))}} is non empty set
multreal . [(addreal . (F,g)),i] is complex ext-real real set
F + g is complex ext-real real Element of REAL
multreal . ((F + g),i) is complex ext-real real Element of REAL
[(F + g),i] is set
{(F + g),i} is non empty V53() V54() V55() set
{(F + g)} is non empty trivial V53() V54() V55() 1 -element set
{{(F + g),i},{(F + g)}} is non empty set
multreal . [(F + g),i] is complex ext-real real set
(F + g) * i is complex ext-real real Element of REAL
g * i is complex ext-real real Element of REAL
(F * i) + (g * i) is complex ext-real real Element of REAL
addreal . ((F * i),(g * i)) is complex ext-real real Element of REAL
[(F * i),(g * i)] is set
{(F * i),(g * i)} is non empty V53() V54() V55() set
{(F * i)} is non empty trivial V53() V54() V55() 1 -element set
{{(F * i),(g * i)},{(F * i)}} is non empty set
addreal . [(F * i),(g * i)] is complex ext-real real set
addreal . ((multreal . (F,i)),(g * i)) is complex ext-real real Element of REAL
[(multreal . (F,i)),(g * i)] is set
{(multreal . (F,i)),(g * i)} is non empty V53() V54() V55() set
{(multreal . (F,i))} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal . (F,i)),(g * i)},{(multreal . (F,i))}} is non empty set
addreal . [(multreal . (F,i)),(g * i)] is complex ext-real real set
multreal . (g,i) is complex ext-real real Element of REAL
multreal . [g,i] is complex ext-real real set
addreal . ((multreal . (F,i)),(multreal . (g,i))) is complex ext-real real Element of REAL
[(multreal . (F,i)),(multreal . (g,i))] is set
{(multreal . (F,i)),(multreal . (g,i))} is non empty V53() V54() V55() set
{{(multreal . (F,i)),(multreal . (g,i))},{(multreal . (F,i))}} is non empty set
addreal . [(multreal . (F,i)),(multreal . (g,i))] is complex ext-real real set
F is complex ext-real real Element of REAL
() . F is complex ext-real real Element of REAL
g is complex ext-real real Element of REAL
multreal . (F,g) is complex ext-real real Element of REAL
[F,g] is set
{F,g} is non empty V53() V54() V55() set
{F} is non empty trivial V53() V54() V55() 1 -element set
{{F,g},{F}} is non empty set
multreal . [F,g] is complex ext-real real set
() . (multreal . (F,g)) is complex ext-real real Element of REAL
() . g is complex ext-real real Element of REAL
multreal . ((() . F),(() . g)) is complex ext-real real Element of REAL
[(() . F),(() . g)] is set
{(() . F),(() . g)} is non empty V53() V54() V55() set
{(() . F)} is non empty trivial V53() V54() V55() 1 -element set
{{(() . F),(() . g)},{(() . F)}} is non empty set
multreal . [(() . F),(() . g)] is complex ext-real real set
multreal . (F,g) is complex ext-real real Element of REAL
() . (multreal . (F,g)) is complex ext-real real Element of REAL
F * g is complex ext-real real Element of REAL
() . (F * g) is complex ext-real real Element of REAL
(F * g) ^2 is complex ext-real real Element of REAL
(F * g) * (F * g) is complex ext-real real set
F ^2 is complex ext-real real Element of REAL
F * F is complex ext-real real set
g ^2 is complex ext-real real Element of REAL
g * g is complex ext-real real set
(F ^2) * (g ^2) is complex ext-real real Element of REAL
multreal . ((F ^2),(g ^2)) is complex ext-real real Element of REAL
[(F ^2),(g ^2)] is set
{(F ^2),(g ^2)} is non empty V53() V54() V55() set
{(F ^2)} is non empty trivial V53() V54() V55() 1 -element set
{{(F ^2),(g ^2)},{(F ^2)}} is non empty set
multreal . [(F ^2),(g ^2)] is complex ext-real real set
() . F is complex ext-real real Element of REAL
multreal . ((() . F),(g ^2)) is complex ext-real real Element of REAL
[(() . F),(g ^2)] is set
{(() . F),(g ^2)} is non empty V53() V54() V55() set
{(() . F)} is non empty trivial V53() V54() V55() 1 -element set
{{(() . F),(g ^2)},{(() . F)}} is non empty set
multreal . [(() . F),(g ^2)] is complex ext-real real set
() . g is complex ext-real real Element of REAL
multreal . ((() . F),(() . g)) is complex ext-real real Element of REAL
[(() . F),(() . g)] is set
{(() . F),(() . g)} is non empty V53() V54() V55() set
{{(() . F),(() . g)},{(() . F)}} is non empty set
multreal . [(() . F),(() . g)] is complex ext-real real set
F is complex ext-real real set
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g is complex ext-real real Element of REAL
multreal [;] (g,(id REAL)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
F is complex ext-real real set
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g is complex ext-real real set
(multreal [;] (F,(id REAL))) . g is set
F * g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
(id REAL) . j is complex ext-real real Element of REAL
multreal . (i,((id REAL) . j)) is complex ext-real real Element of REAL
[i,((id REAL) . j)] is set
{i,((id REAL) . j)} is non empty V53() V54() V55() set
{i} is non empty trivial V53() V54() V55() 1 -element set
{{i,((id REAL) . j)},{i}} is non empty set
multreal . [i,((id REAL) . j)] is complex ext-real real set
multreal . (i,j) is complex ext-real real Element of REAL
[i,j] is set
{i,j} is non empty V53() V54() V55() set
{{i,j},{i}} is non empty set
multreal . [i,j] is complex ext-real real set
F is complex ext-real real set
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g is complex ext-real real set
(F) . g is complex ext-real real Element of REAL
F * g is complex ext-real real Element of REAL
F is complex ext-real real set
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
F is complex ext-real real Element of REAL
compreal . F is complex ext-real real Element of REAL
addreal . (F,(compreal . F)) is complex ext-real real Element of REAL
[F,(compreal . F)] is set
{F,(compreal . F)} is non empty V53() V54() V55() set
{F} is non empty trivial V53() V54() V55() 1 -element set
{{F,(compreal . F)},{F}} is non empty set
addreal . [F,(compreal . F)] is complex ext-real real set
addreal . ((compreal . F),F) is complex ext-real real Element of REAL
[(compreal . F),F] is set
{(compreal . F),F} is non empty V53() V54() V55() set
{(compreal . F)} is non empty trivial V53() V54() V55() 1 -element set
{{(compreal . F),F},{(compreal . F)}} is non empty set
addreal . [(compreal . F),F] is complex ext-real real set
compreal . F is complex ext-real real Element of REAL
addreal . (F,(compreal . F)) is complex ext-real real Element of REAL
[F,(compreal . F)] is set
{F,(compreal . F)} is non empty V53() V54() V55() set
{{F,(compreal . F)},{F}} is non empty set
addreal . [F,(compreal . F)] is complex ext-real real set
F + (compreal . F) is complex ext-real real Element of REAL
- F is complex ext-real real Element of REAL
F + (- F) is complex ext-real real Element of REAL
addreal . ((compreal . F),F) is complex ext-real real Element of REAL
[(compreal . F),F] is set
{(compreal . F),F} is non empty V53() V54() V55() set
{(compreal . F)} is non empty trivial V53() V54() V55() 1 -element set
{{(compreal . F),F},{(compreal . F)}} is non empty set
addreal . [(compreal . F),F] is complex ext-real real set
(compreal . F) + F is complex ext-real real Element of REAL
(- F) + F is complex ext-real real Element of REAL
the_inverseOp_wrt addreal is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is V53() V54() V55() Element of bool REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,g) is Relation-like Function-like set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom addreal is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is V53() V54() V55() Element of bool REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(j) is V53() V54() V55() Element of bool REAL
[:(i),(j):] is Relation-like complex-valued ext-real-valued real-valued set
dom (addreal .: (F,g)) is set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom (F + g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
p3 is set
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
addreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
addreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) + (g . p3) is complex ext-real real Element of REAL
p3 is set
dom q2 is V53() V54() V55() V56() V57() V58() Element of bool NAT
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
addreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
addreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) + (g . p3) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (j,q2) is Relation-like Function-like set
addreal .: (q2,j) is Relation-like Function-like set
dom addreal is set
f3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(f3) is V53() V54() V55() Element of bool REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(p3) is V53() V54() V55() Element of bool REAL
[:(f3),(p3):] is Relation-like complex-valued ext-real-valued real-valued set
[:(p3),(f3):] is Relation-like complex-valued ext-real-valued real-valued set
addreal .: (p3,f3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom (addreal .: (p3,f3)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom p3 is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom f3 is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom p3) /\ (dom f3) is V53() V54() V55() V56() V57() V58() set
addreal .: (f3,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom (addreal .: (f3,p3)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
a is set
i . a is complex ext-real real Element of REAL
f3 . a is complex ext-real real Element of REAL
p3 . a is complex ext-real real Element of REAL
addreal . ((f3 . a),(p3 . a)) is complex ext-real real Element of REAL
[(f3 . a),(p3 . a)] is set
{(f3 . a),(p3 . a)} is non empty V53() V54() V55() set
{(f3 . a)} is non empty trivial V53() V54() V55() 1 -element set
{{(f3 . a),(p3 . a)},{(f3 . a)}} is non empty set
addreal . [(f3 . a),(p3 . a)] is complex ext-real real set
addreal . ((p3 . a),(f3 . a)) is complex ext-real real Element of REAL
[(p3 . a),(f3 . a)] is set
{(p3 . a),(f3 . a)} is non empty V53() V54() V55() set
{(p3 . a)} is non empty trivial V53() V54() V55() 1 -element set
{{(p3 . a),(f3 . a)},{(p3 . a)}} is non empty set
addreal . [(p3 . a),(f3 . a)] is complex ext-real real set
(p3 . a) + (f3 . a) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
REAL * is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g + i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,i) is Relation-like Function-like set
F is set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = g } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
i . F is complex ext-real real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
(g,i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
addreal .: (i,j) is Relation-like Function-like set
(g,i,j) . F is complex ext-real real Element of REAL
j . F is complex ext-real real Element of REAL
(i . F) + (j . F) is complex ext-real real Element of REAL
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
dom j is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
dom i is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
dom (g,i,j) is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
0 + 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT
(i . F) + 0 is complex ext-real real Element of REAL
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
dom (g,i,j) is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
<*> REAL is Relation-like non-zero empty-yielding NAT -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((<*> REAL),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((<*> REAL),F) is Relation-like Function-like set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>,<*g*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (<*F*>,<*g*>) is Relation-like Function-like set
F + g is complex ext-real real Element of REAL
<*(F + g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(F + g)] is set
{1,(F + g)} is non empty V53() V54() V55() set
{{1,(F + g)},{1}} is non empty set
{[1,(F + g)]} is Relation-like Function-like constant non empty trivial 1 -element set
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
j is complex ext-real real Element of REAL
<*j*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*i*>,<*j*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (<*i*>,<*j*>) is Relation-like Function-like set
addreal . (i,j) is complex ext-real real Element of REAL
[i,j] is set
{i,j} is non empty V53() V54() V55() set
{i} is non empty trivial V53() V54() V55() 1 -element set
{{i,j},{i}} is non empty set
addreal . [i,j] is complex ext-real real set
<*(addreal . (i,j))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(addreal . (i,j))] is set
{1,(addreal . (i,j))} is non empty V53() V54() V55() set
{{1,(addreal . (i,j))},{1}} is non empty set
{[1,(addreal . (i,j))]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
i is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> g),(F |-> i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F |-> g),(F |-> i)) is Relation-like Function-like set
g + i is complex ext-real real Element of REAL
F |-> (g + i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (g + i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g + i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g + i)}:]
{(g + i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g + i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g + i)}:] is set
j is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
q2 is complex ext-real real Element of REAL
F |-> q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> q2 is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{q2}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{q2}:]
{q2} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{q2}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{q2}:] is set
(F,(F |-> j),(F |-> q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: ((F |-> j),(F |-> q2)) is Relation-like Function-like set
addreal . (j,q2) is complex ext-real real Element of REAL
[j,q2] is set
{j,q2} is non empty V53() V54() V55() set
{{j,q2},{j}} is non empty set
addreal . [j,q2] is complex ext-real real set
F |-> (addreal . (j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (addreal . (j,q2)) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(addreal . (j,q2))}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(addreal . (j,q2))}:]
{(addreal . (j,q2))} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(addreal . (j,q2))}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(addreal . (j,q2))}:] is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (g,i) is Relation-like Function-like set
(F,(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,(g,i)) is Relation-like Function-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F,g),i) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
(F,g,(F |-> 0)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F |-> 0)) is Relation-like Function-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- 1 is non empty complex ext-real non positive negative real V41() set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is set
(- g) . F is complex ext-real real Element of REAL
g . F is complex ext-real real Element of REAL
- (g . F) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- 1 is non empty complex ext-real non positive negative real V41() set
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom (- F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is V53() V54() V55() Element of bool REAL
dom compreal is non empty set
dom (F (#) compreal) is V53() V54() V55() V56() V57() V58() Element of bool NAT
i is set
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
g . i is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
- (F . i) is complex ext-real real Element of REAL
compreal . (F . i) is complex ext-real real Element of REAL
(F (#) compreal) . i is complex ext-real real Element of REAL
i is set
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(- F) . i is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
- (F . i) is complex ext-real real Element of REAL
compreal . (F . i) is complex ext-real real Element of REAL
(F (#) compreal) . i is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is set
(g) . F is complex ext-real real Element of REAL
g . F is complex ext-real real Element of REAL
- (g . F) is complex ext-real real Element of REAL
((<*> REAL)) is Relation-like NAT -defined REAL -valued RAT -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (<*> REAL) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(<*> REAL) (#) compreal is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) <*F*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*F*> (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- F is complex ext-real real Element of REAL
<*(- F)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(- F)] is set
{1,(- F)} is non empty V53() V54() V55() set
{{1,(- F)},{1}} is non empty set
{[1,(- F)]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*g*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) <*g*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*g*> (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
compreal . g is complex ext-real real Element of REAL
<*(compreal . g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(compreal . g)] is set
{1,(compreal . g)} is non empty V53() V54() V55() set
{{1,(compreal . g)},{1}} is non empty set
{[1,(compreal . g)]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (F |-> g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- g is complex ext-real real Element of REAL
F |-> (- g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (- g) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(- g)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(- g)}:]
{(- g)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(- g)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(- g)}:] is set
i is complex ext-real real Element of REAL
F |-> i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
(F,(F |-> i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) (F |-> i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> i) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
compreal . i is complex ext-real real Element of REAL
F |-> (compreal . i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (compreal . i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(compreal . i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(compreal . i)}:]
{(compreal . i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(compreal . i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(compreal . i)}:] is set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g,(F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F,g)) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is Relation-like Function-like complex-valued set
- F is Relation-like Function-like complex-valued set
(- 1) (#) F is Relation-like Function-like complex-valued set
g is Relation-like Function-like complex-valued set
- g is Relation-like Function-like complex-valued set
(- 1) (#) g is Relation-like Function-like complex-valued set
- (- g) is Relation-like Function-like complex-valued set
(- 1) (#) (- g) is Relation-like Function-like complex-valued set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,j,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (j,i) is Relation-like Function-like set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,i,(F,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (i,(F,i)) is Relation-like Function-like set
(F,g,(F,i,(F,i))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F,i,(F,i))) is Relation-like Function-like set
(F,(F,j,i),(F,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: ((F,j,i),(F,i)) is Relation-like Function-like set
(F,j,(F,i,(F,i))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (j,(F,i,(F,i))) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,j,(F |-> 0)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (j,(F |-> 0)) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),(g)) is Relation-like Function-like set
dom ((F,g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F,g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom ((F),(g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom (F)) /\ (dom (g)) is V53() V54() V55() V56() V57() V58() set
(dom F) /\ (dom (g)) is V53() V54() V55() V56() V57() V58() set
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
((F,g)) . i is complex ext-real real Element of REAL
(F,g) . i is complex ext-real real Element of REAL
- ((F,g) . i) is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
g . i is complex ext-real real Element of REAL
(F . i) + (g . i) is complex ext-real real Element of REAL
- ((F . i) + (g . i)) is complex ext-real real Element of REAL
- (F . i) is complex ext-real real Element of REAL
- (g . i) is complex ext-real real Element of REAL
(- (F . i)) + (- (g . i)) is complex ext-real real Element of REAL
(g) . i is complex ext-real real Element of REAL
(- (F . i)) + ((g) . i) is complex ext-real real Element of REAL
(F) . i is complex ext-real real Element of REAL
((F) . i) + ((g) . i) is complex ext-real real Element of REAL
((F),(g)) . i is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F - g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom (F - g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom diffreal is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is V53() V54() V55() Element of bool REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(j) is V53() V54() V55() Element of bool REAL
[:(i),(j):] is Relation-like complex-valued ext-real-valued real-valued set
dom (diffreal .: (F,g)) is set
p3 is set
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
diffreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
diffreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) - (g . p3) is complex ext-real real Element of REAL
p3 is set
dom q2 is V53() V54() V55() V56() V57() V58() Element of bool NAT
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
diffreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
diffreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) - (g . p3) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g - i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
F is set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = g } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
i . F is complex ext-real real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
(g,i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
- j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i + (- j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (i,(- j)) is Relation-like Function-like set
diffreal .: (i,j) is Relation-like Function-like set
(g,i,j) . F is complex ext-real real Element of REAL
j . F is complex ext-real real Element of REAL
(i . F) - (j . F) is complex ext-real real Element of REAL
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
dom j is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
dom i is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
dom (g,i,j) is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
0 - 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of INT
(i . F) - 0 is complex ext-real real Element of REAL
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
dom (g,i,j) is V53() V54() V55() V56() V57() V58() g -element Element of bool NAT
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((<*> REAL),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(<*> REAL) + (- F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((<*> REAL),(- F)) is Relation-like Function-like set
diffreal .: ((<*> REAL),F) is Relation-like Function-like set
(F,(<*> REAL)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- (<*> REAL) is Relation-like NAT -defined RAT -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- (<*> REAL)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- (<*> REAL))) is Relation-like Function-like set
diffreal .: (F,(<*> REAL)) is Relation-like Function-like set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>,<*g*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- <*g*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) <*g*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*g*> (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*F*> + (- <*g*>) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (<*F*>,(- <*g*>)) is Relation-like Function-like set
diffreal .: (<*F*>,<*g*>) is Relation-like Function-like set
F - g is complex ext-real real Element of REAL
<*(F - g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(F - g)] is set
{1,(F - g)} is non empty V53() V54() V55() set
{{1,(F - g)},{1}} is non empty set
{[1,(F - g)]} is Relation-like Function-like constant non empty trivial 1 -element set
