:: JGRAPH_1 semantic presentation

REAL is V181() V182() V183() V187() V283() V284() V286() set
NAT is non trivial ordinal non finite cardinal limit_cardinal V181() V182() V183() V184() V185() V186() V187() V283() Element of bool REAL
bool REAL is set
{} is set
RAT is V181() V182() V183() V184() V187() set
the V1() non-empty empty-yielding V4( NAT ) V5( RAT ) Function-like one-to-one constant functional empty ordinal natural V28() real ext-real non positive non negative finite finite-yielding V45() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding V172() V173() V174() V181() V182() V183() V184() V185() V186() V187() V283() V284() V285() V286() set is V1() non-empty empty-yielding V4( NAT ) V5( RAT ) Function-like one-to-one constant functional empty ordinal natural V28() real ext-real non positive non negative finite finite-yielding V45() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding V172() V173() V174() V181() V182() V183() V184() V185() V186() V187() V283() V284() V285() V286() set
1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
{{},1} is finite set
COMPLEX is V181() V187() set
INT is V181() V182() V183() V184() V185() V187() set
[:COMPLEX,COMPLEX:] is V1() complex-yielding set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is V1() complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is V1() complex-yielding V172() V173() set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is V1() complex-yielding V172() V173() set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is V1() V5( RAT ) complex-yielding V172() V173() set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is V1() V5( RAT ) complex-yielding V172() V173() set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is V1() V5( RAT ) V5( INT ) complex-yielding V172() V173() set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is V1() V5( RAT ) V5( INT ) complex-yielding V172() V173() set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is V1() V5( RAT ) V5( INT ) complex-yielding V172() V173() V174() set
[:[:NAT,NAT:],NAT:] is V1() V5( RAT ) V5( INT ) complex-yielding V172() V173() V174() set
bool [:[:NAT,NAT:],NAT:] is set
omega is non trivial ordinal non finite cardinal limit_cardinal V181() V182() V183() V184() V185() V186() V187() V283() set
bool omega is non trivial non finite set
bool NAT is non trivial non finite set
K312() is set
[:1,1:] is V1() V5( RAT ) V5( INT ) finite complex-yielding V172() V173() V174() set
bool [:1,1:] is finite V45() set
[:[:1,1:],1:] is V1() V5( RAT ) V5( INT ) finite complex-yielding V172() V173() V174() set
bool [:[:1,1:],1:] is finite V45() set
[:[:1,1:],REAL:] is V1() complex-yielding V172() V173() set
bool [:[:1,1:],REAL:] is set
2 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
[:2,2:] is V1() V5( RAT ) V5( INT ) finite complex-yielding V172() V173() V174() set
[:[:2,2:],REAL:] is V1() complex-yielding V172() V173() set
bool [:[:2,2:],REAL:] is set
K510() is non empty V130() L10()
the carrier of K510() is non empty set
K515() is non empty L10()
K516() is non empty V130() M20(K515())
K517() is non empty V130() V152() V209() M23(K515(),K516())
K519() is non empty V130() V152() V154() V156() L10()
K520() is non empty V130() V152() V209() M20(K519())
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL 2) is functional non empty set
K302( the carrier of (TOP-REAL 2)) is functional non empty FinSequence-membered M9( the carrier of (TOP-REAL 2))
bool the carrier of (TOP-REAL 2) is set
[: the carrier of (TOP-REAL 2),REAL:] is V1() complex-yielding V172() V173() set
bool [: the carrier of (TOP-REAL 2),REAL:] is set
K711() is non empty strict TopSpace-like TopStruct
the carrier of K711() is non empty set
RealSpace is non empty strict Reflexive discerning V105() triangle Discerning MetrStruct
K716() is TopSpace-like TopStruct
the carrier of K716() is set
3 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
I[01] is non empty strict TopSpace-like SubSpace of K716()
the carrier of I[01] is non empty set
0 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
5 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
bool the carrier of I[01] is set
K717(0,1) is non empty strict TopSpace-like SubSpace of K716()
[.0,1.] is V181() V182() V183() V286() Element of bool REAL
f is non empty V76() MultiGraphStruct
the carrier' of f is set
the carrier of f is non empty set
g is V1() V4( NAT ) V5( the carrier' of f) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of f
a is V1() V4( NAT ) V5( the carrier of f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
b is V1() V4( NAT ) V5( the carrier of f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of f
len b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . c is set
a . d is set
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . c is set
a . d is set
f is set
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
f is set
(f) is MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier of (f) is set
f is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . a is set
f . a is set
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f . (a + 1) is set
[(f . a),(f . (a + 1))] is set
{(f . a),(f . (a + 1))} is finite set
{(f . a)} is non empty trivial finite 1 -element set
{{(f . a),(f . (a + 1))},{(f . a)}} is finite V45() set
(a + 1) - 1 is V28() real ext-real Element of REAL
(len f) - 1 is V28() real ext-real Element of REAL
g is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
b is ordinal natural V28() real ext-real non negative finite cardinal set
g . b is set
a . b is set
(len f) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
f . b is set
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f . (b + 1) is set
[(f . b),(f . (b + 1))] is set
{(f . b),(f . (b + 1))} is finite set
{(f . b)} is non empty trivial finite 1 -element set
{{(f . b),(f . (b + 1))},{(f . b)}} is finite V45() set
(len f) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len f) + 1) - 1 is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
0 - 1 is V28() real ext-real Element of REAL
f is non empty set
(f) is MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier of (f) is non empty set
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(g) is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
rng (g) is finite set
a is set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len g) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
dom (g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b is set
(g) . b is set
len (g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (g)) is finite len (g) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) - 1 is V28() real ext-real Element of REAL
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g . (c + 1) is set
rng g is finite Element of bool f
bool f is set
g . c is set
(g) . c is set
[(g . c),(g . (c + 1))] is set
{(g . c),(g . (c + 1))} is finite set
{(g . c)} is non empty trivial finite 1 -element set
{{(g . c),(g . (c + 1))},{(g . c)}} is finite V45() set
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(g) is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,a) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of (f)
len (f,a) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(f,a) . g is set
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len a) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len a) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len a) - 1 is V28() real ext-real Element of REAL
g + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a . (g + 1) is set
rng a is finite Element of bool f
bool f is set
a . g is set
[(a . g),(a . (g + 1))] is set
{(a . g),(a . (g + 1))} is finite set
{(a . g)} is non empty trivial finite 1 -element set
{{(a . g),(a . (g + 1))},{(a . g)}} is finite V45() set
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier' of (f)
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) - 1 is V28() real ext-real Element of REAL
((len g) - 1) + 1 is V28() real ext-real Element of REAL
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len g) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len (f,g)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
the carrier of (f) is non empty set
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . a is set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng g is finite Element of bool f
bool f is set
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . a is set
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g . (a + 1) is set
(f,g) . a is set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng g is finite Element of bool f
bool f is set
(pr2 (f,f)) . ((g . a),(g . (a + 1))) is set
[(g . a),(g . (a + 1))] is set
{(g . a),(g . (a + 1))} is finite set
{(g . a)} is non empty trivial finite 1 -element set
{{(g . a),(g . (a + 1))},{(g . a)}} is finite V45() set
(pr2 (f,f)) . [(g . a),(g . (a + 1))] is set
the Target of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