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
j is complex ext-real real Element of REAL
<*j*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*i*>,<*j*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- <*j*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) <*j*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*j*> (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*i*> + (- <*j*>) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (<*i*>,(- <*j*>)) is Relation-like Function-like set
diffreal .: (<*i*>,<*j*>) is Relation-like Function-like set
diffreal . (i,j) is complex ext-real real Element of REAL
[i,j] is set
{i,j} is non empty V53() V54() V55() set
{i} is non empty trivial V53() V54() V55() 1 -element set
{{i,j},{i}} is non empty set
diffreal . [i,j] is complex ext-real real set
<*(diffreal . (i,j))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(diffreal . (i,j))] is set
{1,(diffreal . (i,j))} is non empty V53() V54() V55() set
{{1,(diffreal . (i,j))},{1}} is non empty set
{[1,(diffreal . (i,j))]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
i is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> g),(F |-> i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- (F |-> i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (F |-> i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> i) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> g) + (- (F |-> i)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F |-> g),(- (F |-> i))) is Relation-like Function-like set
diffreal .: ((F |-> g),(F |-> i)) is Relation-like Function-like set
g - i is complex ext-real real Element of REAL
F |-> (g - i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (g - i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g - i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g - i)}:]
{(g - i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g - i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g - i)}:] is set
j is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
q2 is complex ext-real real Element of REAL
F |-> q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> q2 is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{q2}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{q2}:]
{q2} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{q2}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{q2}:] is set
(F,(F |-> j),(F |-> q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- (F |-> q2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (F |-> q2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> q2) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> j) + (- (F |-> q2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F |-> j),(- (F |-> q2))) is Relation-like Function-like set
diffreal .: ((F |-> j),(F |-> q2)) is Relation-like Function-like set
diffreal . (j,q2) is complex ext-real real Element of REAL
[j,q2] is set
{j,q2} is non empty V53() V54() V55() set
{{j,q2},{j}} is non empty set
diffreal . [j,q2] is complex ext-real real set
F |-> (diffreal . (j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (diffreal . (j,q2)) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(diffreal . (j,q2))}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(diffreal . (j,q2))}:]
{(diffreal . (j,q2))} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(diffreal . (j,q2))}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(diffreal . (j,q2))}:] is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,(g)) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,(F |-> 0)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- (F |-> 0) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (F |-> 0) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> 0) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- (F |-> 0)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- (F |-> 0))) is Relation-like Function-like set
diffreal .: (g,(F |-> 0)) is Relation-like Function-like set
- 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of INT
F |-> (- 0) is Relation-like NAT -defined INT -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on INT
F -tuples_on INT is functional non empty FinSequence-membered FinSequenceSet of INT
INT * is functional non empty FinSequence-membered FinSequenceSet of INT
{ b₁ where b₁ is Relation-like NAT -defined INT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of INT * : len b₁ = F } is set
(Seg F) --> (- 0) is Relation-like Seg F -defined Seg F -defined RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(- 0)}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(- 0)}:]
{(- 0)} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{(- 0)}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{(- 0)}:] is set
(g,(F |-> (- 0))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (g,(F |-> (- 0))) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,(F |-> 0),g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> 0) + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F |-> 0),(- g)) is Relation-like Function-like set
diffreal .: ((F |-> 0),g) is Relation-like Function-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- (g)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- (g))) is Relation-like Function-like set
diffreal .: (F,(g)) is Relation-like Function-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- F)) is Relation-like Function-like set
diffreal .: (g,F) is Relation-like Function-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((g))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),((g))) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),g) is Relation-like Function-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((g))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),((g))) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- g)) is Relation-like Function-like set
diffreal .: (g,g) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,(F,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) (F,i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,i) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F,g),(- i)) is Relation-like Function-like set
diffreal .: ((F,g),i) is Relation-like Function-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (g,i) is Relation-like Function-like set
(F,(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- (g,i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (g,i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- (g,i)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- (g,i))) is Relation-like Function-like set
diffreal .: (F,(g,i)) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
(F,(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,(g,i)) is Relation-like Function-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,g) + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F,g),(- i)) is Relation-like Function-like set
diffreal .: ((F,g),i) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
(F,(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- (g,i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (g,i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- (g,i)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- (g,i))) is Relation-like Function-like set
diffreal .: (F,(g,i)) is Relation-like Function-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F,g),i) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
(F,(F,g,i),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g,i) + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F,g,i),(- i)) is Relation-like Function-like set
diffreal .: ((F,g,i),i) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
(F,g,(F |-> 0)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F |-> 0)) is Relation-like Function-like set
(F,i,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (i,(- i)) is Relation-like Function-like set
diffreal .: (i,i) is Relation-like Function-like set
(F,g,(F,i,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F,i,i)) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
(F,(F,g,i),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: ((F,g,i),i) is Relation-like Function-like set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
(F,g,(F |-> 0)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F |-> 0)) is Relation-like Function-like set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,(F,i),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: ((F,i),i) is Relation-like Function-like set
(F,g,(F,(F,i),i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,(F,(F,i),i)) is Relation-like Function-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is complex ext-real real set
g (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is set
(g (#) i) . F is complex ext-real real Element of REAL
i . F is complex ext-real real Element of REAL
g * (i . F) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is complex ext-real real set
g (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
F (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom (g (#) F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is V53() V54() V55() Element of bool REAL
dom (g) is non empty set
dom (F (#) (g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
j is set
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
i . j is complex ext-real real Element of REAL
F . j is complex ext-real real Element of REAL
g * (F . j) is complex ext-real real Element of REAL
(g) . (F . j) is complex ext-real real Element of REAL
(F (#) (g)) . j is complex ext-real real Element of REAL
j is set
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
(g (#) F) . j is complex ext-real real Element of REAL
F . j is complex ext-real real Element of REAL
g * (F . j) is complex ext-real real Element of REAL
(g) . (F . j) is complex ext-real real Element of REAL
(F (#) (g)) . j is complex ext-real real Element of REAL
((- 1)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((- 1),(id REAL)) is Relation-like Function-like set
(<*> REAL) (#) ((- 1)) is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is complex ext-real real set
i (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (i,(id REAL)) is Relation-like Function-like set
g (#) (i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is complex ext-real real set
(i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is set
(i,g) . F is complex ext-real real Element of REAL
i . F is complex ext-real real Element of REAL
g * (i . F) is complex ext-real real Element of REAL
F is complex ext-real real set
((<*> REAL),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
(<*> REAL) (#) (F) is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
F is complex ext-real real set
g is complex ext-real real set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*g*>,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
<*g*> (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F * g is complex ext-real real Element of REAL
<*(F * g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(F * g)] is set
{1,(F * g)} is non empty V53() V54() V55() set
{{1,(F * g)},{1}} is non empty set
{[1,(F * g)]} is Relation-like Function-like constant non empty trivial 1 -element set
j is complex ext-real real Element of REAL
<*j*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
i is complex ext-real real Element of REAL
(<*j*>,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (i,(id REAL)) is Relation-like Function-like set
<*j*> (#) (i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal [;] (i,(id REAL)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(multreal [;] (i,(id REAL))) . j is complex ext-real real Element of REAL
<*((multreal [;] (i,(id REAL))) . j)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,((multreal [;] (i,(id REAL))) . j)] is set
{1,((multreal [;] (i,(id REAL))) . j)} is non empty V53() V54() V55() set
{{1,((multreal [;] (i,(id REAL))) . j)},{1}} is non empty set
{[1,((multreal [;] (i,(id REAL))) . j)]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
i is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> i),g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
(F |-> i) (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g * i is complex ext-real real Element of REAL
F |-> (g * i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (g * i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g * i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g * i)}:]
{(g * i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g * i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g * i)}:] is set
q2 is complex ext-real real Element of REAL
F |-> q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> q2 is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{q2}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{q2}:]
{q2} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{q2}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{q2}:] is set
j is complex ext-real real Element of REAL
(F,(F |-> q2),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(j) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is Relation-like Function-like set
(F |-> q2) (#) (j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal [;] (j,(id REAL)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(multreal [;] (j,(id REAL))) . q2 is complex ext-real real Element of REAL
F |-> ((multreal [;] (j,(id REAL))) . q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> ((multreal [;] (j,(id REAL))) . q2) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{((multreal [;] (j,(id REAL))) . q2)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{((multreal [;] (j,(id REAL))) . q2)}:]
{((multreal [;] (j,(id REAL))) . q2)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{((multreal [;] (j,(id REAL))) . q2)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{((multreal [;] (j,(id REAL))) . q2)}:] is set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is complex ext-real real set
g is complex ext-real real set
F * g is complex ext-real real Element of REAL
(i,(F * g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((F * g)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((F * g),(id REAL)) is Relation-like Function-like set
i (#) ((F * g)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((i,g),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
(i,g) (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is complex ext-real real set
g is complex ext-real real set
F + g is complex ext-real real Element of REAL
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,(F + g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((F + g)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((F + g),(id REAL)) is Relation-like Function-like set
i (#) ((F + g)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
i (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((i,F),(i,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((i,F),(i,g)) is Relation-like Function-like set
dom (i,(F + g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom ((i,F),(i,g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (i,F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (i,g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom (i,F)) /\ (dom (i,g)) is V53() V54() V55() V56() V57() V58() set
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
(i,(F + g)) . j is complex ext-real real Element of REAL
i . j is complex ext-real real Element of REAL
(F + g) * (i . j) is complex ext-real real Element of REAL
F * (i . j) is complex ext-real real Element of REAL
g * (i . j) is complex ext-real real Element of REAL
(F * (i . j)) + (g * (i . j)) is complex ext-real real Element of REAL
(i,g) . j is complex ext-real real Element of REAL
(F * (i . j)) + ((i,g) . j) is complex ext-real real Element of REAL
(i,F) . j is complex ext-real real Element of REAL
((i,F) . j) + ((i,g) . j) is complex ext-real real Element of REAL
((i,F),(i,g)) . j is complex ext-real real Element of REAL
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (g,i) is Relation-like Function-like set
F is complex ext-real real set
((g,i),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
(g,i) (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
i (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g,F),(i,F)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((g,F),(i,F)) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,1) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(1) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (1,(id REAL)) is Relation-like Function-like set
F (#) (1) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,0) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(0) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (0,(id REAL)) is Relation-like Function-like set
g (#) (0) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is V53() V54() V55() Element of bool REAL
(id REAL) * g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal [;] (0,((id REAL) * g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal [;] (0,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- 1 is non empty complex ext-real non positive negative real V41() V42() Element of INT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,(- 1)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((- 1)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((- 1),(id REAL)) is Relation-like Function-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F ^2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom () is non empty set
(F) is V53() V54() V55() Element of bool REAL
dom (F ^2) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F (#) ()) is V53() V54() V55() V56() V57() V58() Element of bool NAT
len (F ^2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (F (#) ()) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
(F ^2) . i is complex ext-real real set
(F (#) ()) . i is complex ext-real real set
(F ^2) . i is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
(F . i) ^2 is complex ext-real real Element of REAL
(F . i) * (F . i) is complex ext-real real set
() . (F . i) is complex ext-real real Element of REAL
(F (#) ()) . i is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g ^2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
<*F*> (#) <*F*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*F*> (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F ^2 is complex ext-real real set
F * F is complex ext-real real set
<*(F ^2)*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,(F ^2)] is set
{1,(F ^2)} is non empty V53() V54() V55() set
{{1,(F ^2)},{1}} is non empty set
{[1,(F ^2)]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*g*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
<*g*> (#) <*g*> is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*g*> (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
() . g is complex ext-real real Element of REAL
<*(() . g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(() . g)] is set
{1,(() . g)} is non empty V53() V54() V55() set
{{1,(() . g)},{1}} is non empty set
{[1,(() . g)]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F |-> g) (#) (F |-> g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g ^2 is complex ext-real real set
g * g is complex ext-real real set
F |-> (g ^2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
(Seg F) --> (g ^2) is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g ^2)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g ^2)}:]
{(g ^2)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g ^2)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g ^2)}:] is set
i is complex ext-real real Element of REAL
F |-> i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
(F,(F |-> i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F |-> i) (#) (F |-> i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F |-> i) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
() . i is complex ext-real real Element of REAL
F |-> (() . i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (() . i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(() . i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(() . i)}:]
{(() . i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(() . i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(() . i)}:] is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
dom ((F)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F . g is complex ext-real real Element of REAL
(F) . g is complex ext-real real Element of REAL
((F)) . g is complex ext-real real Element of REAL
((F) . g) ^2 is complex ext-real real Element of REAL
((F) . g) * ((F) . g) is complex ext-real real set
- (F . g) is complex ext-real real Element of REAL
(- (F . g)) ^2 is complex ext-real real Element of REAL
(- (F . g)) * (- (F . g)) is complex ext-real real set
(F . g) ^2 is complex ext-real real Element of REAL
(F . g) * (F . g) is complex ext-real real set
(F) . g is complex ext-real real Element of REAL
F is complex ext-real real set
F ^2 is complex ext-real real set
F * F is complex ext-real real set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g,F)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g,F) (#) (g,F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g),(F ^2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((F ^2)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((F ^2),(id REAL)) is Relation-like Function-like set
(g) (#) ((F ^2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
dom (g,F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom ((g),(F ^2)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
dom ((g,F)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
((g,F)) . i is complex ext-real real Element of REAL
(g,F) . i is complex ext-real real Element of REAL
((g,F) . i) ^2 is complex ext-real real Element of REAL
((g,F) . i) * ((g,F) . i) is complex ext-real real set
g . i is complex ext-real real Element of REAL
F * (g . i) is complex ext-real real Element of REAL
(F * (g . i)) ^2 is complex ext-real real Element of REAL
(F * (g . i)) * (F * (g . i)) is complex ext-real real set
(g . i) ^2 is complex ext-real real Element of REAL
(g . i) * (g . i) is complex ext-real real set
(F ^2) * ((g . i) ^2) is complex ext-real real Element of REAL
(g) . i is complex ext-real real Element of REAL
(F ^2) * ((g) . i) is complex ext-real real Element of REAL
((g),(F ^2)) . i is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,g) is Relation-like Function-like set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
dom multreal is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is V53() V54() V55() Element of bool REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(j) is V53() V54() V55() Element of bool REAL
[:(i),(j):] is Relation-like complex-valued ext-real-valued real-valued set
dom (multreal .: (F,g)) is set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom (F (#) g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
p3 is set
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
multreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
multreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) * (g . p3) is complex ext-real real Element of REAL
p3 is set
dom q2 is V53() V54() V55() V56() V57() V58() Element of bool NAT
q2 . p3 is complex ext-real real Element of REAL
F . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
multreal . ((F . p3),(g . p3)) is complex ext-real real Element of REAL
[(F . p3),(g . p3)] is set
{(F . p3),(g . p3)} is non empty V53() V54() V55() set
{(F . p3)} is non empty trivial V53() V54() V55() 1 -element set
{{(F . p3),(g . p3)},{(F . p3)}} is non empty set
multreal . [(F . p3),(g . p3)] is complex ext-real real set
(F . p3) * (g . p3) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (j,q2) is Relation-like Function-like set
multreal .: (q2,j) is Relation-like Function-like set
dom multreal is set
f3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(f3) is V53() V54() V55() Element of bool REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(p3) is V53() V54() V55() Element of bool REAL
[:(f3),(p3):] is Relation-like complex-valued ext-real-valued real-valued set
[:(p3),(f3):] is Relation-like complex-valued ext-real-valued real-valued set
dom (multreal .: (j,q2)) is set
dom j is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom q2 is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom j) /\ (dom q2) is V53() V54() V55() V56() V57() V58() set
dom (multreal .: (q2,j)) is set
a is set
i . a is complex ext-real real Element of REAL
q2 . a is complex ext-real real Element of REAL
j . a is complex ext-real real Element of REAL
multreal . ((q2 . a),(j . a)) is complex ext-real real Element of REAL
[(q2 . a),(j . a)] is set
{(q2 . a),(j . a)} is non empty V53() V54() V55() set
{(q2 . a)} is non empty trivial V53() V54() V55() 1 -element set
{{(q2 . a),(j . a)},{(q2 . a)}} is non empty set
multreal . [(q2 . a),(j . a)] is complex ext-real real set
multreal . ((j . a),(q2 . a)) is complex ext-real real Element of REAL
[(j . a),(q2 . a)] is set
{(j . a),(q2 . a)} is non empty V53() V54() V55() set
{(j . a)} is non empty trivial V53() V54() V55() 1 -element set
{{(j . a),(q2 . a)},{(j . a)}} is non empty set
multreal . [(j . a),(q2 . a)] is complex ext-real real set
(j . a) * (q2 . a) is complex ext-real real Element of REAL
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
F is set
(g,i) . F is complex ext-real real Element of REAL
g . F is complex ext-real real Element of REAL
i . F is complex ext-real real Element of REAL
(g . F) * (i . F) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,i) is Relation-like Function-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
F is set
(g,i) . F is complex ext-real real Element of REAL
g . F is complex ext-real real Element of REAL
i . F is complex ext-real real Element of REAL
(g . F) * (i . F) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((<*> REAL),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((<*> REAL),F) is Relation-like Function-like set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex ext-real real set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>,<*g*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (<*F*>,<*g*>) is Relation-like Function-like set
F * g is complex ext-real real Element of REAL
<*(F * g)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(F * g)] is set
{1,(F * g)} is non empty V53() V54() V55() set
{{1,(F * g)},{1}} is non empty set
{[1,(F * g)]} is Relation-like Function-like constant non empty trivial 1 -element set
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
j is complex ext-real real Element of REAL
<*j*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*i*>,<*j*>) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (<*i*>,<*j*>) is Relation-like Function-like set
multreal . (i,j) is complex ext-real real Element of REAL
[i,j] is set
{i,j} is non empty V53() V54() V55() set
{i} is non empty trivial V53() V54() V55() 1 -element set
{{i,j},{i}} is non empty set
multreal . [i,j] is complex ext-real real set
<*(multreal . (i,j))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(multreal . (i,j))] is set
{1,(multreal . (i,j))} is non empty V53() V54() V55() set
{{1,(multreal . (i,j))},{1}} is non empty set
{[1,(multreal . (i,j))]} is Relation-like Function-like constant non empty trivial 1 -element set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F |-> g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F |-> g),i) is Relation-like Function-like set
(F,i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
(F,(F |-> j),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
multreal .: ((F |-> j),i) is Relation-like Function-like set
multreal [;] (j,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
i is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> g),(F |-> i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F |-> g),(F |-> i)) is Relation-like Function-like set
g * i is complex ext-real real Element of REAL
F |-> (g * i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (g * i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g * i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g * i)}:]
{(g * i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g * i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g * i)}:] is set
j is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
q2 is complex ext-real real Element of REAL
F |-> q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> q2 is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{q2}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{q2}:]
{q2} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{q2}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{q2}:] is set
(F,(F |-> j),(F |-> q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
multreal .: ((F |-> j),(F |-> q2)) is Relation-like Function-like set
(F,(F |-> q2),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(j) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is Relation-like Function-like set
(F |-> q2) (#) (j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
F is complex ext-real real set
((g,i),F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
(g,i) (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g,F),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((g,F),i) is Relation-like Function-like set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g is complex ext-real real set
(F,i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F |-> g),i) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,g) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((F,g),(F,g)) is Relation-like Function-like set
(F,g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g),2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(2) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (2,(id REAL)) is Relation-like Function-like set
(F,g) (#) (2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((F,g),2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),((F,g),2)) is Relation-like Function-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((F),((F,g),2)),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),((F,g),2)),(g)) is Relation-like Function-like set
dom ((F,g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F,g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom ((F),((F,g),2)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom ((F,g),2) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom (F)) /\ (dom ((F,g),2)) is V53() V54() V55() V56() V57() V58() set
(dom F) /\ (dom ((F,g),2)) is V53() V54() V55() V56() V57() V58() set
dom (F,g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom (F,g)) is V53() V54() V55() V56() V57() V58() set
(dom F) /\ ((dom F) /\ (dom g)) is V53() V54() V55() V56() V57() V58() set
(dom F) /\ (dom F) is V53() V54() V55() V56() V57() V58() set
((dom F) /\ (dom F)) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom (((F),((F,g),2)),(g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
((dom F) /\ (dom g)) /\ (dom (g)) is V53() V54() V55() V56() V57() V58() set
((dom F) /\ (dom g)) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
(dom g) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
(dom F) /\ ((dom g) /\ (dom g)) is V53() V54() V55() V56() V57() V58() set
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
(F,g) . i is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
g . i is complex ext-real real Element of REAL
(F) . i is complex ext-real real Element of REAL
(g) . i is complex ext-real real Element of REAL
(F,g) . i is complex ext-real real Element of REAL
((F,g),2) . i is complex ext-real real Element of REAL
((F),((F,g),2)) . i is complex ext-real real Element of REAL
((F,g)) . i is complex ext-real real Element of REAL
((F,g) . i) ^2 is complex ext-real real Element of REAL
((F,g) . i) * ((F,g) . i) is complex ext-real real set
(F . i) + (g . i) is complex ext-real real Element of REAL
((F . i) + (g . i)) ^2 is complex ext-real real Element of REAL
((F . i) + (g . i)) * ((F . i) + (g . i)) is complex ext-real real set
(F . i) ^2 is complex ext-real real Element of REAL
(F . i) * (F . i) is complex ext-real real set
2 * (F . i) is complex ext-real real Element of REAL
(2 * (F . i)) * (g . i) is complex ext-real real Element of REAL
((F . i) ^2) + ((2 * (F . i)) * (g . i)) is complex ext-real real Element of REAL
(g . i) ^2 is complex ext-real real Element of REAL
(g . i) * (g . i) is complex ext-real real set
(((F . i) ^2) + ((2 * (F . i)) * (g . i))) + ((g . i) ^2) is complex ext-real real Element of REAL
(F . i) * (g . i) is complex ext-real real Element of REAL
2 * ((F . i) * (g . i)) is complex ext-real real Element of REAL
((F) . i) + (2 * ((F . i) * (g . i))) is complex ext-real real Element of REAL
(((F) . i) + (2 * ((F . i) * (g . i)))) + ((g . i) ^2) is complex ext-real real Element of REAL
(((F) . i) + (2 * ((F . i) * (g . i)))) + ((g) . i) is complex ext-real real Element of REAL
2 * ((F,g) . i) is complex ext-real real Element of REAL
((F) . i) + (2 * ((F,g) . i)) is complex ext-real real Element of REAL
(((F) . i) + (2 * ((F,g) . i))) + ((g) . i) is complex ext-real real Element of REAL
((F) . i) + (((F,g),2) . i) is complex ext-real real Element of REAL
(((F) . i) + (((F,g),2) . i)) + ((g) . i) is complex ext-real real Element of REAL
(((F),((F,g),2)) . i) + ((g) . i) is complex ext-real real Element of REAL
(((F),((F,g),2)),(g)) . i is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,g) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((F,g),(F,g)) is Relation-like Function-like set
(F,g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g),2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(2) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (2,(id REAL)) is Relation-like Function-like set
(F,g) (#) (2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((F,g),2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- ((F,g),2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) ((F,g),2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g),2) (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g),2) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) + (- ((F,g),2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((F),(- ((F,g),2))) is Relation-like Function-like set
diffreal .: ((F),((F,g),2)) is Relation-like Function-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((F),((F,g),2)),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),((F,g),2)),(g)) is Relation-like Function-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,(g)) is Relation-like Function-like set
((F,(g)),2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,(g)) (#) (2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((F,(g)),2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),((F,(g)),2)) is Relation-like Function-like set
((g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((g),(g)) is Relation-like Function-like set
(g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((F),((F,(g)),2)),((g))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),((F,(g)),2)),((g))) is Relation-like Function-like set
(((F),((F,(g)),2)),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),((F,(g)),2)),(g)) is Relation-like Function-like set
((F,g),(- 1)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((- 1)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((- 1),(id REAL)) is Relation-like Function-like set
(F,g) (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((F,g),(- 1)),2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((F,g),(- 1)) (#) (2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),(((F,g),(- 1)),2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),(((F,g),(- 1)),2)) is Relation-like Function-like set
(((F),(((F,g),(- 1)),2)),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),(((F,g),(- 1)),2)),(g)) is Relation-like Function-like set
(- 1) * 2 is non empty complex ext-real non positive negative real V41() V42() Element of INT
((F,g),((- 1) * 2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(((- 1) * 2)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (((- 1) * 2),(id REAL)) is Relation-like Function-like set
(F,g) (#) (((- 1) * 2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),((F,g),((- 1) * 2))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F),((F,g),((- 1) * 2))) is Relation-like Function-like set
(((F),((F,g),((- 1) * 2))),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (((F),((F,g),((- 1) * 2))),(g)) is Relation-like Function-like set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F,g) (#) (F,g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((F,g),(F,g)) is Relation-like Function-like set
(F,g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F),(g)) is Relation-like Function-like set
dom (F,g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom F) /\ (dom g) is V53() V54() V55() V56() V57() V58() set
dom ((F),(g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(dom (F)) /\ (dom (g)) is V53() V54() V55() V56() V57() V58() set
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
dom ((F,g)) is V53() V54() V55() V56() V57() V58() Element of bool NAT
((F,g)) . i is complex ext-real real Element of REAL
(F,g) . i is complex ext-real real Element of REAL
((F,g) . i) ^2 is complex ext-real real Element of REAL
((F,g) . i) * ((F,g) . i) is complex ext-real real set
F . i is complex ext-real real Element of REAL
g . i is complex ext-real real Element of REAL
(F . i) * (g . i) is complex ext-real real Element of REAL
((F . i) * (g . i)) ^2 is complex ext-real real Element of REAL
((F . i) * (g . i)) * ((F . i) * (g . i)) is complex ext-real real set
(F . i) ^2 is complex ext-real real Element of REAL
(F . i) * (F . i) is complex ext-real real set
(g . i) ^2 is complex ext-real real Element of REAL
(g . i) * (g . i) is complex ext-real real set
((F . i) ^2) * ((g . i) ^2) is complex ext-real real Element of REAL
(F) . i is complex ext-real real Element of REAL
((F) . i) * ((g . i) ^2) is complex ext-real real Element of REAL
(g) . i is complex ext-real real Element of REAL
((F) . i) * ((g) . i) is complex ext-real real Element of REAL
((F),(g)) . i is complex ext-real real Element of REAL
F is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
rng F is V53() set
g is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
addcomplex "**" g is complex Element of COMPLEX
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
g is complex set
addcomplex "**" j is complex Element of COMPLEX
q2 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
i is complex set
addcomplex "**" q2 is complex Element of COMPLEX
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is complex set
i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
addcomplex "**" i is complex Element of COMPLEX
[#] (i,(the_unity_wrt addcomplex)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , COMPLEX ) complex-valued Element of bool [:NAT,COMPLEX:]
[:NAT,COMPLEX:] is Relation-like complex-valued V60() set
bool [:NAT,COMPLEX:] is V60() set
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
finSeg q2 is V60() q2 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
addcomplex $$ ((finSeg q2),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
q2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
finSeg (q2 + 1) is non empty V60() q2 + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 + 1 ) } is set
addcomplex $$ ((finSeg (q2 + 1)),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
p3 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1) is complex Element of COMPLEX
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
i . (p3 + 1) is complex set
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
finSeg p3 is V60() p3 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= p3 ) } is set
addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
Seg p3 is V53() V54() V55() V56() V57() V58() V60() p3 -element Element of bool NAT
{.(p3 + 1).} is non empty trivial V53() V54() V55() V56() V57() V58() 1 -element Element of K101(NAT)
(finSeg p3) \/ {.(p3 + 1).} is non empty Element of K101(NAT)
addcomplex $$ (((finSeg p3) \/ {.(p3 + 1).}),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
addcomplex . ((addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex))))),(([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1))) is complex Element of COMPLEX
[(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex))))),(([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1))] is set
{(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex))))),(([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1))} is non empty V53() set
{(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex)))))} is non empty trivial V53() 1 -element set
{{(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex))))),(([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1))},{(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex)))))}} is non empty set
addcomplex . [(addcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt addcomplex))))),(([#] (i,(the_unity_wrt addcomplex))) . (p3 + 1))] is complex set
a is complex ext-real real set
f3 is complex ext-real real set
a + f3 is complex ext-real real Element of REAL
findom i is V53() V54() V55() V56() V57() V58() Element of K101(NAT)
addcomplex $$ ((findom i),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
{}. NAT is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
finSeg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
addcomplex $$ ((finSeg 0),([#] (i,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg q2 is V53() V54() V55() V56() V57() V58() V60() q2 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is complex ext-real real set
addreal "**" i is complex ext-real real Element of REAL
(i) is V53() V54() V55() Element of bool REAL
[#] (i,(the_unity_wrt addreal)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , REAL ) complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
[:NAT,REAL:] is Relation-like complex-valued ext-real-valued real-valued V60() set
bool [:NAT,REAL:] is V60() set
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
[#] (j,(the_unity_wrt addcomplex)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , COMPLEX ) complex-valued Element of bool [:NAT,COMPLEX:]
[:NAT,COMPLEX:] is Relation-like complex-valued V60() set
bool [:NAT,COMPLEX:] is V60() set
dom j is V53() V54() V55() V56() V57() V58() Element of bool NAT
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg q2 is V53() V54() V55() V56() V57() V58() V60() q2 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
finSeg q2 is V60() q2 -element Element of K101(NAT)
addreal $$ ((finSeg q2),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addcomplex "**" j is complex Element of COMPLEX
addcomplex $$ ((finSeg q2),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
a is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
finSeg a is V60() a -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= a ) } is set
addreal $$ ((finSeg a),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addcomplex $$ ((finSeg a),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
finSeg (a + 1) is non empty V60() a + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= a + 1 ) } is set
addreal $$ ((finSeg (a + 1)),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addcomplex $$ ((finSeg (a + 1)),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
b is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
b + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
([#] (i,(the_unity_wrt addreal))) . (b + 1) is complex ext-real real Element of REAL
([#] (j,(the_unity_wrt addcomplex))) . (b + 1) is complex Element of COMPLEX
i . (b + 1) is complex ext-real real Element of REAL
Seg b is V53() V54() V55() V56() V57() V58() V60() b -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= b ) } is set
finSeg (b + 1) is non empty V60() b + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= b + 1 ) } is set
addreal $$ ((finSeg (b + 1)),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
finSeg b is V60() b -element Element of K101(NAT)
{.(b + 1).} is non empty trivial V53() V54() V55() V56() V57() V58() 1 -element Element of K101(NAT)
(finSeg b) \/ {.(b + 1).} is non empty Element of K101(NAT)
addreal $$ (((finSeg b) \/ {.(b + 1).}),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addreal . ((addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))),(([#] (i,(the_unity_wrt addreal))) . (b + 1))) is complex ext-real real Element of REAL
[(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))),(([#] (i,(the_unity_wrt addreal))) . (b + 1))] is set
{(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))),(([#] (i,(the_unity_wrt addreal))) . (b + 1))} is non empty V53() V54() V55() set
{(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal)))))} is non empty trivial V53() V54() V55() 1 -element set
{{(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))),(([#] (i,(the_unity_wrt addreal))) . (b + 1))},{(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal)))))}} is non empty set
addreal . [(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))),(([#] (i,(the_unity_wrt addreal))) . (b + 1))] is complex ext-real real set
(addreal $$ ((finSeg b),([#] (i,(the_unity_wrt addreal))))) + (([#] (i,(the_unity_wrt addreal))) . (b + 1)) is complex ext-real real Element of REAL
addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
addcomplex . ((addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex))))),(([#] (j,(the_unity_wrt addcomplex))) . (b + 1))) is complex Element of COMPLEX
[(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex))))),(([#] (j,(the_unity_wrt addcomplex))) . (b + 1))] is set
{(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex))))),(([#] (j,(the_unity_wrt addcomplex))) . (b + 1))} is non empty V53() set
{(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex)))))} is non empty trivial V53() 1 -element set
{{(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex))))),(([#] (j,(the_unity_wrt addcomplex))) . (b + 1))},{(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex)))))}} is non empty set
addcomplex . [(addcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt addcomplex))))),(([#] (j,(the_unity_wrt addcomplex))) . (b + 1))] is complex set
addcomplex $$ (((finSeg b) \/ {.(b + 1).}),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
addcomplex $$ ((finSeg (b + 1)),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
{}. NAT is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
finSeg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
addreal $$ ((finSeg 0),([#] (i,(the_unity_wrt addreal)))) is complex ext-real real Element of REAL
addcomplex $$ ((finSeg 0),([#] (j,(the_unity_wrt addcomplex)))) is complex Element of COMPLEX
F is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(F) is complex set
addcomplex "**" F is complex Element of COMPLEX
g is complex Element of COMPLEX
i is complex Element of COMPLEX
F is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is complex ext-real real set
addreal "**" F is complex ext-real real Element of REAL
g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
((<*> REAL)) is complex ext-real real Element of REAL
addreal "**" (<*> REAL) is complex ext-real real Element of REAL
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>) is complex ext-real real set
g is complex ext-real real Element of REAL
<*g*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*g*>) is complex ext-real real Element of REAL
addreal "**" <*g*> is complex ext-real real Element of REAL
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g ^ <*F*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g ^ <*F*>)) is complex ext-real real set
(g) is complex ext-real real set
(g) + F is complex ext-real real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
j ^ <*i*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((j ^ <*i*>)) is complex ext-real real Element of REAL
addreal "**" (j ^ <*i*>) is complex ext-real real Element of REAL
addreal "**" j is complex ext-real real Element of REAL
addreal . ((addreal "**" j),i) is complex ext-real real Element of REAL
[(addreal "**" j),i] is set
{(addreal "**" j),i} is non empty V53() V54() V55() set
{(addreal "**" j)} is non empty trivial V53() V54() V55() 1 -element set
{{(addreal "**" j),i},{(addreal "**" j)}} is non empty set
addreal . [(addreal "**" j),i] is complex ext-real real set
(j) is complex ext-real real Element of REAL
(j) + F is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is complex ext-real real set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F ^ g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F ^ g)) is complex ext-real real set
(g) is complex ext-real real set
(F) + (g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
i ^ j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((i ^ j)) is complex ext-real real Element of REAL
addreal "**" (i ^ j) is complex ext-real real Element of REAL
addreal "**" i is complex ext-real real Element of REAL