[: the carrier' of (f), the carrier of (f):] is V1() set
bool [: the carrier' of (f), the carrier of (f):] is set
the Target of (f) . ((f,g) . a) is set
c is Element of the carrier of (f)
(pr1 (f,f)) . ((g . a),(g . (a + 1))) is set
(pr1 (f,f)) . [(g . a),(g . (a + 1))] is set
the Source of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
the Source of (f) . ((f,g) . a) is set
b is Element of the carrier of (f)
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(f,g) . a is set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len g) + 1) - 1 is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
0 - 1 is V28() real ext-real Element of REAL
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
the Source of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
the carrier of (f) is non empty set
[: the carrier' of (f), the carrier of (f):] is V1() set
bool [: the carrier' of (f), the carrier of (f):] is set
the Target of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len g) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(f,g) . (a + 1) is set
the Source of (f) . ((f,g) . (a + 1)) is set
(f,g) . a is set
the Target of (f) . ((f,g) . a) is set
(len g) - 1 is V28() real ext-real Element of REAL
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g . a is set
rng g is finite Element of bool f
bool f is set
(a + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g . ((a + 1) + 1) is set
g . (a + 1) is set
(pr2 (f,f)) . ((g . a),(g . (a + 1))) is set
[(g . a),(g . (a + 1))] is set
{(g . a),(g . (a + 1))} is finite set
{(g . a)} is non empty trivial finite 1 -element set
{{(g . a),(g . (a + 1))},{(g . a)}} is finite V45() set
(pr2 (f,f)) . [(g . a),(g . (a + 1))] is set
b is Element of the carrier of (f)
(pr1 (f,f)) . ((g . (a + 1)),(g . ((a + 1) + 1))) is set
[(g . (a + 1)),(g . ((a + 1) + 1))] is set
{(g . (a + 1)),(g . ((a + 1) + 1))} is finite set
{(g . (a + 1))} is non empty trivial finite 1 -element set
{{(g . (a + 1)),(g . ((a + 1) + 1))},{(g . (a + 1))}} is finite V45() set
(pr1 (f,f)) . [(g . (a + 1)),(g . ((a + 1) + 1))] is set
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(g) is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier of (f) is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
the carrier' of (f) is set
a is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len g) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a /. b is Element of the carrier of (f)
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a /. (b + 1) is Element of the carrier of (f)
(f,g) . b is set
(len g) - 1 is V28() real ext-real Element of REAL
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g . (b + 1) is set
rng g is finite Element of bool f
bool f is set
g . b is set
(pr1 (f,f)) . ((g . b),(g . (b + 1))) is set
[(g . b),(g . (b + 1))] is set
{(g . b),(g . (b + 1))} is finite set
{(g . b)} is non empty trivial finite 1 -element set
{{(g . b),(g . (b + 1))},{(g . b)}} is finite V45() set
(pr1 (f,f)) . [(g . b),(g . (b + 1))] is set
(pr2 (f,f)) . ((g . b),(g . (b + 1))) is set
(pr2 (f,f)) . [(g . b),(g . (b + 1))] is set
a . (b + 1) is set
the Target of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
[: the carrier' of (f), the carrier of (f):] is V1() set
bool [: the carrier' of (f), the carrier of (f):] is set
the Target of (f) . ((f,g) . b) is set
a . b is set
the Source of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
the Source of (f) . ((f,g) . b) is set
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) - 1 is V28() real ext-real Element of REAL
((len g) - 1) + 1 is V28() real ext-real Element of REAL
(len (f,g)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f is non empty set
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
a is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b is finite set
card b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of omega
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
card (Seg (len g)) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of omega
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
bool (f,g) is finite V45() set
bool g is finite V45() set
the carrier of (f) is non empty set
c is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSubsequence-like Element of bool (f,g)
Seq c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
O is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented simple Chain of (f)
d is V1() V4( NAT ) V5(f) Function-like finite FinSubsequence-like Element of bool g
Seq d is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
I is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len O) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
dom d is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Sgm (dom d) is V1() V4( NAT ) V5( NAT ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() V174() FinSequence of NAT
rng (Sgm (dom d)) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool REAL
d * (Sgm (dom d)) is V1() V4( NAT ) V5(f) Function-like finite set
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Sgm (dom d)) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
len (Sgm (dom d)) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is finite set
card P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of omega
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier of (f) is non empty set
the carrier' of (f) is set
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
bool (f,g) is finite V45() set
a is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
bool a is finite V45() set
a . 1 is set
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . (len a) is set
b is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSubsequence-like Element of bool (f,g)
Seq b is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
d is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented simple Chain of (f)
c is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSubsequence-like Element of bool a
Seq c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
O is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
O . 1 is set
len O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
O . (len O) is set
I is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
a is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,a) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
rng (f,a) is finite Element of bool the carrier' of (f)
bool the carrier' of (f) is set
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
rng (f,g) is finite Element of bool the carrier' of (f)
len (f,a) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len a) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len a) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len a) - 1 is V28() real ext-real Element of REAL
bool (f,g) is finite V45() set
bool g is finite V45() set
the carrier of (f) is non empty set
b is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSubsequence-like Element of bool (f,g)
Seq b is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
d is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented simple Chain of (f)
c is V1() V4( NAT ) V5(f) Function-like finite FinSubsequence-like Element of bool g
Seq c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
O is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
dom b is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Sgm (dom b) is V1() V4( NAT ) V5( NAT ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() V174() FinSequence of NAT
rng (Sgm (dom b)) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool REAL
b * (Sgm (dom b)) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite set
rng b is finite Element of bool the carrier' of (f)
rng d is finite Element of bool the carrier' of (f)
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len g) - 1 is V28() real ext-real Element of REAL
I is set
dom (f,a) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
P is set
(f,a) . P is set
Seg (len (f,a)) is finite len (f,a) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
len d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len d) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O /. f1 is Element of the carrier of (f)
O /. (f1 + 1) is Element of the carrier of (f)
d . f1 is set
dom d is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (f,g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Q is set
(f,g) . Q is set
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (f,g)) is finite len (f,g) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g . g1 is set
g . (g1 + 1) is set
[(g . g1),(g . (g1 + 1))] is set
{(g . g1),(g . (g1 + 1))} is finite set
{(g . g1)} is non empty trivial finite 1 -element set
{{(g . g1),(g . (g1 + 1))},{(g . g1)}} is finite V45() set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng g is finite Element of bool f
bool f is set
the Source of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
[: the carrier' of (f), the carrier of (f):] is V1() set