addreal "**" j is complex ext-real real Element of REAL
addreal . ((addreal "**" i),(addreal "**" j)) is complex ext-real real Element of REAL
[(addreal "**" i),(addreal "**" j)] is set
{(addreal "**" i),(addreal "**" j)} is non empty V53() V54() V55() set
{(addreal "**" i)} is non empty trivial V53() V54() V55() 1 -element set
{{(addreal "**" i),(addreal "**" j)},{(addreal "**" i)}} is non empty set
addreal . [(addreal "**" i),(addreal "**" j)] is complex ext-real real set
(i) is complex ext-real real Element of REAL
(j) is complex ext-real real Element of REAL
(i) + (j) is complex ext-real real Element of REAL
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*F*> ^ g is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((<*F*> ^ g)) is complex ext-real real set
(g) is complex ext-real real set
F + (g) is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*i*>) is complex ext-real real Element of REAL
addreal "**" <*i*> is complex ext-real real Element of REAL
(<*i*>) + (g) is complex ext-real real Element of REAL
F is complex ext-real real set
g is complex ext-real real set
<*F,g*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 2 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
(<*F,g*>) is complex ext-real real set
F + g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*i*>) is complex ext-real real Element of REAL
addreal "**" <*i*> is complex ext-real real Element of REAL
(<*i*>) + g is complex ext-real real Element of REAL
F is complex ext-real real set
g is complex ext-real real set
F + g is complex ext-real real Element of REAL
i is complex ext-real real set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(<*F,g,i*>) is complex ext-real real set
(F + g) + i is complex ext-real real Element of REAL
<*F,g*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 2 -element FinSequence-like FinSubsequence-like set
(<*F,g*>) is complex ext-real real set
(<*F,g*>) + i is complex ext-real real Element of REAL
0 -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = 0 } is set
F is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
(F) is complex ext-real real Element of REAL
addreal "**" F is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is complex ext-real real set
F * g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j |-> i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
j -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j } is set
Seg j is V53() V54() V55() V56() V57() V58() V60() j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
(Seg j) --> i is Relation-like Seg j -defined Seg j -defined REAL -valued Function-like constant V14( Seg j) V14( Seg j) V18( Seg j,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg j),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg j),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg j),{i}:] is set
((j |-> i)) is complex ext-real real Element of REAL
addreal "**" (j |-> i) is complex ext-real real Element of REAL
j * i is complex ext-real real Element of REAL
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j + 1) |-> i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
(j + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j + 1 } is set
Seg (j + 1) is non empty V53() V54() V55() V56() V57() V58() V60() j + 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j + 1 ) } is set
(Seg (j + 1)) --> i is Relation-like Seg (j + 1) -defined Seg (j + 1) -defined REAL -valued Function-like constant non empty V14( Seg (j + 1)) V14( Seg (j + 1)) V18( Seg (j + 1),{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (j + 1)),{i}:]
[:(Seg (j + 1)),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg (j + 1)),{i}:] is set
(((j + 1) |-> i)) is complex ext-real real Element of REAL
addreal "**" ((j + 1) |-> i) is complex ext-real real Element of REAL
(j + 1) * i is complex ext-real real Element of REAL
<*i*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(j |-> i) ^ <*i*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
(((j |-> i) ^ <*i*>)) is complex ext-real real Element of REAL
addreal "**" ((j |-> i) ^ <*i*>) is complex ext-real real Element of REAL
1 * i is complex ext-real real Element of REAL
(j * i) + (1 * i) is complex ext-real real Element of REAL
0 |-> i is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
(Seg 0) --> i is Relation-like non-zero empty-yielding Seg 0 -defined Seg 0 -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty V14( Seg 0) V14( Seg 0) V18( Seg 0,{i}) epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool [:(Seg 0),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg 0),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg 0),{i}:] is set
((0 |-> i)) is complex ext-real real Element of REAL
addreal "**" (0 |-> i) is complex ext-real real Element of REAL
0 * i is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
((F |-> 0)) is complex ext-real real Element of REAL
addreal "**" (F |-> 0) is complex ext-real real Element of REAL
F * 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is complex ext-real real Element of REAL
addreal "**" g is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(i) is complex ext-real real Element of REAL
addreal "**" i is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j } is set
Seg j is V53() V54() V55() V56() V57() V58() V60() j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j + 1 } is set
Seg (j + 1) is non empty V53() V54() V55() V56() V57() V58() V60() j + 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j + 1 ) } is set
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
f3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(f3) is complex ext-real real Element of REAL
addreal "**" f3 is complex ext-real real Element of REAL
a is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
b is complex ext-real real Element of REAL
<*b*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,b] is set
{1,b} is non empty V53() V54() V55() set
{{1,b},{1}} is non empty set
{[1,b]} is Relation-like Function-like constant non empty trivial 1 -element set
a ^ <*b*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
d is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
e is complex ext-real real Element of REAL
<*e*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,e] is set
{1,e} is non empty V53() V54() V55() set
{{1,e},{1}} is non empty set
{[1,e]} is Relation-like Function-like constant non empty trivial 1 -element set
d ^ <*e*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
R is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
a . R is complex ext-real real Element of REAL
d . R is complex ext-real real Element of REAL
len d is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len d) is V53() V54() V55() V56() V57() V58() V60() len d -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len d ) } is set
dom d is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
f3 . R is complex ext-real real Element of REAL
len a is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len a) is V53() V54() V55() V56() V57() V58() V60() len a -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len a ) } is set
dom a is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
p3 . R is complex ext-real real Element of REAL
(a) is complex ext-real real Element of REAL
addreal "**" a is complex ext-real real Element of REAL
(d) is complex ext-real real Element of REAL
addreal "**" d is complex ext-real real Element of REAL
f3 . (j + 1) is complex ext-real real Element of REAL
p3 . (j + 1) is complex ext-real real Element of REAL
(d) + e is complex ext-real real Element of REAL
(a) + b is complex ext-real real Element of REAL
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
j is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
q2 is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
(j) is complex ext-real real Element of REAL
addreal "**" j is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is complex ext-real real Element of REAL
addreal "**" g is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(i) is complex ext-real real Element of REAL
addreal "**" i is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j } is set
Seg j is V53() V54() V55() V56() V57() V58() V60() j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j + 1 } is set
Seg (j + 1) is non empty V53() V54() V55() V56() V57() V58() V60() j + 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j + 1 ) } is set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
f3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
p3 . f3 is complex ext-real real Element of REAL
q2 . f3 is complex ext-real real Element of REAL
a is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
b is complex ext-real real Element of REAL
<*b*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,b] is set
{1,b} is non empty V53() V54() V55() set
{{1,b},{1}} is non empty set
{[1,b]} is Relation-like Function-like constant non empty trivial 1 -element set
a ^ <*b*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
d is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
e is complex ext-real real Element of REAL
<*e*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,e] is set
{1,e} is non empty V53() V54() V55() set
{{1,e},{1}} is non empty set
{[1,e]} is Relation-like Function-like constant non empty trivial 1 -element set
d ^ <*e*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
R is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
a . R is complex ext-real real Element of REAL
d . R is complex ext-real real Element of REAL
len d is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len d) is V53() V54() V55() V56() V57() V58() V60() len d -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len d ) } is set
dom d is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
p3 . R is complex ext-real real Element of REAL
len a is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len a) is V53() V54() V55() V56() V57() V58() V60() len a -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len a ) } is set
dom a is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
q2 . R is complex ext-real real Element of REAL
p3 . (j + 1) is complex ext-real real Element of REAL
q2 . (j + 1) is complex ext-real real Element of REAL
len d is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len d) is V53() V54() V55() V56() V57() V58() V60() len d -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len d ) } is set
dom d is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
d . f3 is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
(a) is complex ext-real real Element of REAL
addreal "**" a is complex ext-real real Element of REAL
(a) + b is complex ext-real real Element of REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(d) is complex ext-real real Element of REAL
addreal "**" d is complex ext-real real Element of REAL
(d) + e is complex ext-real real Element of REAL
len a is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len a) is V53() V54() V55() V56() V57() V58() V60() len a -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len a ) } is set
dom a is V53() V54() V55() V56() V57() V58() j -element Element of bool NAT
a . f3 is complex ext-real real Element of REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(d) is complex ext-real real Element of REAL
addreal "**" d is complex ext-real real Element of REAL
(d) + e is complex ext-real real Element of REAL
(a) is complex ext-real real Element of REAL
addreal "**" a is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
(a) + b is complex ext-real real Element of REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j + 1 } is set
j -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j } is set
Seg j is V53() V54() V55() V56() V57() V58() V60() j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j ) } is set
Seg (j + 1) is non empty V53() V54() V55() V56() V57() V58() V60() j + 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= j + 1 ) } is set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
f3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
p3 . f3 is complex ext-real real Element of REAL
q2 . f3 is complex ext-real real Element of REAL
(p3) is complex ext-real real Element of REAL
addreal "**" p3 is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
j is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
q2 is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
q2 . p3 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
j . p3 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
(j) is complex ext-real real Element of REAL
addreal "**" j is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
i . j is complex ext-real real Element of REAL
g . j is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is complex ext-real real set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
(Seg (len F)) --> 0 is Relation-like Seg (len F) -defined Seg (len F) -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg (len F)) V14( Seg (len F)) V18( Seg (len F),{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg (len F)),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg (len F)),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg (len F)),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
((len F) |-> 0) . p3 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
q2 . p3 is complex ext-real real Element of REAL
(((len F) |-> 0)) is complex ext-real real Element of REAL
addreal "**" ((len F) |-> 0) is complex ext-real real Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is complex ext-real real set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) |-> 0 is Relation-like empty-yielding NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
(Seg (len F)) --> 0 is Relation-like Seg (len F) -defined Seg (len F) -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg (len F)) V14( Seg (len F)) V18( Seg (len F),{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg (len F)),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg (len F)),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg (len F)),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
((len F) |-> 0) . p3 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
q2 . p3 is complex ext-real real Element of REAL
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F . p3 is complex ext-real real Element of REAL
((len F) |-> 0) . p3 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
(q2) is complex ext-real real Element of REAL
addreal "**" q2 is complex ext-real real Element of REAL
(((len F) |-> 0)) is complex ext-real real Element of REAL
addreal "**" ((len F) |-> 0) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F)) is complex ext-real real Element of REAL
addreal "**" (F) is complex ext-real real Element of REAL
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
F . g is complex ext-real real Element of REAL
(F . g) ^2 is complex ext-real real Element of REAL
(F . g) * (F . g) is complex ext-real real set
(F) . g is complex ext-real real Element of REAL
F is complex ext-real real set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((g,F)) is complex ext-real real Element of REAL
addreal "**" (g,F) is complex ext-real real Element of REAL
(g) is complex ext-real real set
F * (g) is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
multreal [;] (j,(id REAL)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal "**" i is complex ext-real real Element of REAL
(multreal [;] (j,(id REAL))) . (addreal "**" i) is complex ext-real real Element of REAL
(i) is complex ext-real real Element of REAL
F * (i) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F)) is complex ext-real real Element of REAL
addreal "**" (F) is complex ext-real real Element of REAL
(F) is complex ext-real real set
- (F) is complex ext-real real Element of REAL
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal "**" g is complex ext-real real Element of REAL
compreal . (addreal "**" g) is complex ext-real real Element of REAL
(g) is complex ext-real real Element of REAL
- (g) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is complex ext-real real Element of REAL
addreal "**" g is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
((F,g,i)) is complex ext-real real Element of REAL
addreal "**" (F,g,i) is complex ext-real real Element of REAL
(i) is complex ext-real real Element of REAL
addreal "**" i is complex ext-real real Element of REAL
(g) + (i) is complex ext-real real Element of REAL
addreal . ((addreal "**" g),(addreal "**" i)) is complex ext-real real Element of REAL
[(addreal "**" g),(addreal "**" i)] is set
{(addreal "**" g),(addreal "**" i)} is non empty V53() V54() V55() set
{(addreal "**" g)} is non empty trivial V53() V54() V55() 1 -element set
{{(addreal "**" g),(addreal "**" i)},{(addreal "**" g)}} is non empty set
addreal . [(addreal "**" g),(addreal "**" i)] is complex ext-real real set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is complex ext-real real Element of REAL
addreal "**" g is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
((F,g,i)) is complex ext-real real Element of REAL
addreal "**" (F,g,i) is complex ext-real real Element of REAL
(i) is complex ext-real real Element of REAL
addreal "**" i is complex ext-real real Element of REAL
(g) - (i) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
(g) + ((F,i)) is complex ext-real real Element of REAL
- (i) is complex ext-real real Element of REAL
(g) + (- (i)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
F |-> 0 is Relation-like empty-yielding NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 0 is Relation-like Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{0}) complex-valued ext-real-valued real-valued natural-valued V60() Function-yielding V70() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{0}:]
{0} is functional non empty trivial V53() V54() V55() V56() V57() V58() 1 -element set
[:(Seg F),{0}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{0}:] is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (F |-> 0) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
dom g is V53() V54() V55() V56() V57() V58() F -element Element of bool NAT
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g . i is complex ext-real real Element of REAL
(F |-> 0) . i is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of REAL
(F,g) . i is complex ext-real real Element of REAL
Seg (len g) is V53() V54() V55() V56() V57() V58() V60() len g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len g ) } is set
(g . i) ^2 is complex ext-real real Element of REAL
(g . i) * (g . i) is complex ext-real real set
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
dom (F,g) is V53() V54() V55() V56() V57() V58() F -element Element of bool NAT
(F,g) . p3 is complex ext-real real Element of REAL
g . p3 is complex ext-real real Element of REAL
(g . p3) ^2 is complex ext-real real Element of REAL
(g . p3) * (g . p3) is complex ext-real real set
len (F,g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len (F,g)) is V53() V54() V55() V56() V57() V58() V60() len (F,g) -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len (F,g) ) } is set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
multreal .: (g,i) is Relation-like Function-like set
((F,g,i)) is complex ext-real real Element of REAL
addreal "**" (F,g,i) is complex ext-real real Element of REAL
((F,g,i)) ^2 is complex ext-real real Element of REAL
((F,g,i)) * ((F,g,i)) is complex ext-real real set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (i,i) is Relation-like Function-like set
i (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
((F,g)) * ((F,i)) is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j } is set
j + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j + 1) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = j + 1 } is set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
((j + 1),q2,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
multreal .: (q2,p3) is Relation-like Function-like set
(((j + 1),q2,p3)) is complex ext-real real Element of REAL
addreal "**" ((j + 1),q2,p3) is complex ext-real real Element of REAL
(((j + 1),q2,p3)) ^2 is complex ext-real real Element of REAL
(((j + 1),q2,p3)) * (((j + 1),q2,p3)) is complex ext-real real set
((j + 1),q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
q2 (#) q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (q2,q2) is Relation-like Function-like set
q2 (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((j + 1),q2)) is complex ext-real real Element of REAL
addreal "**" ((j + 1),q2) is complex ext-real real Element of REAL
((j + 1),p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like Element of (j + 1) -tuples_on REAL
p3 (#) p3 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (p3,p3) is Relation-like Function-like set
p3 (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((j + 1),p3)) is complex ext-real real Element of REAL
addreal "**" ((j + 1),p3) is complex ext-real real Element of REAL
(((j + 1),q2)) * (((j + 1),p3)) is complex ext-real real Element of REAL
f3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
a is complex ext-real real Element of REAL
<*a*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,a] is set
{1,a} is non empty V53() V54() V55() set
{{1,a},{1}} is non empty set
{[1,a]} is Relation-like Function-like constant non empty trivial 1 -element set
f3 ^ <*a*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
b is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
d is complex ext-real real Element of REAL
<*d*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,d] is set
{1,d} is non empty V53() V54() V55() set
{{1,d},{1}} is non empty set
{[1,d]} is Relation-like Function-like constant non empty trivial 1 -element set
b ^ <*d*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
e is complex ext-real real set
<*e*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,e] is set
{1,e} is non empty V53() V54() V55() set
{{1,e},{1}} is non empty set
{[1,e]} is Relation-like Function-like constant non empty trivial 1 -element set
e ^2 is complex ext-real real set
e * e is complex ext-real real set
R is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
R ^ <*e*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like set
((R ^ <*e*>)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(R ^ <*e*>) (#) (R ^ <*e*>) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((R ^ <*e*>),(R ^ <*e*>)) is Relation-like Function-like set
(R ^ <*e*>) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((R ^ <*e*>))) is complex ext-real real Element of REAL
addreal "**" ((R ^ <*e*>)) is complex ext-real real Element of REAL
(j,R) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
R (#) R is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (R,R) is Relation-like Function-like set
R (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,R)) is complex ext-real real Element of REAL
addreal "**" (j,R) is complex ext-real real Element of REAL
((j,R)) + (e ^2) is complex ext-real real Element of REAL
s is complex ext-real real Element of REAL
<*s*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,s] is set
{1,s} is non empty V53() V54() V55() set
{{1,s},{1}} is non empty set
{[1,s]} is Relation-like Function-like constant non empty trivial 1 -element set
R ^ <*s*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
((R ^ <*s*>)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(R ^ <*s*>) (#) (R ^ <*s*>) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((R ^ <*s*>),(R ^ <*s*>)) is Relation-like Function-like set
(R ^ <*s*>) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
() * R is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
() . s is complex ext-real real Element of REAL
<*(() . s)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(() . s)] is set
{1,(() . s)} is non empty V53() V54() V55() set
{{1,(() . s)},{1}} is non empty set
{[1,(() . s)]} is Relation-like Function-like constant non empty trivial 1 -element set
(() * R) ^ <*(() . s)*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
<*(e ^2)*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,(e ^2)] is set
{1,(e ^2)} is non empty V53() V54() V55() set
{{1,(e ^2)},{1}} is non empty set
{[1,(e ^2)]} is Relation-like Function-like constant non empty trivial 1 -element set
(j,R) ^ <*(e ^2)*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like set
(j,b) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
b (#) b is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (b,b) is Relation-like Function-like set