bool [: the carrier' of (f), the carrier of (f):] is set
the Source of (f) . ((g . g1),(g . (g1 + 1))) is set
the Source of (f) . [(g . g1),(g . (g1 + 1))] is set
a . f1 is set
a . (f1 + 1) is set
[(a . f1),(a . (f1 + 1))] is set
{(a . f1),(a . (f1 + 1))} is finite set
{(a . f1)} is non empty trivial finite 1 -element set
{{(a . f1),(a . (f1 + 1))},{(a . f1)}} is finite V45() set
the Target of (f) is V1() V4( the carrier' of (f)) V5( the carrier of (f)) Function-like total V18( the carrier' of (f), the carrier of (f)) Element of bool [: the carrier' of (f), the carrier of (f):]
the Target of (f) . ((g . g1),(g . (g1 + 1))) is set
the Target of (f) . [(g . g1),(g . (g1 + 1))] is set
len O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f is non empty set
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
g . 1 is set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . (len g) is set
a is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
a . 1 is set
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . (len a) is set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
the carrier' of (f) is set
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
bool (f,g) is finite V45() set
bool g is finite V45() set
the carrier of (f) is non empty set
b is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSubsequence-like Element of bool (f,g)
Seq b is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
d is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented simple Chain of (f)
c is V1() V4( NAT ) V5(f) Function-like finite FinSubsequence-like Element of bool g
Seq c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
O is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
I is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len d) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
P is set
K48(a) is finite set
f1 is set
a . P is set
a . f1 is set
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len a) is finite len a -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Q is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
TOP-REAL f is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL f) is functional non empty set
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,g) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,a) is functional Element of bool the carrier of (TOP-REAL 2)
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg (f,1) is functional Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (f,((len f) -' 1)) is functional Element of bool the carrier of (TOP-REAL 2)
a is ordinal natural V28() real ext-real non negative finite cardinal set
g is ordinal natural V28() real ext-real non negative finite cardinal set
g + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,g) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,a) is functional Element of bool the carrier of (TOP-REAL 2)
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,a)) is functional Element of bool the carrier of (TOP-REAL 2)
( the carrier of (TOP-REAL 2)) is non empty V76() MultiGraphStruct
[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):] is V1() set
pr1 ( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
[:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is V1() set
bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):] is set
pr2 ( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
MultiGraphStruct(# the carrier of (TOP-REAL 2),[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):],(pr1 ( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))),(pr2 ( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) #) is strict MultiGraphStruct
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
( the carrier of (TOP-REAL 2),f) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
the carrier' of ( the carrier of (TOP-REAL 2)) is set
the carrier of ( the carrier of (TOP-REAL 2)) is non empty set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g is V1() V4( NAT ) V5( the carrier of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of (TOP-REAL 2))
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,a) is functional Element of bool the carrier of (TOP-REAL 2)
b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,b) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
f . a is V1() Function-like set
{(f . a)} is functional non empty trivial finite 1 -element set
f . b is V1() Function-like set
f . (b + 1) is V1() Function-like set
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
f . (a + 1) is V1() Function-like set
{(f . (a + 1))} is functional non empty trivial finite 1 -element set
f . b is V1() Function-like set
f . (b + 1) is V1() Function-like set
f /. a is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (a + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. a),(f /. (a + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. a)) + (b₁ * (f /. (a + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f /. b is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (b + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. b),(f /. (b + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. b)) + (b₁ * (f /. (b + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f . b is V1() Function-like set
f . (b + 1) is V1() Function-like set
f . a is V1() Function-like set
f . (a + 1) is V1() Function-like set
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
f . a is V1() Function-like set
{(f . a)} is functional non empty trivial finite 1 -element set
f . b is V1() Function-like set
f . (b + 1) is V1() Function-like set
f . (a + 1) is V1() Function-like set
{(f . (a + 1))} is functional non empty trivial finite 1 -element set
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
f . a is V1() Function-like set
{(f . a)} is functional non empty trivial finite 1 -element set
f . b is V1() Function-like set
f . (b + 1) is V1() Function-like set
f . (a + 1) is V1() Function-like set
{(f . (a + 1))} is functional non empty trivial finite 1 -element set
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,a) is functional Element of bool the carrier of (TOP-REAL 2)
b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,b) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
( the carrier of (TOP-REAL 2),f) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
the carrier' of ( the carrier of (TOP-REAL 2)) is set
f . 1 is V1() Function-like set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . (len f) is V1() Function-like set
the carrier of ( the carrier of (TOP-REAL 2)) is non empty set
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g is V1() V4( NAT ) V5( the carrier of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of ( the carrier of (TOP-REAL 2))
1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
((len f) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,1) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,((len f) -' 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,1)) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{(f . 1)} is functional non empty trivial finite 1 -element set
f . ((len f) -' 1) is V1() Function-like set
f . (((len f) -' 1) + 1) is V1() Function-like set
(LSeg (f,1)) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f . (1 + 1) is V1() Function-like set
{(f . (1 + 1))} is functional non empty trivial finite 1 -element set
f . ((len f) -' 1) is V1() Function-like set
f . (((len f) -' 1) + 1) is V1() Function-like set
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. 1),(f /. (1 + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. (1 + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f /. ((len f) -' 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (((len f) -' 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. ((len f) -' 1)),(f /. (((len f) -' 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((len f) -' 1))) + (b₁ * (f /. (((len f) -' 1) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f . ((len f) -' 1) is V1() Function-like set
f . (1 + 1) is V1() Function-like set
f . (((len f) -' 1) + 1) is V1() Function-like set
(LSeg (f,1)) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{(f . 1)} is functional non empty trivial finite 1 -element set
f . ((len f) -' 1) is V1() Function-like set
f . (((len f) -' 1) + 1) is V1() Function-like set
f . (1 + 1) is V1() Function-like set
{(f . (1 + 1))} is functional non empty trivial finite 1 -element set
(LSeg (f,1)) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{(f . 1)} is functional non empty trivial finite 1 -element set
f . ((len f) -' 1) is V1() Function-like set
f . (((len f) -' 1) + 1) is V1() Function-like set
f . (1 + 1) is V1() Function-like set
{(f . (1 + 1))} is functional non empty trivial finite 1 -element set
b is ordinal natural V28() real ext-real non negative finite cardinal set
a is ordinal natural V28() real ext-real non negative finite cardinal set
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,a) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,b) is functional Element of bool the carrier of (TOP-REAL 2)
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(a + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(1 + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
((1 + 1) + 1) - 1 is V28() real ext-real Element of REAL
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,a)) /\ (LSeg (f,b)) is functional Element of bool the carrier of (TOP-REAL 2)
b + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
TOP-REAL f is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL f) is functional non empty set
a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
LSeg (g,a) is functional Element of bool the carrier of (TOP-REAL f)
bool the carrier of (TOP-REAL f) is set
{ (((1 - b₁) * g) + (b₁ * a)) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
LSeg (a,b) is functional Element of bool the carrier of (TOP-REAL f)
{ (((1 - b₁) * a) + (b₁ * b)) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (g,a)) /\ (LSeg (a,b)) is functional Element of bool the carrier of (TOP-REAL f)
c is set
d is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
O is V28() real ext-real Element of REAL
1 - O is V28() real ext-real Element of REAL
(1 - O) * g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - O) * g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
O * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
O * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) * g) + (O * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) is V1() V4([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):]) V5( the carrier of (TOP-REAL f)) Function-like total V18([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f)) Element of bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):]
[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):] is V1() set
[:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is V1() set
bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is set
the U7 of (TOP-REAL f) . (((1 - O) * g),(O * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - O) * g),(O * a)] is set
{((1 - O) * g),(O * a)} is functional finite V45() set
{((1 - O) * g)} is functional non empty trivial finite V45() 1 -element set
{{((1 - O) * g),(O * a)},{((1 - O) * g)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - O) * g),(O * a)] is V1() Function-like set
((1 - O) * g) + (O * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
I is V28() real ext-real Element of REAL
1 - I is V28() real ext-real Element of REAL
(1 - I) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - I) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
I * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
I * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - I) * a) + (I * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - I) * a),(I * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - I) * a),(I * b)] is set
{((1 - I) * a),(I * b)} is functional finite V45() set
{((1 - I) * a)} is functional non empty trivial finite V45() 1 -element set
{{((1 - I) * a),(I * b)},{((1 - I) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - I) * a),(I * b)] is V1() Function-like set
((1 - I) * a) + (I * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - O) * g) + (O * a)) - ((1 - I) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- ((1 - I) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- ((1 - I) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),(((1 - O) * g) + (O * a)),(- ((1 - I) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - O) * g) + (O * a)),(- ((1 - I) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - O) * g) + (O * a)),(- ((1 - I) * a))] is set
{(((1 - O) * g) + (O * a)),(- ((1 - I) * a))} is functional finite V45() set
{(((1 - O) * g) + (O * a))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - O) * g) + (O * a)),(- ((1 - I) * a))},{(((1 - O) * g) + (O * a))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - O) * g) + (O * a)),(- ((1 - I) * a))] is V1() Function-like set
(((1 - O) * g) + (O * a)) + (- ((1 - I) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - O) * g) + (O * a)) - ((1 - I) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(O * a) - ((1 - I) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
K385((TOP-REAL f),(O * a),(- ((1 - I) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((O * a),(- ((1 - I) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(O * a),(- ((1 - I) * a))] is set
{(O * a),(- ((1 - I) * a))} is functional finite V45() set
{(O * a)} is functional non empty trivial finite V45() 1 -element set
{{(O * a),(- ((1 - I) * a))},{(O * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(O * a),(- ((1 - I) * a))] is V1() Function-like set
(O * a) + (- ((1 - I) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(O * a) - ((1 - I) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) * g) + ((O * a) - ((1 - I) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - O) * g),((O * a) - ((1 - I) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - O) * g),((O * a) - ((1 - I) * a))] is set
{((1 - O) * g),((O * a) - ((1 - I) * a))} is functional finite V45() set
{{((1 - O) * g),((O * a) - ((1 - I) * a))},{((1 - O) * g)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - O) * g),((O * a) - ((1 - I) * a))] is V1() Function-like set
((1 - O) * g) + ((O * a) - ((1 - I) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
I " is V28() real ext-real Element of REAL
(I ") * (I * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(I ") * (I * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
O - (1 - I) is V28() real ext-real Element of REAL
(O - (1 - I)) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(O - (1 - I)) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) * g) + ((O - (1 - I)) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - O) * g),((O - (1 - I)) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - O) * g),((O - (1 - I)) * a)] is set
{((1 - O) * g),((O - (1 - I)) * a)} is functional finite V45() set
{{((1 - O) * g),((O - (1 - I)) * a)},{((1 - O) * g)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - O) * g),((O - (1 - I)) * a)] is V1() Function-like set
((1 - O) * g) + ((O - (1 - I)) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * (((1 - O) * g) + ((O - (1 - I)) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(I ") * (((1 - O) * g) + ((O - (1 - I)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * I is V28() real ext-real Element of REAL
((I ") * I) * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((I ") * I) * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * ((1 - O) * g) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(I ") * ((1 - O) * g) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * ((O - (1 - I)) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(I ") * ((O - (1 - I)) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((I ") * ((1 - O) * g)) + ((I ") * ((O - (1 - I)) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((I ") * ((1 - O) * g)),((I ") * ((O - (1 - I)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((I ") * ((1 - O) * g)),((I ") * ((O - (1 - I)) * a))] is set
{((I ") * ((1 - O) * g)),((I ") * ((O - (1 - I)) * a))} is functional finite V45() set
{((I ") * ((1 - O) * g))} is functional non empty trivial finite V45() 1 -element set
{{((I ") * ((1 - O) * g)),((I ") * ((O - (1 - I)) * a))},{((I ") * ((1 - O) * g))}} is finite V45() set
the U7 of (TOP-REAL f) . [((I ") * ((1 - O) * g)),((I ") * ((O - (1 - I)) * a))] is V1() Function-like set
((I ") * ((1 - O) * g)) + ((I ") * ((O - (1 - I)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * (1 - O) is V28() real ext-real Element of REAL
((I ") * (1 - O)) * g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((I ") * (1 - O)) * g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((I ") * (1 - O)) * g) + ((I ") * ((O - (1 - I)) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((I ") * (1 - O)) * g),((I ") * ((O - (1 - I)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((I ") * (1 - O)) * g),((I ") * ((O - (1 - I)) * a))] is set
{(((I ") * (1 - O)) * g),((I ") * ((O - (1 - I)) * a))} is functional finite V45() set
{(((I ") * (1 - O)) * g)} is functional non empty trivial finite V45() 1 -element set
{{(((I ") * (1 - O)) * g),((I ") * ((O - (1 - I)) * a))},{(((I ") * (1 - O)) * g)}} is finite V45() set
the U7 of (TOP-REAL f) . [(((I ") * (1 - O)) * g),((I ") * ((O - (1 - I)) * a))] is V1() Function-like set
(((I ") * (1 - O)) * g) + ((I ") * ((O - (1 - I)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(I ") * (O - (1 - I)) is V28() real ext-real Element of REAL
((I ") * (O - (1 - I))) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((I ") * (O - (1 - I))) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((I ") * (1 - O)) * g) + (((I ") * (O - (1 - I))) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((I ") * (1 - O)) * g),(((I ") * (O - (1 - I))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((I ") * (1 - O)) * g),(((I ") * (O - (1 - I))) * a)] is set