b (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,b)) is complex ext-real real Element of REAL
addreal "**" (j,b) is complex ext-real real Element of REAL
d ^2 is complex ext-real real Element of REAL
d * d is complex ext-real real set
((j,b)) + (d ^2) is complex ext-real real Element of REAL
(j,f3,b) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
multreal .: (f3,b) is Relation-like Function-like set
((j,f3,b)) is complex ext-real real Element of REAL
addreal "**" (j,f3,b) is complex ext-real real Element of REAL
((j,f3,b)) ^2 is complex ext-real real Element of REAL
((j,f3,b)) * ((j,f3,b)) is complex ext-real real set
(((j,f3,b)) ^2) + 0 is complex ext-real real Element of REAL
(j,f3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
f3 (#) f3 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (f3,f3) is Relation-like Function-like set
f3 (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,f3)) is complex ext-real real Element of REAL
addreal "**" (j,f3) is complex ext-real real Element of REAL
((j,f3)) * ((j,b)) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) - (((j,f3,b)) ^2) is complex ext-real real Element of REAL
((f3 ^ <*a*>),(b ^ <*d*>)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((f3 ^ <*a*>),(b ^ <*d*>)) is Relation-like Function-like set
multreal .: (f3,b) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal . (a,d) is complex ext-real real Element of REAL
[a,d] is set
{a,d} is non empty V53() V54() V55() set
{a} is non empty trivial V53() V54() V55() 1 -element set
{{a,d},{a}} is non empty set
multreal . [a,d] is complex ext-real real set
<*(multreal . (a,d))*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(multreal . (a,d))] is set
{1,(multreal . (a,d))} is non empty V53() V54() V55() set
{{1,(multreal . (a,d))},{1}} is non empty set
{[1,(multreal . (a,d))]} is Relation-like Function-like constant non empty trivial 1 -element set
(multreal .: (f3,b)) ^ <*(multreal . (a,d))*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
a * d is complex ext-real real Element of REAL
<*(a * d)*> is Relation-like NAT -defined REAL -valued Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
[1,(a * d)] is set
{1,(a * d)} is non empty V53() V54() V55() set
{{1,(a * d)},{1}} is non empty set
{[1,(a * d)]} is Relation-like Function-like constant non empty trivial 1 -element set
(j,f3,b) ^ <*(a * d)*> is Relation-like NAT -defined REAL -valued Function-like non empty complex-valued ext-real-valued real-valued V60() j + 1 -element FinSequence-like FinSubsequence-like FinSequence of REAL
(((f3 ^ <*a*>),(b ^ <*d*>))) is complex ext-real real Element of REAL
addreal "**" ((f3 ^ <*a*>),(b ^ <*d*>)) is complex ext-real real Element of REAL
((j,f3,b)) + (a * d) is complex ext-real real Element of REAL
2 * (a * d) is complex ext-real real Element of REAL
(2 * (a * d)) * ((j,f3,b)) is complex ext-real real Element of REAL
(a * d) * ((j,f3,b)) is complex ext-real real Element of REAL
2 * ((a * d) * ((j,f3,b))) is complex ext-real real Element of REAL
(j,(j,f3,b),(a * d)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
((a * d)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((a * d),(id REAL)) is Relation-like Function-like set
(j,f3,b) (#) ((a * d)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,f3,b),(a * d))) is complex ext-real real Element of REAL
addreal "**" (j,(j,f3,b),(a * d)) is complex ext-real real Element of REAL
2 * ((j,(j,f3,b),(a * d))) is complex ext-real real Element of REAL
(j,(j,f3,b),d) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(d) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (d,(id REAL)) is Relation-like Function-like set
(j,f3,b) (#) (d) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,(j,(j,f3,b),d),a) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(a) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (a,(id REAL)) is Relation-like Function-like set
(j,(j,f3,b),d) (#) (a) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,(j,f3,b),d),a)) is complex ext-real real Element of REAL
addreal "**" (j,(j,(j,f3,b),d),a) is complex ext-real real Element of REAL
2 * ((j,(j,(j,f3,b),d),a)) is complex ext-real real Element of REAL
(j,f3,d) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
f3 (#) (d) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,b,(j,f3,d)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
multreal .: (b,(j,f3,d)) is Relation-like Function-like set
(j,(j,b,(j,f3,d)),a) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(j,b,(j,f3,d)) (#) (a) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,b,(j,f3,d)),a)) is complex ext-real real Element of REAL
addreal "**" (j,(j,b,(j,f3,d)),a) is complex ext-real real Element of REAL
2 * ((j,(j,b,(j,f3,d)),a)) is complex ext-real real Element of REAL
(j,b,a) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
b (#) (a) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,(j,b,a),(j,f3,d)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
multreal .: ((j,b,a),(j,f3,d)) is Relation-like Function-like set
((j,(j,b,a),(j,f3,d))) is complex ext-real real Element of REAL
addreal "**" (j,(j,b,a),(j,f3,d)) is complex ext-real real Element of REAL
2 * ((j,(j,b,a),(j,f3,d))) is complex ext-real real Element of REAL
(((j,f3,b)) + (a * d)) ^2 is complex ext-real real Element of REAL
(((j,f3,b)) + (a * d)) * (((j,f3,b)) + (a * d)) is complex ext-real real set
- ((((j,f3,b)) + (a * d)) ^2) is complex ext-real real Element of REAL
(a * d) ^2 is complex ext-real real Element of REAL
(a * d) * (a * d) is complex ext-real real set
- ((a * d) ^2) is complex ext-real real Element of REAL
((2 * (a * d)) * ((j,f3,b))) + (((j,f3,b)) ^2) is complex ext-real real Element of REAL
- (((2 * (a * d)) * ((j,f3,b))) + (((j,f3,b)) ^2)) is complex ext-real real Element of REAL
(- ((a * d) ^2)) + (- (((2 * (a * d)) * ((j,f3,b))) + (((j,f3,b)) ^2))) is complex ext-real real Element of REAL
a ^2 is complex ext-real real Element of REAL
a * a is complex ext-real real set
(a ^2) * (d ^2) is complex ext-real real Element of REAL
- ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
- (((j,f3,b)) ^2) is complex ext-real real Element of REAL
- (2 * ((j,(j,b,a),(j,f3,d)))) is complex ext-real real Element of REAL
(- (((j,f3,b)) ^2)) + (- (2 * ((j,(j,b,a),(j,f3,d))))) is complex ext-real real Element of REAL
(- ((a ^2) * (d ^2))) + ((- (((j,f3,b)) ^2)) + (- (2 * ((j,(j,b,a),(j,f3,d)))))) is complex ext-real real Element of REAL
(j,(j,b,a),(j,f3,d)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
- (j,f3,d) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (j,f3,d) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,f3,d) (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,f3,d) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,b,a) + (- (j,f3,d)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((j,b,a),(- (j,f3,d))) is Relation-like Function-like set
diffreal .: ((j,b,a),(j,f3,d)) is Relation-like Function-like set
(j,(j,(j,b,a),(j,f3,d))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(j,(j,b,a),(j,f3,d)) (#) (j,(j,b,a),(j,f3,d)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((j,(j,b,a),(j,f3,d)),(j,(j,b,a),(j,f3,d))) is Relation-like Function-like set
(j,(j,b,a),(j,f3,d)) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,(j,b,a),(j,f3,d)))) is complex ext-real real Element of REAL
addreal "**" (j,(j,(j,b,a),(j,f3,d))) is complex ext-real real Element of REAL
((j,f3)) + (a ^2) is complex ext-real real Element of REAL
(((j,f3)) + (a ^2)) * (((j,b)) + (d ^2)) is complex ext-real real Element of REAL
(a ^2) * ((j,b)) is complex ext-real real Element of REAL
((j,f3)) * (d ^2) is complex ext-real real Element of REAL
((a ^2) * ((j,b))) + (((j,f3)) * (d ^2)) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (((a ^2) * ((j,b))) + (((j,f3)) * (d ^2))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (((a ^2) * ((j,b))) + (((j,f3)) * (d ^2)))) + ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
(j,(j,b),(a ^2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
((a ^2)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((a ^2),(id REAL)) is Relation-like Function-like set
(j,b) (#) ((a ^2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,b),(a ^2))) is complex ext-real real Element of REAL
addreal "**" (j,(j,b),(a ^2)) is complex ext-real real Element of REAL
((j,(j,b),(a ^2))) + (((j,f3)) * (d ^2)) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (((j,(j,b),(a ^2))) + (((j,f3)) * (d ^2))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (((j,(j,b),(a ^2))) + (((j,f3)) * (d ^2)))) + ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
(j,(j,b,a)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(j,b,a) (#) (j,b,a) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((j,b,a),(j,b,a)) is Relation-like Function-like set
(j,b,a) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,b,a))) is complex ext-real real Element of REAL
addreal "**" (j,(j,b,a)) is complex ext-real real Element of REAL
(d ^2) * ((j,f3)) is complex ext-real real Element of REAL
((j,(j,b,a))) + ((d ^2) * ((j,f3))) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((d ^2) * ((j,f3)))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((d ^2) * ((j,f3))))) + ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
(j,(j,f3),(d ^2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
((d ^2)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((d ^2),(id REAL)) is Relation-like Function-like set
(j,f3) (#) ((d ^2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,f3),(d ^2))) is complex ext-real real Element of REAL
addreal "**" (j,(j,f3),(d ^2)) is complex ext-real real Element of REAL
((j,(j,b,a))) + ((j,(j,f3),(d ^2))) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((j,(j,f3),(d ^2)))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((j,(j,f3),(d ^2))))) + ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
(j,(j,f3,d)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(j,f3,d) (#) (j,f3,d) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((j,f3,d),(j,f3,d)) is Relation-like Function-like set
(j,f3,d) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,f3,d))) is complex ext-real real Element of REAL
addreal "**" (j,(j,f3,d)) is complex ext-real real Element of REAL
((j,(j,b,a))) + ((j,(j,f3,d))) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((j,(j,f3,d)))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (((j,(j,b,a))) + ((j,(j,f3,d))))) + ((a ^2) * (d ^2)) is complex ext-real real Element of REAL
(((j,(j,b,a))) + ((j,(j,f3,d)))) + (- (2 * ((j,(j,b,a),(j,f3,d))))) is complex ext-real real Element of REAL
((j,(j,b,a))) - (2 * ((j,(j,b,a),(j,f3,d)))) is complex ext-real real Element of REAL
(((j,(j,b,a))) - (2 * ((j,(j,b,a),(j,f3,d))))) + ((j,(j,f3,d))) is complex ext-real real Element of REAL
(j,(j,(j,b,a),(j,f3,d)),2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
(2) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (2,(id REAL)) is Relation-like Function-like set
(j,(j,b,a),(j,f3,d)) (#) (2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((j,(j,(j,b,a),(j,f3,d)),2)) is complex ext-real real Element of REAL
addreal "**" (j,(j,(j,b,a),(j,f3,d)),2) is complex ext-real real Element of REAL
((j,(j,b,a))) - ((j,(j,(j,b,a),(j,f3,d)),2)) is complex ext-real real Element of REAL
(((j,(j,b,a))) - ((j,(j,(j,b,a),(j,f3,d)),2))) + ((j,(j,f3,d))) is complex ext-real real Element of REAL
(j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
- (j,(j,(j,b,a),(j,f3,d)),2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) (j,(j,(j,b,a),(j,f3,d)),2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,(j,(j,b,a),(j,f3,d)),2) (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,(j,(j,b,a),(j,f3,d)),2) (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,(j,b,a)) + (- (j,(j,(j,b,a),(j,f3,d)),2)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: ((j,(j,b,a)),(- (j,(j,(j,b,a),(j,f3,d)),2))) is Relation-like Function-like set
diffreal .: ((j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)) is Relation-like Function-like set
((j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2))) is complex ext-real real Element of REAL
addreal "**" (j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)) is complex ext-real real Element of REAL
((j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2))) + ((j,(j,f3,d))) is complex ext-real real Element of REAL
(j,(j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)),(j,(j,f3,d))) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() j -element FinSequence-like FinSubsequence-like Element of j -tuples_on REAL
addreal .: ((j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)),(j,(j,f3,d))) is Relation-like Function-like set
((j,(j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)),(j,(j,f3,d)))) is complex ext-real real Element of REAL
addreal "**" (j,(j,(j,(j,b,a)),(j,(j,(j,b,a),(j,f3,d)),2)),(j,(j,f3,d))) is complex ext-real real Element of REAL
((((j + 1),q2)) * (((j + 1),p3))) - ((((j + 1),q2,p3)) ^2) is complex ext-real real Element of REAL
((((j,f3)) + (a ^2)) * (((j,b)) + (d ^2))) + (- ((((j,f3,b)) + (a * d)) ^2)) is complex ext-real real Element of REAL
(((j,f3)) * ((j,b))) + (- (((j,f3,b)) ^2)) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) + (- (((j,f3,b)) ^2))) + ((((j,(j,b,a))) + ((j,(j,f3,d)))) + (- (2 * ((j,(j,b,a),(j,f3,d)))))) is complex ext-real real Element of REAL
((((j,f3)) * ((j,b))) - (((j,f3,b)) ^2)) + ((j,(j,(j,b,a),(j,f3,d)))) is complex ext-real real Element of REAL
((((j + 1),q2,p3)) ^2) + 0 is complex ext-real real Element of REAL
j is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
q2 is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
(0,j,q2) is Relation-like non-zero empty-yielding NAT -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
multreal .: (j,q2) is Relation-like Function-like set
((0,j,q2)) is complex ext-real real Element of REAL
addreal "**" (0,j,q2) is complex ext-real real Element of REAL
((0,j,q2)) ^2 is complex ext-real real Element of REAL
((0,j,q2)) * ((0,j,q2)) is complex ext-real real set
(0,j) is Relation-like non-zero empty-yielding NAT -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
j (#) j is Relation-like NAT -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (j,j) is Relation-like Function-like set
j (#) () is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
((0,j)) is complex ext-real real Element of REAL
addreal "**" (0,j) is complex ext-real real Element of REAL
(0,q2) is Relation-like non-zero empty-yielding NAT -defined REAL -valued RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
q2 (#) q2 is Relation-like NAT -defined RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (q2,q2) is Relation-like Function-like set
q2 (#) () is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
((0,q2)) is complex ext-real real Element of REAL
addreal "**" (0,q2) is complex ext-real real Element of REAL
((0,j)) * ((0,q2)) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
rng F is V53() set
g is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
multcomplex "**" g is complex Element of COMPLEX
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
g is complex set
multcomplex "**" j is complex Element of COMPLEX
q2 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
i is complex set
multcomplex "**" q2 is complex Element of COMPLEX
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is complex set
i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
multcomplex "**" i is complex Element of COMPLEX
[#] (i,(the_unity_wrt multcomplex)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , COMPLEX ) complex-valued Element of bool [:NAT,COMPLEX:]
[:NAT,COMPLEX:] is Relation-like complex-valued V60() set
bool [:NAT,COMPLEX:] is V60() set
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
finSeg q2 is V60() q2 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
multcomplex $$ ((finSeg q2),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
q2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
finSeg (q2 + 1) is non empty V60() q2 + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 + 1 ) } is set
multcomplex $$ ((finSeg (q2 + 1)),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
p3 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1) is complex Element of COMPLEX
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
i . (p3 + 1) is complex set
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
finSeg p3 is V60() p3 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= p3 ) } is set
multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
Seg p3 is V53() V54() V55() V56() V57() V58() V60() p3 -element Element of bool NAT
{.(p3 + 1).} is non empty trivial V53() V54() V55() V56() V57() V58() 1 -element Element of K101(NAT)
(finSeg p3) \/ {.(p3 + 1).} is non empty Element of K101(NAT)
multcomplex $$ (((finSeg p3) \/ {.(p3 + 1).}),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
multcomplex . ((multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex))))),(([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1))) is complex Element of COMPLEX
[(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex))))),(([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1))] is set
{(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex))))),(([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1))} is non empty V53() set
{(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex)))))} is non empty trivial V53() 1 -element set
{{(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex))))),(([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1))},{(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex)))))}} is non empty set
multcomplex . [(multcomplex $$ ((finSeg p3),([#] (i,(the_unity_wrt multcomplex))))),(([#] (i,(the_unity_wrt multcomplex))) . (p3 + 1))] is complex set
a is complex ext-real real set
f3 is complex ext-real real set
a * f3 is complex ext-real real Element of REAL
findom i is V53() V54() V55() V56() V57() V58() Element of K101(NAT)
multcomplex $$ ((findom i),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
dom i is V53() V54() V55() V56() V57() V58() Element of bool NAT
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
{}. NAT is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
finSeg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
multcomplex $$ ((finSeg 0),([#] (i,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg q2 is V53() V54() V55() V56() V57() V58() V60() q2 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is complex ext-real real set
multreal "**" i is complex ext-real real Element of REAL
(i) is V53() V54() V55() Element of bool REAL
[#] (i,(the_unity_wrt multreal)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , REAL ) complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
[:NAT,REAL:] is Relation-like complex-valued ext-real-valued real-valued V60() set
bool [:NAT,REAL:] is V60() set
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
[#] (j,(the_unity_wrt multcomplex)) is Relation-like Function-like non empty V14( NAT ) V18( NAT , COMPLEX ) complex-valued Element of bool [:NAT,COMPLEX:]
[:NAT,COMPLEX:] is Relation-like complex-valued V60() set
bool [:NAT,COMPLEX:] is V60() set
dom j is V53() V54() V55() V56() V57() V58() Element of bool NAT
q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg q2 is V53() V54() V55() V56() V57() V58() V60() q2 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= q2 ) } is set
finSeg q2 is V60() q2 -element Element of K101(NAT)
multreal $$ ((finSeg q2),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
multcomplex "**" j is complex Element of COMPLEX
multcomplex $$ ((finSeg q2),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
a is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
finSeg a is V60() a -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= a ) } is set
multreal $$ ((finSeg a),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
multcomplex $$ ((finSeg a),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
finSeg (a + 1) is non empty V60() a + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= a + 1 ) } is set
multreal $$ ((finSeg (a + 1)),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
multcomplex $$ ((finSeg (a + 1)),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
([#] (i,(the_unity_wrt multreal))) . (a + 1) is complex ext-real real Element of REAL
([#] (j,(the_unity_wrt multcomplex))) . (a + 1) is complex Element of COMPLEX
i . (a + 1) is complex ext-real real Element of REAL
Seg a is V53() V54() V55() V56() V57() V58() V60() a -element Element of bool NAT
b is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
b + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
finSeg (b + 1) is non empty V60() b + 1 -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= b + 1 ) } is set
multreal $$ ((finSeg (b + 1)),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
finSeg b is V60() b -element Element of K101(NAT)
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= b ) } is set
{.(b + 1).} is non empty trivial V53() V54() V55() V56() V57() V58() 1 -element Element of K101(NAT)
(finSeg b) \/ {.(b + 1).} is non empty Element of K101(NAT)
multreal $$ (((finSeg b) \/ {.(b + 1).}),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
([#] (i,(the_unity_wrt multreal))) . (b + 1) is complex ext-real real Element of REAL
multreal . ((multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))),(([#] (i,(the_unity_wrt multreal))) . (b + 1))) is complex ext-real real Element of REAL
[(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))),(([#] (i,(the_unity_wrt multreal))) . (b + 1))] is set
{(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))),(([#] (i,(the_unity_wrt multreal))) . (b + 1))} is non empty V53() V54() V55() set
{(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal)))))} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))),(([#] (i,(the_unity_wrt multreal))) . (b + 1))},{(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal)))))}} is non empty set
multreal . [(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))),(([#] (i,(the_unity_wrt multreal))) . (b + 1))] is complex ext-real real set
(multreal $$ ((finSeg b),([#] (i,(the_unity_wrt multreal))))) * (([#] (i,(the_unity_wrt multreal))) . (b + 1)) is complex ext-real real Element of REAL
multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
([#] (j,(the_unity_wrt multcomplex))) . (b + 1) is complex Element of COMPLEX
multcomplex . ((multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex))))),(([#] (j,(the_unity_wrt multcomplex))) . (b + 1))) is complex Element of COMPLEX
[(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex))))),(([#] (j,(the_unity_wrt multcomplex))) . (b + 1))] is set
{(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex))))),(([#] (j,(the_unity_wrt multcomplex))) . (b + 1))} is non empty V53() set
{(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex)))))} is non empty trivial V53() 1 -element set
{{(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex))))),(([#] (j,(the_unity_wrt multcomplex))) . (b + 1))},{(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex)))))}} is non empty set
multcomplex . [(multcomplex $$ ((finSeg b),([#] (j,(the_unity_wrt multcomplex))))),(([#] (j,(the_unity_wrt multcomplex))) . (b + 1))] is complex set
multcomplex $$ (((finSeg b) \/ {.(b + 1).}),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
multcomplex $$ ((finSeg (b + 1)),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
{}. NAT is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
finSeg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of K101(NAT)
multreal $$ ((finSeg 0),([#] (i,(the_unity_wrt multreal)))) is complex ext-real real Element of REAL
multcomplex $$ ((finSeg 0),([#] (j,(the_unity_wrt multcomplex)))) is complex Element of COMPLEX
F is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(F) is complex set
multcomplex "**" F is complex Element of COMPLEX
g is complex Element of COMPLEX
i is complex Element of COMPLEX
F is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is complex ext-real real set
multreal "**" F is complex ext-real real Element of REAL
g is complex ext-real real Element of REAL
i is complex ext-real real Element of REAL
((<*> REAL)) is complex ext-real real Element of REAL
multreal "**" (<*> REAL) is complex ext-real real Element of REAL
F is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered set
(F) is complex ext-real real set
((<*> REAL)) is complex ext-real real Element of REAL
multreal "**" (<*> REAL) is complex ext-real real Element of REAL