{(((I ") * (1 - O)) * g),(((I ") * (O - (1 - I))) * a)} is functional finite V45() set
{{(((I ") * (1 - O)) * g),(((I ") * (O - (1 - I))) * a)},{(((I ") * (1 - O)) * g)}} is finite V45() set
the U7 of (TOP-REAL f) . [(((I ") * (1 - O)) * g),(((I ") * (O - (1 - I))) * a)] is V1() Function-like set
(((I ") * (1 - O)) * g) + (((I ") * (O - (1 - I))) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 + 0 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O - 1 is V28() real ext-real Element of REAL
(O - 1) + I is V28() real ext-real Element of REAL
0 + I is V28() real ext-real Element of REAL
((I ") * (1 - O)) + ((I ") * (O - (1 - I))) is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
(1 - 1) + I is V28() real ext-real Element of REAL
(I ") * ((1 - 1) + I) is V28() real ext-real Element of REAL
1 - ((I ") * (O - (1 - I))) is V28() real ext-real Element of REAL
1 * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
0. (TOP-REAL f) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like V71( TOP-REAL f) complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the ZeroF of (TOP-REAL f) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 * a) + (0. (TOP-REAL f)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((1 * a),(0. (TOP-REAL f))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(1 * a),(0. (TOP-REAL f))] is set
{(1 * a),(0. (TOP-REAL f))} is functional finite V45() set
{(1 * a)} is functional non empty trivial finite V45() 1 -element set
{{(1 * a),(0. (TOP-REAL f))},{(1 * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(1 * a),(0. (TOP-REAL f))] is V1() Function-like set
(1 * a) + (0. (TOP-REAL f)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
a + (0. (TOP-REAL f)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (a,(0. (TOP-REAL f))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[a,(0. (TOP-REAL f))] is set
{a,(0. (TOP-REAL f))} is functional finite V45() set
{a} is functional non empty trivial finite V45() 1 -element set
{{a,(0. (TOP-REAL f))},{a}} is finite V45() set
the U7 of (TOP-REAL f) . [a,(0. (TOP-REAL f))] is V1() Function-like set
a + (0. (TOP-REAL f)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 - (1 - O) is V28() real ext-real Element of REAL
(1 - (1 - O)) + (1 - O) is V28() real ext-real Element of REAL
1 + (1 - O) is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
0 + (1 - I) is V28() real ext-real Element of REAL
1 - (1 - I) is V28() real ext-real Element of REAL
(1 - (1 - I)) + (1 - I) is V28() real ext-real Element of REAL
(1 - (1 - I)) * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - (1 - I)) * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - (1 - I)) * b) + ((1 - I) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - (1 - I)) * b),((1 - I) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - (1 - I)) * b),((1 - I) * a)] is set
{((1 - (1 - I)) * b),((1 - I) * a)} is functional finite V45() set
{((1 - (1 - I)) * b)} is functional non empty trivial finite V45() 1 -element set
{{((1 - (1 - I)) * b),((1 - I) * a)},{((1 - (1 - I)) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - (1 - I)) * b),((1 - I) * a)] is V1() Function-like set
((1 - (1 - I)) * b) + ((1 - I) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(1 - (1 - O)) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - (1 - O)) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - (1 - I)) * b) + ((1 - I) * a)) - ((1 - (1 - O)) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- ((1 - (1 - O)) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- ((1 - (1 - O)) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),(((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))] is set
{(((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))} is functional finite V45() set
{(((1 - (1 - I)) * b) + ((1 - I) * a))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))},{(((1 - (1 - I)) * b) + ((1 - I) * a))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - (1 - I)) * b) + ((1 - I) * a)),(- ((1 - (1 - O)) * a))] is V1() Function-like set
(((1 - (1 - I)) * b) + ((1 - I) * a)) + (- ((1 - (1 - O)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - (1 - I)) * b) + ((1 - I) * a)) - ((1 - (1 - O)) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - I) * a) - ((1 - (1 - O)) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
K385((TOP-REAL f),((1 - I) * a),(- ((1 - (1 - O)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - I) * a),(- ((1 - (1 - O)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - I) * a),(- ((1 - (1 - O)) * a))] is set
{((1 - I) * a),(- ((1 - (1 - O)) * a))} is functional finite V45() set
{{((1 - I) * a),(- ((1 - (1 - O)) * a))},{((1 - I) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - I) * a),(- ((1 - (1 - O)) * a))] is V1() Function-like set
((1 - I) * a) + (- ((1 - (1 - O)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - I) * a) - ((1 - (1 - O)) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - (1 - I)) * b) + (((1 - I) * a) - ((1 - (1 - O)) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - (1 - I)) * b),(((1 - I) * a) - ((1 - (1 - O)) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - (1 - I)) * b),(((1 - I) * a) - ((1 - (1 - O)) * a))] is set
{((1 - (1 - I)) * b),(((1 - I) * a) - ((1 - (1 - O)) * a))} is functional finite V45() set
{{((1 - (1 - I)) * b),(((1 - I) * a) - ((1 - (1 - O)) * a))},{((1 - (1 - I)) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - (1 - I)) * b),(((1 - I) * a) - ((1 - (1 - O)) * a))] is V1() Function-like set
((1 - (1 - I)) * b) + (((1 - I) * a) - ((1 - (1 - O)) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(1 - I) - (1 - (1 - O)) is V28() real ext-real Element of REAL
((1 - I) - (1 - (1 - O))) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 - I) - (1 - (1 - O))) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - (1 - I)) * b) + (((1 - I) - (1 - (1 - O))) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - (1 - I)) * b),(((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - (1 - I)) * b),(((1 - I) - (1 - (1 - O))) * a)] is set
{((1 - (1 - I)) * b),(((1 - I) - (1 - (1 - O))) * a)} is functional finite V45() set
{{((1 - (1 - I)) * b),(((1 - I) - (1 - (1 - O))) * a)},{((1 - (1 - I)) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - (1 - I)) * b),(((1 - I) - (1 - (1 - O))) * a)] is V1() Function-like set
((1 - (1 - I)) * b) + (((1 - I) - (1 - (1 - O))) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(1 - O) " is V28() real ext-real Element of REAL
((1 - O) ") * (1 - O) is V28() real ext-real Element of REAL
(((1 - O) ") * (1 - O)) * g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(((1 - O) ") * (1 - O)) * g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) ") * (((1 - (1 - I)) * b) + (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 - O) ") * (((1 - (1 - I)) * b) + (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 * g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) ") * ((1 - (1 - I)) * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 - O) ") * ((1 - (1 - I)) * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - O) ") * ((1 - (1 - I)) * b)) + (((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - O) ") * ((1 - (1 - I)) * b)),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - O) ") * ((1 - (1 - I)) * b)),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))] is set
{(((1 - O) ") * ((1 - (1 - I)) * b)),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))} is functional finite V45() set
{(((1 - O) ") * ((1 - (1 - I)) * b))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - O) ") * ((1 - (1 - I)) * b)),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))},{(((1 - O) ") * ((1 - (1 - I)) * b))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - O) ") * ((1 - (1 - I)) * b)),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))] is V1() Function-like set
(((1 - O) ") * ((1 - (1 - I)) * b)) + (((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) ") * (1 - (1 - I)) is V28() real ext-real Element of REAL
(((1 - O) ") * (1 - (1 - I))) * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(((1 - O) ") * (1 - (1 - I))) * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((((1 - O) ") * (1 - (1 - I))) * b) + (((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((((1 - O) ") * (1 - (1 - I))) * b),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((((1 - O) ") * (1 - (1 - I))) * b),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))] is set
{((((1 - O) ") * (1 - (1 - I))) * b),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))} is functional finite V45() set
{((((1 - O) ") * (1 - (1 - I))) * b)} is functional non empty trivial finite V45() 1 -element set
{{((((1 - O) ") * (1 - (1 - I))) * b),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))},{((((1 - O) ") * (1 - (1 - I))) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((((1 - O) ") * (1 - (1 - I))) * b),(((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a))] is V1() Function-like set
((((1 - O) ") * (1 - (1 - I))) * b) + (((1 - O) ") * (((1 - I) - (1 - (1 - O))) * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - O) ") * ((1 - I) - (1 - (1 - O))) is V28() real ext-real Element of REAL
(((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((((1 - O) ") * (1 - (1 - I))) * b) + ((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((((1 - O) ") * (1 - (1 - I))) * b),((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((((1 - O) ") * (1 - (1 - I))) * b),((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a)] is set
{((((1 - O) ") * (1 - (1 - I))) * b),((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a)} is functional finite V45() set
{{((((1 - O) ") * (1 - (1 - I))) * b),((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a)},{((((1 - O) ") * (1 - (1 - I))) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((((1 - O) ") * (1 - (1 - I))) * b),((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a)] is V1() Function-like set
((((1 - O) ") * (1 - (1 - I))) * b) + ((((1 - O) ") * ((1 - I) - (1 - (1 - O)))) * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 + 0 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(1 - I) - 1 is V28() real ext-real Element of REAL
((1 - I) - 1) + (1 - O) is V28() real ext-real Element of REAL
0 + (1 - O) is V28() real ext-real Element of REAL
(((1 - O) ") * (1 - (1 - I))) + (((1 - O) ") * ((1 - I) - (1 - (1 - O)))) is V28() real ext-real Element of REAL
(1 - 1) + (1 - O) is V28() real ext-real Element of REAL
((1 - O) ") * ((1 - 1) + (1 - O)) is V28() real ext-real Element of REAL
1 - (((1 - O) ") * ((1 - I) - (1 - (1 - O)))) is V28() real ext-real Element of REAL
{ (((1 - b₁) * b) + (b₁ * a)) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
1 * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
0. (TOP-REAL f) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like V71( TOP-REAL f) complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the ZeroF of (TOP-REAL f) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 * a) + (0. (TOP-REAL f)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((1 * a),(0. (TOP-REAL f))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(1 * a),(0. (TOP-REAL f))] is set
{(1 * a),(0. (TOP-REAL f))} is functional finite V45() set
{(1 * a)} is functional non empty trivial finite V45() 1 -element set
{{(1 * a),(0. (TOP-REAL f))},{(1 * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(1 * a),(0. (TOP-REAL f))] is V1() Function-like set
(1 * a) + (0. (TOP-REAL f)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
a + (0. (TOP-REAL f)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (a,(0. (TOP-REAL f))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[a,(0. (TOP-REAL f))] is set
{a,(0. (TOP-REAL f))} is functional finite V45() set
{a} is functional non empty trivial finite V45() 1 -element set
{{a,(0. (TOP-REAL f))},{a}} is finite V45() set
the U7 of (TOP-REAL f) . [a,(0. (TOP-REAL f))] is V1() Function-like set
a + (0. (TOP-REAL f)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg (f,1) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,(1 + 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,1)) /\ (LSeg (f,(1 + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
{(f /. (1 + 1))} is functional non empty trivial finite V45() 1 -element set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) -' 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (f,((len f) -' 2)) is functional Element of bool the carrier of (TOP-REAL 2)
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (f,((len f) -' 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,((len f) -' 2))) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f /. ((len f) -' 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
{(f /. ((len f) -' 1))} is functional non empty trivial finite V45() 1 -element set
g is ordinal natural V28() real ext-real non negative finite cardinal set
g + 2 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,g) is functional Element of bool the carrier of (TOP-REAL 2)
g + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,(g + 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,(g + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (g + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
{(f /. (g + 1))} is functional non empty trivial finite V45() 1 -element set
(g + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. ((g + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. (g + 1)),(f /. ((g + 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. (g + 1))) + (b₁ * (f /. ((g + 1) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f /. g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. g),(f /. (g + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. g)) + (b₁ * (f /. (g + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(len f) - 2 is V28() real ext-real Element of REAL
(len f) - 1 is V28() real ext-real Element of REAL
(1 + 1) - 1 is V28() real ext-real Element of REAL
g - 1 is V28() real ext-real Element of REAL
((g + 1) + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a is set
LSeg (f,((g + 1) + 1)) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (((g + 1) + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. ((g + 1) + 1)),(f /. (((g + 1) + 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((g + 1) + 1))) + (b₁ * (f /. (((g + 1) + 1) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
g -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(g -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,(g -' 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,(g -' 1))) /\ (LSeg (f,(g + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (g -' 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. ((g -' 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. (g -' 1)),(f /. ((g -' 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. (g -' 1))) + (b₁ * (f /. ((g -' 1) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(LSeg (f,g)) /\ (LSeg (f,((g + 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
the carrier' of (f) is set
g . 1 is set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . (len g) is set
the carrier of (f) is non empty set
b is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (f,g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len (f,g)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len (f,g)) + 1) - 1 is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is set
g . c is set
d is set
g . d is set
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len g) + 1) - 1 is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is set
d is set
g . c is set
g . d is set
f is non empty set
(f) is non empty V76() MultiGraphStruct
[:f,f:] is V1() set
pr1 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
[:[:f,f:],f:] is V1() set
bool [:[:f,f:],f:] is set
pr2 (f,f) is V1() V4([:f,f:]) V5(f) Function-like total V18([:f,f:],f) Element of bool [:[:f,f:],f:]
MultiGraphStruct(# f,[:f,f:],(pr1 (f,f)),(pr2 (f,f)) #) is strict MultiGraphStruct
g is V1() V4( NAT ) V5(f) Function-like finite FinSequence-like FinSubsequence-like FinSequence of f
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(f,g) is V1() V4( NAT ) V5( the carrier' of (f)) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of (f)
the carrier' of (f) is set
g . 1 is set
g . (len g) is set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
the carrier of (f) is non empty set
a is V1() V4( NAT ) V5( the carrier of (f)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (f)
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . b is set
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a . c is set
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
( the carrier of (TOP-REAL 2),f) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
the carrier' of ( the carrier of (TOP-REAL 2)) is set
f . 1 is V1() Function-like set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . (len f) is V1() Function-like set
2 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f . 2 is V1() Function-like set
f /. 2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg (f,2) is functional Element of bool the carrier of (TOP-REAL 2)
LSeg (f,1) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,1)) /\ (LSeg (f,2)) is functional Element of bool the carrier of (TOP-REAL 2)
(len f) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. 1),(f /. (1 + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 1)) + (b₁ * (f /. (1 + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
(len f) -' 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) - 2 is V28() real ext-real Element of REAL
f /. (2 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. 2),(f /. (2 + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. 2)) + (b₁ * (f /. (2 + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