F is complex set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is complex Element of COMPLEX
<*g*> is Relation-like NAT -defined COMPLEX -valued Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of COMPLEX
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
F is complex set
g is complex set
<*F,g*> is Relation-like NAT -defined Function-like non empty V60() 2 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
i is complex Element of COMPLEX
j is complex Element of COMPLEX
<*i,j*> is Relation-like NAT -defined COMPLEX -valued Function-like non empty complex-valued V60() 2 -element FinSequence-like FinSubsequence-like FinSequence of COMPLEX
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
<*j*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*i*> ^ <*j*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
q2 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
F is complex set
g is complex set
i is complex set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
j is complex Element of COMPLEX
q2 is complex Element of COMPLEX
p3 is complex Element of COMPLEX
<*j,q2,p3*> is Relation-like NAT -defined COMPLEX -valued Function-like non empty complex-valued V60() 3 -element FinSequence-like FinSubsequence-like FinSequence of COMPLEX
<*j*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*q2*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,q2] is set
{1,q2} is non empty V53() set
{{1,q2},{1}} is non empty set
{[1,q2]} is Relation-like Function-like constant non empty trivial 1 -element set
<*j*> ^ <*q2*> is Relation-like NAT -defined Function-like non empty V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*p3*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,p3] is set
{1,p3} is non empty V53() set
{{1,p3},{1}} is non empty set
{[1,p3]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*j*> ^ <*q2*>) ^ <*p3*> is Relation-like NAT -defined Function-like non empty V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
f3 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
F is complex set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*>) is complex set
g is complex Element of COMPLEX
<*g*> is Relation-like NAT -defined COMPLEX -valued Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of COMPLEX
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
multcomplex "**" i is complex Element of COMPLEX
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
F ^ g is Relation-like NAT -defined Function-like V60() FinSequence-like FinSubsequence-like set
rng (F ^ g) is set
rng F is V53() set
rng g is V53() set
(rng F) \/ (rng g) is V53() set
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
(F) is complex set
g is complex set
<*g*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
F ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued V60() FinSequence-like FinSubsequence-like set
((F ^ <*g*>)) is complex set
(F) * g is complex Element of COMPLEX
rng F is V53() set
i is complex Element of COMPLEX
<*i*> is Relation-like NAT -defined COMPLEX -valued Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like FinSequence of COMPLEX
[1,i] is set
{1,i} is non empty V53() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
F ^ <*i*> is Relation-like NAT -defined Function-like non empty complex-valued V60() FinSequence-like FinSubsequence-like set
rng (F ^ <*i*>) is non empty V53() set
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
multcomplex "**" j is complex Element of COMPLEX
q2 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(q2) is complex Element of COMPLEX
multcomplex "**" q2 is complex Element of COMPLEX
multcomplex . ((q2),i) is complex Element of COMPLEX
[(q2),i] is set
{(q2),i} is non empty V53() set
{(q2)} is non empty trivial V53() 1 -element set
{{(q2),i},{(q2)}} is non empty set
multcomplex . [(q2),i] is complex set
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
F ^ g is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
((F ^ g)) is complex set
(F) is complex set
(g) is complex set
(F) * (g) is complex Element of COMPLEX
rng (F ^ g) is V53() set
rng F is V53() set
rng g is V53() set
i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
multcomplex "**" i is complex Element of COMPLEX
j is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(j) is complex Element of COMPLEX
multcomplex "**" j is complex Element of COMPLEX
q2 is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(q2) is complex Element of COMPLEX
multcomplex "**" q2 is complex Element of COMPLEX
multcomplex . ((j),(q2)) is complex Element of COMPLEX
[(j),(q2)] is set
{(j),(q2)} is non empty V53() set
{(j)} is non empty trivial V53() 1 -element set
{{(j),(q2)},{(j)}} is non empty set
multcomplex . [(j),(q2)] is complex set
F is complex ext-real real set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
<*F*> ^ g is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((<*F*> ^ g)) is complex ext-real real set
(g) is complex ext-real real set
F * (g) is complex ext-real real Element of REAL
(<*F*>) is complex ext-real real set
(<*F*>) * (g) is complex ext-real real Element of REAL
F is complex set
g is complex set
<*F,g*> is Relation-like NAT -defined Function-like non empty complex-valued V60() 2 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
(<*F,g*>) is complex set
F * g is complex Element of COMPLEX
(<*F*>) is complex set
(<*F*>) * g is complex Element of COMPLEX
F is complex set
g is complex set
i is complex set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty complex-valued V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty complex-valued V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
(<*F,g,i*>) is complex set
F * g is complex Element of COMPLEX
(F * g) * i is complex Element of COMPLEX
<*F,g*> is Relation-like NAT -defined Function-like non empty complex-valued V60() 2 -element FinSequence-like FinSubsequence-like set
(<*F,g*>) is complex set
(<*F,g*>) * i is complex Element of COMPLEX
F is Relation-like non-zero empty-yielding NAT -defined REAL -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of 0 -tuples_on REAL
(F) is complex ext-real real Element of REAL
multreal "**" F is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F |-> 1 is Relation-like NAT -defined NAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on NAT
F -tuples_on NAT is functional non empty FinSequence-membered FinSequenceSet of NAT
NAT * is functional non empty FinSequence-membered FinSequenceSet of NAT
{ b₁ where b₁ is Relation-like NAT -defined NAT -valued Function-like V60() FinSequence-like FinSubsequence-like Element of NAT * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> 1 is Relation-like non-zero Seg F -defined Seg F -defined NAT -valued RAT -valued INT -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{1}) complex-valued ext-real-valued real-valued natural-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{1}:]
[:(Seg F),{1}:] is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
bool [:(Seg F),{1}:] is set
((F |-> 1)) is complex ext-real real set
F |-> (the_unity_wrt multreal) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (the_unity_wrt multreal) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(the_unity_wrt multreal)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(the_unity_wrt multreal)}:]
{(the_unity_wrt multreal)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(the_unity_wrt multreal)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(the_unity_wrt multreal)}:] is set
((F |-> (the_unity_wrt multreal))) is complex ext-real real Element of REAL
multreal "**" (F |-> (the_unity_wrt multreal)) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like V60() FinSequence-like FinSubsequence-like set
i is set
<*i*> is Relation-like NAT -defined Function-like constant non empty trivial V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
g ^ <*i*> is Relation-like NAT -defined Function-like non empty V60() FinSequence-like FinSubsequence-like set
rng F is V53() set
dom g is V53() V54() V55() V56() V57() V58() Element of bool NAT
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g . j is set
F . j is complex set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len g) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F . (len F) is complex set
F is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is complex set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
g + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (g + 1) is non empty V53() V54() V55() V56() V57() V58() V60() g + 1 -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g + 1 ) } is set
i is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(i) is complex set
j is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
q2 is complex set
<*q2*> is Relation-like NAT -defined Function-like constant non empty trivial complex-valued V60() 1 -element FinSequence-like FinSubsequence-like set
[1,q2] is set
{1,q2} is non empty V53() set
{{1,q2},{1}} is non empty set
{[1,q2]} is Relation-like Function-like constant non empty trivial 1 -element set
j ^ <*q2*> is Relation-like NAT -defined Function-like non empty complex-valued V60() FinSequence-like FinSubsequence-like set
len j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len j) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural complex ext-real positive non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(j) is complex set
(j) * q2 is complex Element of COMPLEX
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
i . p3 is complex set
Seg (len j) is V53() V54() V55() V56() V57() V58() V60() len j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len j ) } is set
dom j is V53() V54() V55() V56() V57() V58() Element of bool NAT
j . p3 is complex set
p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
j . p3 is complex set
Seg (len j) is V53() V54() V55() V56() V57() V58() V60() len j -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len j ) } is set
dom j is V53() V54() V55() V56() V57() V58() Element of bool NAT
i . p3 is complex set
i . (g + 1) is complex set
Seg 0 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= 0 ) } is set
g is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(g) is complex set
<*> COMPLEX is Relation-like non-zero empty-yielding NAT -defined RAT -valued COMPLEX -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of COMPLEX
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g . i is complex set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F . g is complex set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F + g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is complex ext-real real set
(F + g) |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F + g -element FinSequence-like FinSubsequence-like set
Seg (F + g) is V53() V54() V55() V56() V57() V58() V60() F + g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F + g ) } is set
(Seg (F + g)) --> i is Relation-like Seg (F + g) -defined Seg (F + g) -defined Function-like constant V14( Seg (F + g)) V14( Seg (F + g)) V18( Seg (F + g),{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F + g)),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg (F + g)),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg (F + g)),{i}:] is set
(((F + g) |-> i)) is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex ext-real real set
g |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like set
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
(Seg g) --> i is Relation-like Seg g -defined Seg g -defined Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{i}:]
[:(Seg g),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg g),{i}:] is set
((g |-> i)) is complex ext-real real set
((F |-> i)) * ((g |-> i)) is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
(F + g) |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F + g -element FinSequence-like FinSubsequence-like Element of (F + g) -tuples_on REAL
(F + g) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F + g } is set
(Seg (F + g)) --> j is Relation-like Seg (F + g) -defined Seg (F + g) -defined REAL -valued Function-like constant V14( Seg (F + g)) V14( Seg (F + g)) V18( Seg (F + g),{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F + g)),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg (F + g)),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg (F + g)),{j}:] is set
(((F + g) |-> j)) is complex ext-real real Element of REAL
multreal "**" ((F + g) |-> j) is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
multreal "**" (F |-> j) is complex ext-real real Element of REAL
g |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
g -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = g } is set
(Seg g) --> j is Relation-like Seg g -defined Seg g -defined REAL -valued Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{j}:]
[:(Seg g),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg g),{j}:] is set
multreal "**" (g |-> j) is complex ext-real real Element of REAL
multreal . ((multreal "**" (F |-> j)),(multreal "**" (g |-> j))) is complex ext-real real Element of REAL
[(multreal "**" (F |-> j)),(multreal "**" (g |-> j))] is set
{(multreal "**" (F |-> j)),(multreal "**" (g |-> j))} is non empty V53() V54() V55() set
{(multreal "**" (F |-> j))} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal "**" (F |-> j)),(multreal "**" (g |-> j))},{(multreal "**" (F |-> j))}} is non empty set
multreal . [(multreal "**" (F |-> j)),(multreal "**" (g |-> j))] is complex ext-real real set
((F |-> j)) is complex ext-real real Element of REAL
((g |-> j)) is complex ext-real real Element of REAL
((F |-> j)) * ((g |-> j)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F * g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is complex ext-real real set
(F * g) |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F * g -element FinSequence-like FinSubsequence-like set
Seg (F * g) is V53() V54() V55() V56() V57() V58() V60() F * g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F * g ) } is set
(Seg (F * g)) --> i is Relation-like Seg (F * g) -defined Seg (F * g) -defined Function-like constant V14( Seg (F * g)) V14( Seg (F * g)) V18( Seg (F * g),{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F * g)),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg (F * g)),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg (F * g)),{i}:] is set
(((F * g) |-> i)) is complex ext-real real set
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex ext-real real set
g |-> ((F |-> i)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like set
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
(Seg g) --> ((F |-> i)) is Relation-like Seg g -defined Seg g -defined Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{((F |-> i))}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{((F |-> i))}:]
{((F |-> i))} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg g),{((F |-> i))}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg g),{((F |-> i))}:] is set
((g |-> ((F |-> i)))) is complex ext-real real set
j is complex ext-real real Element of REAL
(F * g) |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F * g -element FinSequence-like FinSubsequence-like Element of (F * g) -tuples_on REAL
(F * g) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F * g } is set
(Seg (F * g)) --> j is Relation-like Seg (F * g) -defined Seg (F * g) -defined REAL -valued Function-like constant V14( Seg (F * g)) V14( Seg (F * g)) V18( Seg (F * g),{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F * g)),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg (F * g)),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg (F * g)),{j}:] is set
(((F * g) |-> j)) is complex ext-real real Element of REAL
multreal "**" ((F * g) |-> j) is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
((F |-> j)) is complex ext-real real Element of REAL
multreal "**" (F |-> j) is complex ext-real real Element of REAL
g |-> ((F |-> j)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on REAL
g -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = g } is set
(Seg g) --> ((F |-> j)) is Relation-like Seg g -defined Seg g -defined REAL -valued Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{((F |-> j))}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{((F |-> j))}:]
{((F |-> j))} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg g),{((F |-> j))}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg g),{((F |-> j))}:] is set
((g |-> ((F |-> j)))) is complex ext-real real Element of REAL
multreal "**" (g |-> ((F |-> j))) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is complex ext-real real set
i is complex ext-real real set
g * i is complex ext-real real Element of REAL
F |-> (g * i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
(Seg F) --> (g * i) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g * i)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g * i)}:]
{(g * i)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(g * i)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(g * i)}:] is set
((F |-> (g * i))) is complex ext-real real Element of REAL
multreal "**" (F |-> (g * i)) is complex ext-real real Element of REAL
F |-> i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex ext-real real set
((F |-> g)) * ((F |-> i)) is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
q2 is complex ext-real real Element of REAL
j * q2 is complex ext-real real Element of REAL
F |-> (j * q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (j * q2) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(j * q2)}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(j * q2)}:]
{(j * q2)} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(j * q2)}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(j * q2)}:] is set
((F |-> (j * q2))) is complex ext-real real Element of REAL
multreal "**" (F |-> (j * q2)) is complex ext-real real Element of REAL
multreal . (j,q2) is complex ext-real real Element of REAL
[j,q2] is set
{j,q2} is non empty V53() V54() V55() set
{j} is non empty trivial V53() V54() V55() 1 -element set
{{j,q2},{j}} is non empty set
multreal . [j,q2] is complex ext-real real set
F |-> (multreal . (j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> (multreal . (j,q2)) is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(multreal . (j,q2))}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(multreal . (j,q2))}:]
{(multreal . (j,q2))} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{(multreal . (j,q2))}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{(multreal . (j,q2))}:] is set
multreal "**" (F |-> (multreal . (j,q2))) is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
multreal "**" (F |-> j) is complex ext-real real Element of REAL
F |-> q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> q2 is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{q2}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{q2}:]
{q2} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{q2}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{q2}:] is set
multreal "**" (F |-> q2) is complex ext-real real Element of REAL
multreal . ((multreal "**" (F |-> j)),(multreal "**" (F |-> q2))) is complex ext-real real Element of REAL
[(multreal "**" (F |-> j)),(multreal "**" (F |-> q2))] is set
{(multreal "**" (F |-> j)),(multreal "**" (F |-> q2))} is non empty V53() V54() V55() set
{(multreal "**" (F |-> j))} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal "**" (F |-> j)),(multreal "**" (F |-> q2))},{(multreal "**" (F |-> j))}} is non empty set
multreal . [(multreal "**" (F |-> j)),(multreal "**" (F |-> q2))] is complex ext-real real set
((F |-> j)) is complex ext-real real Element of REAL
((F |-> q2)) is complex ext-real real Element of REAL
((F |-> j)) * ((F |-> q2)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is complex ext-real real Element of REAL
multreal "**" g is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
multreal .: (g,i) is Relation-like Function-like set
((F,g,i)) is complex ext-real real Element of REAL
multreal "**" (F,g,i) is complex ext-real real Element of REAL
(i) is complex ext-real real Element of REAL
multreal "**" i is complex ext-real real Element of REAL
(g) * (i) is complex ext-real real Element of REAL
multreal . ((multreal "**" g),(multreal "**" i)) is complex ext-real real Element of REAL
[(multreal "**" g),(multreal "**" i)] is set
{(multreal "**" g),(multreal "**" i)} is non empty V53() V54() V55() set
{(multreal "**" g)} is non empty trivial V53() V54() V55() 1 -element set
{{(multreal "**" g),(multreal "**" i)},{(multreal "**" g)}} is non empty set
multreal . [(multreal "**" g),(multreal "**" i)] is complex ext-real real set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is complex ext-real real set
F |-> g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is complex ext-real real set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,i,g)) is complex ext-real real Element of REAL
multreal "**" (F,i,g) is complex ext-real real Element of REAL
(i) is complex ext-real real Element of REAL
multreal "**" i is complex ext-real real Element of REAL
((F |-> g)) * (i) is complex ext-real real Element of REAL
j is complex ext-real real Element of REAL
F |-> j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(Seg F) --> j is Relation-like Seg F -defined Seg F -defined REAL -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{j}) complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{j}:]
{j} is non empty trivial V53() V54() V55() 1 -element set
[:(Seg F),{j}:] is Relation-like complex-valued ext-real-valued real-valued set
bool [:(Seg F),{j}:] is set
(F,(F |-> j),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
multreal .: ((F |-> j),i) is Relation-like Function-like set
((F,(F |-> j),i)) is complex ext-real real Element of REAL
multreal "**" (F,(F |-> j),i) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g)) is complex ext-real real Element of REAL
multreal "**" (F,g) is complex ext-real real Element of REAL
(g) is complex ext-real real Element of REAL
multreal "**" g is complex ext-real real Element of REAL
(g) ^2 is complex ext-real real Element of REAL
(g) * (g) is complex ext-real real set
F is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() FinSequence-like FinSubsequence-like FinSequence of COMPLEX
(F) is complex Element of COMPLEX
multcomplex "**" F is complex Element of COMPLEX
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F + g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is complex Element of COMPLEX
(F + g) |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F + g -element FinSequence-like FinSubsequence-like Element of (F + g) -tuples_on COMPLEX
(F + g) -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
COMPLEX * is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = F + g } is set
Seg (F + g) is V53() V54() V55() V56() V57() V58() V60() F + g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F + g ) } is set
(Seg (F + g)) --> i is Relation-like Seg (F + g) -defined Seg (F + g) -defined COMPLEX -valued Function-like constant V14( Seg (F + g)) V14( Seg (F + g)) V18( Seg (F + g),{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F + g)),{i}:]
{i} is non empty trivial V53() 1 -element set
[:(Seg (F + g)),{i}:] is Relation-like complex-valued set
bool [:(Seg (F + g)),{i}:] is set
(((F + g) |-> i)) is complex Element of COMPLEX
multcomplex "**" ((F + g) |-> i) is complex Element of COMPLEX
F |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
F -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
[:(Seg F),{i}:] is Relation-like complex-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex Element of COMPLEX
multcomplex "**" (F |-> i) is complex Element of COMPLEX
g |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on COMPLEX
g -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = g } is set
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
(Seg g) --> i is Relation-like Seg g -defined Seg g -defined COMPLEX -valued Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{i}:]
[:(Seg g),{i}:] is Relation-like complex-valued set
bool [:(Seg g),{i}:] is set
((g |-> i)) is complex Element of COMPLEX
multcomplex "**" (g |-> i) is complex Element of COMPLEX
((F |-> i)) * ((g |-> i)) is complex Element of COMPLEX
multcomplex . ((multcomplex "**" (F |-> i)),(multcomplex "**" (g |-> i))) is complex Element of COMPLEX
[(multcomplex "**" (F |-> i)),(multcomplex "**" (g |-> i))] is set
{(multcomplex "**" (F |-> i)),(multcomplex "**" (g |-> i))} is non empty V53() set
{(multcomplex "**" (F |-> i))} is non empty trivial V53() 1 -element set
{{(multcomplex "**" (F |-> i)),(multcomplex "**" (g |-> i))},{(multcomplex "**" (F |-> i))}} is non empty set
multcomplex . [(multcomplex "**" (F |-> i)),(multcomplex "**" (g |-> i))] is complex set
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F * g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is complex Element of COMPLEX
(F * g) |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F * g -element FinSequence-like FinSubsequence-like Element of (F * g) -tuples_on COMPLEX
(F * g) -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
COMPLEX * is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = F * g } is set
Seg (F * g) is V53() V54() V55() V56() V57() V58() V60() F * g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F * g ) } is set
(Seg (F * g)) --> i is Relation-like Seg (F * g) -defined Seg (F * g) -defined COMPLEX -valued Function-like constant V14( Seg (F * g)) V14( Seg (F * g)) V18( Seg (F * g),{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg (F * g)),{i}:]
{i} is non empty trivial V53() 1 -element set
[:(Seg (F * g)),{i}:] is Relation-like complex-valued set
bool [:(Seg (F * g)),{i}:] is set
(((F * g) |-> i)) is complex Element of COMPLEX
multcomplex "**" ((F * g) |-> i) is complex Element of COMPLEX
F |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
F -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
[:(Seg F),{i}:] is Relation-like complex-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex Element of COMPLEX
multcomplex "**" (F |-> i) is complex Element of COMPLEX
g |-> ((F |-> i)) is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() g -element FinSequence-like FinSubsequence-like Element of g -tuples_on COMPLEX
g -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = g } is set
Seg g is V53() V54() V55() V56() V57() V58() V60() g -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= g ) } is set
(Seg g) --> ((F |-> i)) is Relation-like Seg g -defined Seg g -defined COMPLEX -valued Function-like constant V14( Seg g) V14( Seg g) V18( Seg g,{((F |-> i))}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg g),{((F |-> i))}:]
{((F |-> i))} is non empty trivial V53() 1 -element set
[:(Seg g),{((F |-> i))}:] is Relation-like complex-valued set
bool [:(Seg g),{((F |-> i))}:] is set
((g |-> ((F |-> i)))) is complex Element of COMPLEX
multcomplex "**" (g |-> ((F |-> i))) is complex Element of COMPLEX
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
g is complex Element of COMPLEX
F |-> g is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
F -tuples_on COMPLEX is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
COMPLEX * is functional non empty FinSequence-membered FinSequenceSet of COMPLEX
{ b₁ where b₁ is Relation-like NAT -defined COMPLEX -valued Function-like V60() FinSequence-like FinSubsequence-like Element of COMPLEX * : len b₁ = F } is set
Seg F is V53() V54() V55() V56() V57() V58() V60() F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= F ) } is set
(Seg F) --> g is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{g}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{g}:]
{g} is non empty trivial V53() 1 -element set
[:(Seg F),{g}:] is Relation-like complex-valued set
bool [:(Seg F),{g}:] is set
((F |-> g)) is complex Element of COMPLEX
multcomplex "**" (F |-> g) is complex Element of COMPLEX
i is complex Element of COMPLEX
g * i is complex Element of COMPLEX
F |-> (g * i) is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
(Seg F) --> (g * i) is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(g * i)}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(g * i)}:]
{(g * i)} is non empty trivial V53() 1 -element set
[:(Seg F),{(g * i)}:] is Relation-like complex-valued set
bool [:(Seg F),{(g * i)}:] is set
((F |-> (g * i))) is complex Element of COMPLEX
multcomplex "**" (F |-> (g * i)) is complex Element of COMPLEX
F |-> i is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
(Seg F) --> i is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{i}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{i}:]
{i} is non empty trivial V53() 1 -element set
[:(Seg F),{i}:] is Relation-like complex-valued set
bool [:(Seg F),{i}:] is set
((F |-> i)) is complex Element of COMPLEX
multcomplex "**" (F |-> i) is complex Element of COMPLEX
((F |-> g)) * ((F |-> i)) is complex Element of COMPLEX
multcomplex . (g,i) is complex Element of COMPLEX
[g,i] is set
{g,i} is non empty V53() set
{{g,i},{g}} is non empty set
multcomplex . [g,i] is complex set
F |-> (multcomplex . (g,i)) is Relation-like NAT -defined COMPLEX -valued Function-like complex-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on COMPLEX
(Seg F) --> (multcomplex . (g,i)) is Relation-like Seg F -defined Seg F -defined COMPLEX -valued Function-like constant V14( Seg F) V14( Seg F) V18( Seg F,{(multcomplex . (g,i))}) complex-valued V60() FinSequence-like FinSubsequence-like Element of bool [:(Seg F),{(multcomplex . (g,i))}:]
{(multcomplex . (g,i))} is non empty trivial V53() 1 -element set
[:(Seg F),{(multcomplex . (g,i))}:] is Relation-like complex-valued set
bool [:(Seg F),{(multcomplex . (g,i))}:] is set
multcomplex "**" (F |-> (multcomplex . (g,i))) is complex Element of COMPLEX
multcomplex . ((multcomplex "**" (F |-> g)),(multcomplex "**" (F |-> i))) is complex Element of COMPLEX
[(multcomplex "**" (F |-> g)),(multcomplex "**" (F |-> i))] is set
{(multcomplex "**" (F |-> g)),(multcomplex "**" (F |-> i))} is non empty V53() set
{(multcomplex "**" (F |-> g))} is non empty trivial V53() 1 -element set
{{(multcomplex "**" (F |-> g)),(multcomplex "**" (F |-> i))},{(multcomplex "**" (F |-> g))}} is non empty set
multcomplex . [(multcomplex "**" (F |-> g)),(multcomplex "**" (F |-> i))] is complex set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len (F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
len (F,g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
addreal .: (j,q2) is Relation-like Function-like set
dom ((len F),j,q2) is V53() V54() V55() V56() V57() V58() len F -element Element of bool NAT
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
len (F,g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
- q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j + (- q2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (j,(- q2)) is Relation-like Function-like set
diffreal .: (j,q2) is Relation-like Function-like set
dom ((len F),j,q2) is V53() V54() V55() V56() V57() V58() len F -element Element of bool NAT
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
F is complex ext-real real set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
g (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len (g,F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len g) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len g } is set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len g -element FinSequence-like FinSubsequence-like Element of (len g) -tuples_on REAL
((len g),j,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len g -element FinSequence-like FinSubsequence-like Element of (len g) -tuples_on REAL
j (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len ((len g),j,F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),i) is Relation-like Function-like set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,i) is Relation-like Function-like set
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((F,i),(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F,i),(g,i)) is Relation-like Function-like set
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
dom ((F,g),i) is V53() V54() V55() V56() V57() V58() Element of bool NAT
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
addreal .: (j,q2) is Relation-like Function-like set
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),((len F),j,q2),p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (((len F),j,q2),p3) is Relation-like Function-like set
len ((len F),((len F),j,q2),p3) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len ((len F),((len F),j,q2),p3)) is V53() V54() V55() V56() V57() V58() V60() len ((len F),((len F),j,q2),p3) -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len ((len F),((len F),j,q2),p3) ) } is set
Seg (len F) is V53() V54() V55() V56() V57() V58() V60() len F -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len F ) } is set
((len F),j,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (j,p3) is Relation-like Function-like set
((len F),q2,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (q2,p3) is Relation-like Function-like set
((len F),((len F),j,p3),((len F),q2,p3)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
addreal .: (((len F),j,p3),((len F),q2,p3)) is Relation-like Function-like set
len ((len F),((len F),j,p3),((len F),q2,p3)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len ((len F),((len F),j,p3),((len F),q2,p3))) is V53() V54() V55() V56() V57() V58() V60() len ((len F),((len F),j,p3),((len F),q2,p3)) -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len ((len F),((len F),j,p3),((len F),q2,p3)) ) } is set
dom ((len F),((len F),j,p3),((len F),q2,p3)) is V53() V54() V55() V56() V57() V58() len F -element Element of bool NAT
dom (F,i) is V53() V54() V55() V56() V57() V58() Element of bool NAT
len ((len F),j,p3) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
Seg (len ((len F),j,p3)) is V53() V54() V55() V56() V57() V58() V60() len ((len F),j,p3) -element Element of bool NAT
{ b₁ where b₁ is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT : ( 1 <= b₁ & b₁ <= len ((len F),j,p3) ) } is set
f3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
((F,g),i) . f3 is complex ext-real real Element of REAL
((F,i),(g,i)) . f3 is complex ext-real real Element of REAL
F . f3 is complex ext-real real Element of REAL
g . f3 is complex ext-real real Element of REAL
(F,g) . f3 is complex ext-real real Element of REAL
i . f3 is complex ext-real real Element of REAL
len ((len F),j,q2) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
dom ((len F),j,q2) is V53() V54() V55() V56() V57() V58() len F -element Element of bool NAT
(F . f3) + (g . f3) is complex ext-real real Element of REAL
((F,g) . f3) * (i . f3) is complex ext-real real Element of REAL
(F . f3) * (i . f3) is complex ext-real real Element of REAL
(g . f3) * (i . f3) is complex ext-real real Element of REAL
((F . f3) * (i . f3)) + ((g . f3) * (i . f3)) is complex ext-real real Element of REAL
(F,i) . f3 is complex ext-real real Element of REAL
((F,i) . f3) + ((g . f3) * (i . f3)) is complex ext-real real Element of REAL
(g,i) . f3 is complex ext-real real Element of REAL
((F,i) . f3) + ((g,i) . f3) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
i is complex ext-real real set
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (j,q2) is Relation-like Function-like set
((j,q2)) is complex ext-real real Element of REAL
addreal "**" (j,q2) is complex ext-real real Element of REAL
(q2,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (q2,j) is Relation-like Function-like set
((q2,j)) is complex ext-real real Element of REAL
addreal "**" (q2,j) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,g) is complex ext-real real set
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,j) is complex ext-real real set
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
(j,i) is complex ext-real real set
(j,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (j,i) is Relation-like Function-like set
((j,i)) is complex ext-real real Element of REAL
addreal "**" (j,i) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,F) is complex ext-real real Element of REAL
(F,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,F) is Relation-like Function-like set
((F,F)) is complex ext-real real Element of REAL
addreal "**" (F,F) is complex ext-real real Element of REAL
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
i (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (i,i) is Relation-like Function-like set
i (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((len F),i)) is complex ext-real real Element of REAL
addreal "**" ((len F),i) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g),i) is complex ext-real real Element of REAL
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),i) is Relation-like Function-like set
(((F,g),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g),i) is complex ext-real real Element of REAL
(F,i) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,i) is Relation-like Function-like set
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
(F,i) + (g,i) is complex ext-real real Element of REAL
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
((F,i),(g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((F,i),(g,i)) is Relation-like Function-like set
(((F,i),(g,i))) is complex ext-real real Element of REAL
addreal "**" ((F,i),(g,i)) is complex ext-real real Element of REAL
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),j,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (j,p3) is Relation-like Function-like set
(((len F),j,p3)) is complex ext-real real Element of REAL
addreal "**" ((len F),j,p3) is complex ext-real real Element of REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),q2,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (q2,p3) is Relation-like Function-like set
(((len F),q2,p3)) is complex ext-real real Element of REAL
addreal "**" ((len F),q2,p3) is complex ext-real real Element of REAL
(((len F),j,p3)) + (((len F),q2,p3)) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is complex ext-real real Element of REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
i is complex ext-real real set
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(i) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (i,(id REAL)) is Relation-like Function-like set
F (#) (i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,i),g) is complex ext-real real Element of REAL
((F,i),g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,i),g) is Relation-like Function-like set
(((F,i),g)) is complex ext-real real Element of REAL
addreal "**" ((F,i),g) is complex ext-real real Element of REAL
i * (F,g) is complex ext-real real Element of REAL
(len F) -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = len F } is set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
((len F),q2,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
multreal .: (q2,p3) is Relation-like Function-like set
j is complex ext-real real Element of REAL
((len F),((len F),q2,p3),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() len F -element FinSequence-like FinSubsequence-like Element of (len F) -tuples_on REAL
(j) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is Relation-like Function-like set
((len F),q2,p3) (#) (j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(((len F),((len F),q2,p3),j)) is complex ext-real real Element of REAL
addreal "**" ((len F),((len F),q2,p3),j) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),g) is complex ext-real real Element of REAL
((F),g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F),g) is Relation-like Function-like set
(((F),g)) is complex ext-real real Element of REAL
addreal "**" ((F),g) is complex ext-real real Element of REAL
(F,g) is complex ext-real real Element of REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
- (F,g) is complex ext-real real Element of REAL
(- 1) * (F,g) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F),(g)) is complex ext-real real Element of REAL
((F),(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F),(g)) is Relation-like Function-like set
(((F),(g))) is complex ext-real real Element of REAL
addreal "**" ((F),(g)) is complex ext-real real Element of REAL
(F,g) is complex ext-real real Element of REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
len (g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,(g)) is complex ext-real real Element of REAL
(F,(g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,(g)) is Relation-like Function-like set
((F,(g))) is complex ext-real real Element of REAL
addreal "**" (F,(g)) is complex ext-real real Element of REAL
- (F,(g)) is complex ext-real real Element of REAL
- (F,g) is complex ext-real real Element of REAL
- (- (F,g)) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g),i) is complex ext-real real Element of REAL
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),i) is Relation-like Function-like set
(((F,g),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g),i) is complex ext-real real Element of REAL
(F,i) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,i) is Relation-like Function-like set
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
(F,i) - (g,i) is complex ext-real real Element of REAL
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
len (g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
((g),i) is complex ext-real real Element of REAL
((g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((g),i) is Relation-like Function-like set
(((g),i)) is complex ext-real real Element of REAL
addreal "**" ((g),i) is complex ext-real real Element of REAL
(F,i) + ((g),i) is complex ext-real real Element of REAL
- (g,i) is complex ext-real real Element of REAL
(F,i) + (- (g,i)) is complex ext-real real Element of REAL
F is complex ext-real real set
g is complex ext-real real set
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(i,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (F,(id REAL)) is Relation-like Function-like set
i (#) (F) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(j,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
j (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((i,F),(j,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: ((i,F),(j,g)) is Relation-like Function-like set
(((i,F),(j,g)),q2) is complex ext-real real Element of REAL
(((i,F),(j,g)),q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (((i,F),(j,g)),q2) is Relation-like Function-like set
((((i,F),(j,g)),q2)) is complex ext-real real Element of REAL
addreal "**" (((i,F),(j,g)),q2) is complex ext-real real Element of REAL
(i,q2) is complex ext-real real Element of REAL
(i,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,q2) is Relation-like Function-like set
((i,q2)) is complex ext-real real Element of REAL
addreal "**" (i,q2) is complex ext-real real Element of REAL
F * (i,q2) is complex ext-real real Element of REAL
(j,q2) is complex ext-real real Element of REAL
(j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (j,q2) is Relation-like Function-like set
((j,q2)) is complex ext-real real Element of REAL
addreal "**" (j,q2) is complex ext-real real Element of REAL
g * (j,q2) is complex ext-real real Element of REAL
(F * (i,q2)) + (g * (j,q2)) is complex ext-real real Element of REAL
len (i,F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (j,g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
((i,F),q2) is complex ext-real real Element of REAL
((i,F),q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((i,F),q2) is Relation-like Function-like set
(((i,F),q2)) is complex ext-real real Element of REAL
addreal "**" ((i,F),q2) is complex ext-real real Element of REAL
((j,g),q2) is complex ext-real real Element of REAL
((j,g),q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((j,g),q2) is Relation-like Function-like set
(((j,g),q2)) is complex ext-real real Element of REAL
addreal "**" ((j,g),q2) is complex ext-real real Element of REAL
((i,F),q2) + ((j,g),q2) is complex ext-real real Element of REAL
(F * (i,q2)) + ((j,g),q2) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (i,j) is Relation-like Function-like set
((F,g),(i,j)) is complex ext-real real Element of REAL
((F,g),(i,j)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),(i,j)) is Relation-like Function-like set
(((F,g),(i,j))) is complex ext-real real Element of REAL
addreal "**" ((F,g),(i,j)) is complex ext-real real Element of REAL
(F,i) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,i) is Relation-like Function-like set
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
(F,j) is complex ext-real real Element of REAL
(F,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,j) is Relation-like Function-like set
((F,j)) is complex ext-real real Element of REAL
addreal "**" (F,j) is complex ext-real real Element of REAL
(F,i) + (F,j) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
((F,i) + (F,j)) + (g,i) is complex ext-real real Element of REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(((F,i) + (F,j)) + (g,i)) + (g,j) is complex ext-real real Element of REAL
((F,g),j) is complex ext-real real Element of REAL
((F,g),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),j) is Relation-like Function-like set
(((F,g),j)) is complex ext-real real Element of REAL
addreal "**" ((F,g),j) is complex ext-real real Element of REAL
(F,j) + (g,j) is complex ext-real real Element of REAL
((F,g),i) is complex ext-real real Element of REAL
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),i) is Relation-like Function-like set
(((F,g),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g),i) is complex ext-real real Element of REAL
((F,g),i) + ((F,g),j) is complex ext-real real Element of REAL
(F,i) + (g,i) is complex ext-real real Element of REAL
((F,i) + (g,i)) + ((F,j) + (g,j)) is complex ext-real real Element of REAL
len (F,g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i + (- j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (i,(- j)) is Relation-like Function-like set
diffreal .: (i,j) is Relation-like Function-like set
((F,g),(i,j)) is complex ext-real real Element of REAL
((F,g),(i,j)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),(i,j)) is Relation-like Function-like set
(((F,g),(i,j))) is complex ext-real real Element of REAL
addreal "**" ((F,g),(i,j)) is complex ext-real real Element of REAL
(F,i) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,i) is Relation-like Function-like set
((F,i)) is complex ext-real real Element of REAL
addreal "**" (F,i) is complex ext-real real Element of REAL
(F,j) is complex ext-real real Element of REAL
(F,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,j) is Relation-like Function-like set
((F,j)) is complex ext-real real Element of REAL
addreal "**" (F,j) is complex ext-real real Element of REAL
(F,i) - (F,j) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
((F,i) - (F,j)) - (g,i) is complex ext-real real Element of REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(((F,i) - (F,j)) - (g,i)) + (g,j) is complex ext-real real Element of REAL
(F,(i,j)) is complex ext-real real Element of REAL
(F,(i,j)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,(i,j)) is Relation-like Function-like set
((F,(i,j))) is complex ext-real real Element of REAL
addreal "**" (F,(i,j)) is complex ext-real real Element of REAL
(g,(i,j)) is complex ext-real real Element of REAL
(g,(i,j)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,(i,j)) is Relation-like Function-like set
((g,(i,j))) is complex ext-real real Element of REAL
addreal "**" (g,(i,j)) is complex ext-real real Element of REAL
(F,(i,j)) - (g,(i,j)) is complex ext-real real Element of REAL
(g,i) - (g,j) is complex ext-real real Element of REAL
((F,i) - (F,j)) - ((g,i) - (g,j)) is complex ext-real real Element of REAL
len (i,j) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
addreal .: (F,g) is Relation-like Function-like set
((F,g),(F,g)) is complex ext-real real Element of REAL
((F,g),(F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),(F,g)) is Relation-like Function-like set
(((F,g),(F,g))) is complex ext-real real Element of REAL
addreal "**" ((F,g),(F,g)) is complex ext-real real Element of REAL
(F,F) is complex ext-real real Element of REAL
(F,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,F) is Relation-like Function-like set
((F,F)) is complex ext-real real Element of REAL
addreal "**" (F,F) is complex ext-real real Element of REAL
(F,g) is complex ext-real real Element of REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
2 * (F,g) is complex ext-real real Element of REAL
(F,F) + (2 * (F,g)) is complex ext-real real Element of REAL
(g,g) is complex ext-real real Element of REAL
(g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,g) is Relation-like Function-like set
((g,g)) is complex ext-real real Element of REAL
addreal "**" (g,g) is complex ext-real real Element of REAL
((F,F) + (2 * (F,g))) + (g,g) is complex ext-real real Element of REAL