f . (2 + 1) is V1() Function-like set
{(f . 1)} is functional non empty trivial finite 1 -element set
f . (2 + 1) is V1() Function-like set
f . (1 + 1) is V1() Function-like set
{(f . (1 + 1))} is functional non empty trivial finite 1 -element set
LSeg (f,(1 + 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,1)) /\ (LSeg (f,(1 + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{(f /. (1 + 1))} is functional non empty trivial finite V45() 1 -element set
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len f) -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(1 + 1) - 1 is V28() real ext-real Element of REAL
f . ((len f) -' 1) is V1() Function-like set
f /. ((len f) -' 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(2 + 1) - 2 is V28() real ext-real Element of REAL
LSeg (f,((len f) -' 2)) is functional Element of bool the carrier of (TOP-REAL 2)
f /. ((len f) -' 2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((len f) -' 2) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (((len f) -' 2) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. ((len f) -' 2)),(f /. (((len f) -' 2) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((len f) -' 2))) + (b₁ * (f /. (((len f) -' 2) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
((len f) - 1) - 1 is V28() real ext-real Element of REAL
f . ((len f) -' 2) is V1() Function-like set
LSeg (f,((len f) -' 1)) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (((len f) -' 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f /. ((len f) -' 1)),(f /. (((len f) -' 1) + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f /. ((len f) -' 1))) + (b₁ * (f /. (((len f) -' 1) + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f . (((len f) -' 1) + 1) is V1() Function-like set
(len f) - ((1 + 1) - 1) is V28() real ext-real Element of REAL
(LSeg (f,((len f) -' 2))) /\ (LSeg (f,((len f) -' 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{(f . ((len f) -' 2))} is functional non empty trivial finite 1 -element set
f . (((len f) -' 1) + 1) is V1() Function-like set
f . (((len f) -' 2) + 1) is V1() Function-like set
{(f . (((len f) -' 2) + 1))} is functional non empty trivial finite 1 -element set
{(f /. ((len f) -' 1))} is functional non empty trivial finite V45() 1 -element set
g is ordinal natural V28() real ext-real non negative finite cardinal set
g + 2 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,g) is functional Element of bool the carrier of (TOP-REAL 2)
g + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
LSeg (f,(g + 1)) is functional Element of bool the carrier of (TOP-REAL 2)
(LSeg (f,g)) /\ (LSeg (f,(g + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
f /. (g + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
{(f /. (g + 1))} is functional non empty trivial finite V45() 1 -element set
2 - 2 is V28() real ext-real Element of REAL
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g /. a is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. (a + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g . a is V1() Function-like set
g . (a + 1) is V1() Function-like set
( the carrier of (TOP-REAL 2),g) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
the carrier' of ( the carrier of (TOP-REAL 2)) is set
len ( the carrier of (TOP-REAL 2),g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
( the carrier of (TOP-REAL 2),g) . a is set
[(g . a),(g . (a + 1))] is set
{(g . a),(g . (a + 1))} is functional finite set
{(g . a)} is functional non empty trivial finite 1 -element set
{{(g . a),(g . (a + 1))},{(g . a)}} is finite V45() set
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
( the carrier of (TOP-REAL 2),f) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
len ( the carrier of (TOP-REAL 2),f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) - 1 is V28() real ext-real Element of REAL
dom ( the carrier of (TOP-REAL 2),g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng ( the carrier of (TOP-REAL 2),g) is finite Element of bool the carrier' of ( the carrier of (TOP-REAL 2))
bool the carrier' of ( the carrier of (TOP-REAL 2)) is set
rng ( the carrier of (TOP-REAL 2),f) is finite Element of bool the carrier' of ( the carrier of (TOP-REAL 2))
dom ( the carrier of (TOP-REAL 2),f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b is set
( the carrier of (TOP-REAL 2),f) . b is set
Seg (len ( the carrier of (TOP-REAL 2),f)) is finite len ( the carrier of (TOP-REAL 2),f) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len f) - 1) + 1 is V28() real ext-real Element of REAL
f . c is V1() Function-like set
f . (c + 1) is V1() Function-like set
[(f . c),(f . (c + 1))] is set
{(f . c),(f . (c + 1))} is functional finite set
{(f . c)} is functional non empty trivial finite 1 -element set
{{(f . c),(f . (c + 1))},{(f . c)}} is finite V45() set
f /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng g is functional finite Element of bool the carrier of (TOP-REAL 2)
rng f is functional finite Element of bool the carrier of (TOP-REAL 2)
a is set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b is set
g . b is V1() Function-like set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g . c is V1() Function-like set
g . (c + 1) is V1() Function-like set
d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f . d is V1() Function-like set
f . (d + 1) is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c - 1 is V28() real ext-real Element of REAL
1 - 1 is V28() real ext-real Element of REAL
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g /. (c -' 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(c -' 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g /. ((c -' 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g . (c -' 1) is V1() Function-like set
g . ((c -' 1) + 1) is V1() Function-like set
d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f . d is V1() Function-like set
f . (d + 1) is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f . 1 is V1() Function-like set
g . 1 is V1() Function-like set
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ g is functional Element of bool the carrier of (TOP-REAL 2)
L~ f is functional Element of bool the carrier of (TOP-REAL 2)
a is set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
{ (LSeg (g,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
union { (LSeg (g,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g ) } is set
b is set
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (g,c) is functional Element of bool the carrier of (TOP-REAL 2)
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g . c is V1() Function-like set
g . (c + 1) is V1() Function-like set
d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f . d is V1() Function-like set
f . (d + 1) is V1() Function-like set
LSeg (f,d) is functional Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
LSeg ((g /. c),(g /. (c + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (g /. c)) + (b₁ * (g /. (c + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
union { (LSeg (f,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f ) } is set
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
( the carrier of (TOP-REAL 2),g) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
the carrier' of ( the carrier of (TOP-REAL 2)) is set
len ( the carrier of (TOP-REAL 2),g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len g) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a is ordinal natural V28() real ext-real non negative finite cardinal set
a + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g /. a is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g /. a) `1 is V28() real ext-real Element of REAL
(g /. a) . 1 is V28() real ext-real Element of REAL
g /. (a + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g /. (a + 1)) `1 is V28() real ext-real Element of REAL
(g /. (a + 1)) . 1 is V28() real ext-real Element of REAL
(g /. a) `2 is V28() real ext-real Element of REAL
(g /. a) . 2 is V28() real ext-real Element of REAL
(g /. (a + 1)) `2 is V28() real ext-real Element of REAL
(g /. (a + 1)) . 2 is V28() real ext-real Element of REAL
g . a is V1() Function-like set
(len f) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) - 1 is V28() real ext-real Element of REAL
(len g) - 1 is V28() real ext-real Element of REAL
dom ( the carrier of (TOP-REAL 2),g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
( the carrier of (TOP-REAL 2),g) . a is set
g . (a + 1) is V1() Function-like set
[(g . a),(g . (a + 1))] is set
{(g . a),(g . (a + 1))} is functional finite set
{(g . a)} is functional non empty trivial finite 1 -element set
{{(g . a),(g . (a + 1))},{(g . a)}} is finite V45() set
rng ( the carrier of (TOP-REAL 2),g) is finite Element of bool the carrier' of ( the carrier of (TOP-REAL 2))
bool the carrier' of ( the carrier of (TOP-REAL 2)) is set