(F,F) + (F,g) is complex ext-real real Element of REAL
((F,F) + (F,g)) + (F,g) is complex ext-real real Element of REAL
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
- g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
F + (- g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (F,(- g)) is Relation-like Function-like set
diffreal .: (F,g) is Relation-like Function-like set
((F,g),(F,g)) is complex ext-real real Element of REAL
((F,g),(F,g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),(F,g)) is Relation-like Function-like set
(((F,g),(F,g))) is complex ext-real real Element of REAL
addreal "**" ((F,g),(F,g)) is complex ext-real real Element of REAL
(F,F) is complex ext-real real Element of REAL
(F,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,F) is Relation-like Function-like set
((F,F)) is complex ext-real real Element of REAL
addreal "**" (F,F) is complex ext-real real Element of REAL
(F,g) is complex ext-real real Element of REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (F,g) is Relation-like Function-like set
((F,g)) is complex ext-real real Element of REAL
addreal "**" (F,g) is complex ext-real real Element of REAL
2 * (F,g) is complex ext-real real Element of REAL
(F,F) - (2 * (F,g)) is complex ext-real real Element of REAL
(g,g) is complex ext-real real Element of REAL
(g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,g) is Relation-like Function-like set
((g,g)) is complex ext-real real Element of REAL
addreal "**" (g,g) is complex ext-real real Element of REAL
((F,F) - (2 * (F,g))) + (g,g) is complex ext-real real Element of REAL
(F,F) - (F,g) is complex ext-real real Element of REAL
(g,F) is complex ext-real real Element of REAL
(g,F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,F) is Relation-like Function-like set
((g,F)) is complex ext-real real Element of REAL
addreal "**" (g,F) is complex ext-real real Element of REAL
((F,F) - (F,g)) - (g,F) is complex ext-real real Element of REAL
(((F,F) - (F,g)) - (g,F)) + (g,g) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,g,i),j) is complex ext-real real Element of REAL
((F,g,i),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),j) is Relation-like Function-like set
(((F,g,i),j)) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),j) is complex ext-real real Element of REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
(g,j) + (i,j) is complex ext-real real Element of REAL
p3 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
f3 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len f3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
j is complex ext-real real set
(F,g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(j) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (j,(id REAL)) is Relation-like Function-like set
g (#) (j) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g,j),i) is complex ext-real real Element of REAL
((F,g,j),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,j),i) is Relation-like Function-like set
(((F,g,j),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g,j),i) is complex ext-real real Element of REAL
j * (g,i) is complex ext-real real Element of REAL
q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len q2 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
p3 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len p3 is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,g),i) is complex ext-real real Element of REAL
((F,g),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),i) is Relation-like Function-like set
(((F,g),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g),i) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
- (g,i) is complex ext-real real Element of REAL
(F,g,(- 1)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((- 1)) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] ((- 1),(id REAL)) is Relation-like Function-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g,(- 1)),i) is complex ext-real real Element of REAL
((F,g,(- 1)),i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,(- 1)),i) is Relation-like Function-like set
(((F,g,(- 1)),i)) is complex ext-real real Element of REAL
addreal "**" ((F,g,(- 1)),i) is complex ext-real real Element of REAL
(- 1) * (g,i) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
((F,g),(F,i)) is complex ext-real real Element of REAL
((F,g),(F,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g),(F,i)) is Relation-like Function-like set
(((F,g),(F,i))) is complex ext-real real Element of REAL
addreal "**" ((F,g),(F,i)) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
(g,(F,i)) is complex ext-real real Element of REAL
(g,(F,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,(F,i)) is Relation-like Function-like set
((g,(F,i))) is complex ext-real real Element of REAL
addreal "**" (g,(F,i)) is complex ext-real real Element of REAL
- (g,(F,i)) is complex ext-real real Element of REAL
- (g,i) is complex ext-real real Element of REAL
- (- (g,i)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,g,i),j) is complex ext-real real Element of REAL
((F,g,i),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),j) is Relation-like Function-like set
(((F,g,i),j)) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),j) is complex ext-real real Element of REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
(g,j) - (i,j) is complex ext-real real Element of REAL
(F,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,i),j) is complex ext-real real Element of REAL
((F,i),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,i),j) is Relation-like Function-like set
(((F,i),j)) is complex ext-real real Element of REAL
addreal "**" ((F,i),j) is complex ext-real real Element of REAL
(g,j) + ((F,i),j) is complex ext-real real Element of REAL
- (i,j) is complex ext-real real Element of REAL
(g,j) + (- (i,j)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is complex ext-real real set
i is complex ext-real real set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,j,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
j (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,q2,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(i) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (i,(id REAL)) is Relation-like Function-like set
q2 (#) (i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F,(F,j,g),(F,q2,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: ((F,j,g),(F,q2,i)) is Relation-like Function-like set
p3 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
((F,(F,j,g),(F,q2,i)),p3) is complex ext-real real Element of REAL
((F,(F,j,g),(F,q2,i)),p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,(F,j,g),(F,q2,i)),p3) is Relation-like Function-like set
(((F,(F,j,g),(F,q2,i)),p3)) is complex ext-real real Element of REAL
addreal "**" ((F,(F,j,g),(F,q2,i)),p3) is complex ext-real real Element of REAL
(j,p3) is complex ext-real real Element of REAL
(j,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (j,p3) is Relation-like Function-like set
((j,p3)) is complex ext-real real Element of REAL
addreal "**" (j,p3) is complex ext-real real Element of REAL
g * (j,p3) is complex ext-real real Element of REAL
(q2,p3) is complex ext-real real Element of REAL
(q2,p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (q2,p3) is Relation-like Function-like set
((q2,p3)) is complex ext-real real Element of REAL
addreal "**" (q2,p3) is complex ext-real real Element of REAL
i * (q2,p3) is complex ext-real real Element of REAL
(g * (j,p3)) + (i * (q2,p3)) is complex ext-real real Element of REAL
((F,j,g),p3) is complex ext-real real Element of REAL
((F,j,g),p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,j,g),p3) is Relation-like Function-like set
(((F,j,g),p3)) is complex ext-real real Element of REAL
addreal "**" ((F,j,g),p3) is complex ext-real real Element of REAL
((F,q2,i),p3) is complex ext-real real Element of REAL
((F,q2,i),p3) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,q2,i),p3) is Relation-like Function-like set
(((F,q2,i),p3)) is complex ext-real real Element of REAL
addreal "**" ((F,q2,i),p3) is complex ext-real real Element of REAL
((F,j,g),p3) + ((F,q2,i),p3) is complex ext-real real Element of REAL
(g * (j,p3)) + ((F,q2,i),p3) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (j,q2) is Relation-like Function-like set
((F,g,i),(F,j,q2)) is complex ext-real real Element of REAL
((F,g,i),(F,j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),(F,j,q2)) is Relation-like Function-like set
(((F,g,i),(F,j,q2))) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),(F,j,q2)) is complex ext-real real Element of REAL
(g,q2) is complex ext-real real Element of REAL
(g,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,q2) is Relation-like Function-like set
((g,q2)) is complex ext-real real Element of REAL
addreal "**" (g,q2) is complex ext-real real Element of REAL
(g,j) + (g,q2) is complex ext-real real Element of REAL
((g,j) + (g,q2)) + (i,j) is complex ext-real real Element of REAL
(i,q2) is complex ext-real real Element of REAL
(i,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,q2) is Relation-like Function-like set
((i,q2)) is complex ext-real real Element of REAL
addreal "**" (i,q2) is complex ext-real real Element of REAL
(((g,j) + (g,q2)) + (i,j)) + (i,q2) is complex ext-real real Element of REAL
((F,g,i),j) is complex ext-real real Element of REAL
((F,g,i),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),j) is Relation-like Function-like set
(((F,g,i),j)) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),j) is complex ext-real real Element of REAL
(g,j) + (i,j) is complex ext-real real Element of REAL
((F,g,i),q2) is complex ext-real real Element of REAL
((F,g,i),q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),q2) is Relation-like Function-like set
(((F,g,i),q2)) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),q2) is complex ext-real real Element of REAL
(g,q2) + (i,q2) is complex ext-real real Element of REAL
((F,g,i),j) + ((F,g,i),q2) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,j) is complex ext-real real Element of REAL
(g,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,j) is Relation-like Function-like set
((g,j)) is complex ext-real real Element of REAL
addreal "**" (g,j) is complex ext-real real Element of REAL
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
q2 is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,j,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) q2 is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
q2 (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j + (- q2) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (j,(- q2)) is Relation-like Function-like set
diffreal .: (j,q2) is Relation-like Function-like set
((F,g,i),(F,j,q2)) is complex ext-real real Element of REAL
((F,g,i),(F,j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),(F,j,q2)) is Relation-like Function-like set
(((F,g,i),(F,j,q2))) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),(F,j,q2)) is complex ext-real real Element of REAL
(g,q2) is complex ext-real real Element of REAL
(g,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,q2) is Relation-like Function-like set
((g,q2)) is complex ext-real real Element of REAL
addreal "**" (g,q2) is complex ext-real real Element of REAL
(g,j) - (g,q2) is complex ext-real real Element of REAL
((g,j) - (g,q2)) - (i,j) is complex ext-real real Element of REAL
(i,q2) is complex ext-real real Element of REAL
(i,q2) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,q2) is Relation-like Function-like set
((i,q2)) is complex ext-real real Element of REAL
addreal "**" (i,q2) is complex ext-real real Element of REAL
(((g,j) - (g,q2)) - (i,j)) + (i,q2) is complex ext-real real Element of REAL
(g,(F,j,q2)) is complex ext-real real Element of REAL
(g,(F,j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,(F,j,q2)) is Relation-like Function-like set
((g,(F,j,q2))) is complex ext-real real Element of REAL
addreal "**" (g,(F,j,q2)) is complex ext-real real Element of REAL
(i,(F,j,q2)) is complex ext-real real Element of REAL
(i,(F,j,q2)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,(F,j,q2)) is Relation-like Function-like set
((i,(F,j,q2))) is complex ext-real real Element of REAL
addreal "**" (i,(F,j,q2)) is complex ext-real real Element of REAL
(i,j) - (i,q2) is complex ext-real real Element of REAL
(g,(F,j,q2)) - (i,(F,j,q2)) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,g) is complex ext-real real Element of REAL
(g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,g) is Relation-like Function-like set
((g,g)) is complex ext-real real Element of REAL
addreal "**" (g,g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
addreal .: (g,i) is Relation-like Function-like set
((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
((F,g,i),(F,g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),(F,g,i)) is Relation-like Function-like set
(((F,g,i),(F,g,i))) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
2 * (g,i) is complex ext-real real Element of REAL
(g,g) + (2 * (g,i)) is complex ext-real real Element of REAL
(i,i) is complex ext-real real Element of REAL
(i,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,i) is Relation-like Function-like set
((i,i)) is complex ext-real real Element of REAL
addreal "**" (i,i) is complex ext-real real Element of REAL
((g,g) + (2 * (g,i))) + (i,i) is complex ext-real real Element of REAL
(g,g) + (g,i) is complex ext-real real Element of REAL
((g,g) + (g,i)) + (g,i) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,g) is complex ext-real real Element of REAL
(g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,g) is Relation-like Function-like set
((g,g)) is complex ext-real real Element of REAL
addreal "**" (g,g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
((F,g,i),(F,g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),(F,g,i)) is Relation-like Function-like set
(((F,g,i),(F,g,i))) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
2 * (g,i) is complex ext-real real Element of REAL
(g,g) - (2 * (g,i)) is complex ext-real real Element of REAL
(i,i) is complex ext-real real Element of REAL
(i,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,i) is Relation-like Function-like set
((i,i)) is complex ext-real real Element of REAL
addreal "**" (i,i) is complex ext-real real Element of REAL
((g,g) - (2 * (g,i))) + (i,i) is complex ext-real real Element of REAL
(g,g) - (g,i) is complex ext-real real Element of REAL
((g,g) - (g,i)) - (g,i) is complex ext-real real Element of REAL
(((g,g) - (g,i)) - (g,i)) + (i,i) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,g) is complex ext-real real Element of REAL
(g,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,g) is Relation-like Function-like set
((g,g)) is complex ext-real real Element of REAL
addreal "**" (g,g) is complex ext-real real Element of REAL
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g,i) is complex ext-real real Element of REAL
(g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (g,i) is Relation-like Function-like set
((g,i)) is complex ext-real real Element of REAL
addreal "**" (g,i) is complex ext-real real Element of REAL
(i,i) is complex ext-real real Element of REAL
(i,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,i) is Relation-like Function-like set
((i,i)) is complex ext-real real Element of REAL
addreal "**" (i,i) is complex ext-real real Element of REAL
(g,g) + (i,i) is complex ext-real real Element of REAL
0 / 2 is Relation-like non-zero empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex ext-real non positive non negative real V41() V42() complex-valued ext-real-valued real-valued natural-valued V53() V54() V55() V56() V57() V58() V59() V60() Function-yielding V70() cardinal 0 -element FinSequence-like FinSubsequence-like FinSequence-membered Element of RAT
((g,g) + (i,i)) / 2 is complex ext-real real Element of REAL
(F,g,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
- i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(- 1) (#) i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) ((- 1)) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
i (#) compreal is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g + (- i) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
addreal .: (g,(- i)) is Relation-like Function-like set
diffreal .: (g,i) is Relation-like Function-like set
((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
((F,g,i),(F,g,i)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,g,i),(F,g,i)) is Relation-like Function-like set
(((F,g,i),(F,g,i))) is complex ext-real real Element of REAL
addreal "**" ((F,g,i),(F,g,i)) is complex ext-real real Element of REAL
2 * (g,i) is complex ext-real real Element of REAL
(g,g) - (2 * (g,i)) is complex ext-real real Element of REAL
((g,g) - (2 * (g,i))) + (i,i) is complex ext-real real Element of REAL
((g,g) + (i,i)) - (2 * (g,i)) is complex ext-real real Element of REAL
((g,g) + (i,i)) - 0 is complex ext-real real Element of REAL
(2 * (g,i)) / 2 is complex ext-real real Element of REAL
0 + (g,i) is complex ext-real real Element of REAL
(((g,g) + (i,i)) / 2) + (((g,g) + (i,i)) / 2) is complex ext-real real Element of REAL
i is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
(j,i) is complex ext-real real Element of REAL
(j,i) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (j,i) is Relation-like Function-like set
((j,i)) is complex ext-real real Element of REAL
addreal "**" (j,i) is complex ext-real real Element of REAL
F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
F -tuples_on REAL is functional non empty FinSequence-membered FinSequenceSet of REAL
{ b₁ where b₁ is Relation-like NAT -defined REAL -valued Function-like V60() FinSequence-like FinSubsequence-like Element of REAL * : len b₁ = F } is set
g is complex ext-real real set
i is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(F,i,g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(g) is Relation-like Function-like non empty V14( REAL ) V18( REAL , REAL ) complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
multreal [;] (g,(id REAL)) is Relation-like Function-like set
i (#) (g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
j is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() F -element FinSequence-like FinSubsequence-like Element of F -tuples_on REAL
(i,j) is complex ext-real real Element of REAL
(i,j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: (i,j) is Relation-like Function-like set
((i,j)) is complex ext-real real Element of REAL
addreal "**" (i,j) is complex ext-real real Element of REAL
g * (i,j) is complex ext-real real Element of REAL
((F,i,g),j) is complex ext-real real Element of REAL
((F,i,g),j) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
multreal .: ((F,i,g),j) is Relation-like Function-like set
(((F,i,g),j)) is complex ext-real real Element of REAL
addreal "**" ((F,i,g),j) is complex ext-real real Element of REAL
F is complex ext-real real set
g is complex ext-real real set
F + g is complex ext-real real Element of REAL
i is complex ext-real real set
(F + g) + i is complex ext-real real Element of REAL
j is complex ext-real real set
<*F,g,i,j*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 4 -element FinSequence-like FinSubsequence-like set
<*F,g,i*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 3 -element FinSequence-like FinSubsequence-like set
<*F*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,F] is set
{1,F} is non empty V53() V54() V55() set
{{1,F},{1}} is non empty set
{[1,F]} is Relation-like Function-like constant non empty trivial 1 -element set
<*g*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,g] is set
{1,g} is non empty V53() V54() V55() set
{{1,g},{1}} is non empty set
{[1,g]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F*> ^ <*g*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 1 + 1 -element FinSequence-like FinSubsequence-like set
<*i*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,i] is set
{1,i} is non empty V53() V54() V55() set
{{1,i},{1}} is non empty set
{[1,i]} is Relation-like Function-like constant non empty trivial 1 -element set
(<*F*> ^ <*g*>) ^ <*i*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() (1 + 1) + 1 -element FinSequence-like FinSubsequence-like set
<*j*> is Relation-like NAT -defined Function-like one-to-one constant non empty trivial complex-valued ext-real-valued real-valued V47() decreasing non-decreasing non-increasing V60() 1 -element FinSequence-like FinSubsequence-like set
[1,j] is set
{1,j} is non empty V53() V54() V55() set
{{1,j},{1}} is non empty set
{[1,j]} is Relation-like Function-like constant non empty trivial 1 -element set
<*F,g,i*> ^ <*j*> is Relation-like NAT -defined Function-like non empty complex-valued ext-real-valued real-valued V60() 3 + 1 -element FinSequence-like FinSubsequence-like set
(<*F,g,i,j*>) is complex ext-real real set
((F + g) + i) + j is complex ext-real real Element of REAL
(<*F,g,i*>) is complex ext-real real set
(<*F,g,i*>) + j is complex ext-real real Element of REAL
F is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
len (F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
(F) is V53() V54() V55() Element of bool REAL
dom () is non empty set
() * F is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
len (() * F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F (#) F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (F,F) is Relation-like Function-like set
F (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
F ^ g is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
((F ^ g)) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(F ^ g) (#) (F ^ g) is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: ((F ^ g),(F ^ g)) is Relation-like Function-like set
(F ^ g) (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
g (#) g is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
multreal .: (g,g) is Relation-like Function-like set
g (#) () is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) ^ (g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
len F is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (F) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len ((F ^ g)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (F ^ g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len g is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
len (g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
(len F) + (len g) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
i is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V60() cardinal set
((F ^ g)) . i is complex ext-real real Element of REAL
((F) ^ (g)) . i is complex ext-real real Element of REAL
dom (F ^ g) is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
dom (F) is V53() V54() V55() V56() V57() V58() Element of bool NAT
() * (F ^ g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(() * (F ^ g)) . i is complex ext-real real Element of REAL
(F ^ g) . i is complex ext-real real Element of REAL
() . ((F ^ g) . i) is complex ext-real real Element of REAL
F . i is complex ext-real real Element of REAL
() . (F . i) is complex ext-real real Element of REAL
(F . i) ^2 is complex ext-real real Element of REAL
(F . i) * (F . i) is complex ext-real real set
(F) . i is complex ext-real real Element of REAL
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
i - (len F) is complex ext-real real V41() V42() Element of INT
len ((F) ^ (g)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
() * (F ^ g) is Relation-like NAT -defined REAL -valued Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like FinSequence of REAL
(() * (F ^ g)) . i is complex ext-real real Element of REAL
(F ^ g) . i is complex ext-real real Element of REAL
() . ((F ^ g) . i) is complex ext-real real Element of REAL
j is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
g . j is complex ext-real real Element of REAL
() . (g . j) is complex ext-real real Element of REAL
(g . j) ^2 is complex ext-real real Element of REAL
(g . j) * (g . j) is complex ext-real real set
(g) . j is complex ext-real real Element of REAL
dom F is V53() V54() V55() V56() V57() V58() Element of bool NAT
len ((F) ^ (g)) is epsilon-transitive epsilon-connected ordinal natural complex ext-real non negative real V41() V42() V53() V54() V55() V56() V57() V58() V60() cardinal Element of NAT
F is Relation-like NAT -defined Function-like complex-valued ext-real-valued real-valued V60() FinSequence-like FinSubsequence-like set
(F) is V53() V54() V55() Element of bool REAL