( the carrier of (TOP-REAL 2),f) is V1() V4( NAT ) V5( the carrier' of ( the carrier of (TOP-REAL 2))) Function-like finite FinSequence-like FinSubsequence-like oriented Chain of ( the carrier of (TOP-REAL 2))
rng ( the carrier of (TOP-REAL 2),f) is finite Element of bool the carrier' of ( the carrier of (TOP-REAL 2))
dom ( the carrier of (TOP-REAL 2),f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b is set
( the carrier of (TOP-REAL 2),f) . b is set
len ( the carrier of (TOP-REAL 2),f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len ( the carrier of (TOP-REAL 2),f)) is finite len ( the carrier of (TOP-REAL 2),f) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((len f) - 1) + 1 is V28() real ext-real Element of REAL
( the carrier of (TOP-REAL 2),f) . c is set
f . c is V1() Function-like set
f . (c + 1) is V1() Function-like set
[(f . c),(f . (c + 1))] is set
{(f . c),(f . (c + 1))} is functional finite set
{(f . c)} is functional non empty trivial finite 1 -element set
{{(f . c),(f . (c + 1))},{(f . c)}} is finite V45() set
f /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . 1 is V1() Function-like set
f . (len f) is V1() Function-like set
L~ f is functional Element of bool the carrier of (TOP-REAL 2)
rng f is functional finite Element of bool the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g . 1 is V1() Function-like set
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . (len g) is V1() Function-like set
L~ g is functional Element of bool the carrier of (TOP-REAL 2)
rng g is functional finite Element of bool the carrier of (TOP-REAL 2)
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . 1 is V1() Function-like set
f . (len f) is V1() Function-like set
g . 1 is V1() Function-like set
g . (len g) is V1() Function-like set
X_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(X_axis f) . 1 is V28() real ext-real Element of REAL
(X_axis f) . (len f) is V28() real ext-real Element of REAL
X_axis g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Y_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Y_axis g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(Y_axis g) . 1 is V28() real ext-real Element of REAL
(Y_axis g) . (len g) is V28() real ext-real Element of REAL
L~ f is functional Element of bool the carrier of (TOP-REAL 2)
L~ g is functional Element of bool the carrier of (TOP-REAL 2)
rng f is functional finite Element of bool the carrier of (TOP-REAL 2)
a is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len a is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
L~ a is functional Element of bool the carrier of (TOP-REAL 2)
a . 1 is V1() Function-like set
a . (len a) is V1() Function-like set
rng a is functional finite Element of bool the carrier of (TOP-REAL 2)
rng g is functional finite Element of bool the carrier of (TOP-REAL 2)
b is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len b is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
L~ b is functional Element of bool the carrier of (TOP-REAL 2)
b . 1 is V1() Function-like set
b . (len b) is V1() Function-like set
rng b is functional finite Element of bool the carrier of (TOP-REAL 2)
dom b is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
b /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
b /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
b . c is V1() Function-like set
b . (c + 1) is V1() Function-like set
Y_axis a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (Y_axis a) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Y_axis b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(Y_axis b) . 1 is V28() real ext-real Element of REAL
(Y_axis b) . (len b) is V28() real ext-real Element of REAL
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis a) . c is V28() real ext-real Element of REAL
len (Y_axis g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
len (Y_axis b) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len b) is finite len b -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis b) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
b /. (len b) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. (len g) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(a /. c) `2 is V28() real ext-real Element of REAL
(a /. c) . 2 is V28() real ext-real Element of REAL
len (Y_axis a) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len a) is finite len a -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a . c is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d is set
f . d is V1() Function-like set
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . O is V1() Function-like set
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
len (Y_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis f) . O is V28() real ext-real Element of REAL
(f /. O) `2 is V28() real ext-real Element of REAL
(f /. O) . 2 is V28() real ext-real Element of REAL
(b /. (len b)) `2 is V28() real ext-real Element of REAL
(b /. (len b)) . 2 is V28() real ext-real Element of REAL
(b /. 1) `2 is V28() real ext-real Element of REAL
(b /. 1) . 2 is V28() real ext-real Element of REAL
X_axis b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (X_axis b) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
X_axis a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(X_axis a) . 1 is V28() real ext-real Element of REAL
(X_axis a) . (len a) is V28() real ext-real Element of REAL
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis b) . c is V28() real ext-real Element of REAL
len (X_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
len (X_axis a) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len a) is finite len a -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis a) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a /. (len a) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
b /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(b /. c) `1 is V28() real ext-real Element of REAL
(b /. c) . 1 is V28() real ext-real Element of REAL
len (X_axis b) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len b) is finite len b -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b . c is V1() Function-like set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d is set
g . d is V1() Function-like set
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . O is V1() Function-like set
g /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
len (X_axis g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis g) . O is V28() real ext-real Element of REAL
(g /. O) `1 is V28() real ext-real Element of REAL
(g /. O) . 1 is V28() real ext-real Element of REAL
(a /. (len a)) `1 is V28() real ext-real Element of REAL
(a /. (len a)) . 1 is V28() real ext-real Element of REAL
(a /. 1) `1 is V28() real ext-real Element of REAL
(a /. 1) . 1 is V28() real ext-real Element of REAL
dom (Y_axis b) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis b) . c is V28() real ext-real Element of REAL
len (Y_axis g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len g) is finite len g -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
len (Y_axis b) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (Y_axis b)) is finite len (Y_axis b) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b /. (len b) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g /. (len g) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
Seg (len b) is finite len b -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
b /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(b /. c) `2 is V28() real ext-real Element of REAL
(b /. c) . 2 is V28() real ext-real Element of REAL
b . c is V1() Function-like set
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d is set
g . d is V1() Function-like set
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g . O is V1() Function-like set
g /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(Y_axis g) . O is V28() real ext-real Element of REAL
(g /. O) `2 is V28() real ext-real Element of REAL
(g /. O) . 2 is V28() real ext-real Element of REAL
(b /. (len b)) `2 is V28() real ext-real Element of REAL
(b /. (len b)) . 2 is V28() real ext-real Element of REAL
(b /. 1) `2 is V28() real ext-real Element of REAL
(b /. 1) . 2 is V28() real ext-real Element of REAL
dom (X_axis a) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis a) . c is V28() real ext-real Element of REAL
len (X_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
a /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(a /. c) `1 is V28() real ext-real Element of REAL
(a /. c) . 1 is V28() real ext-real Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a /. (len a) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
len (X_axis a) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len a) is finite len a -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a . c is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d is set
f . d is V1() Function-like set
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f . O is V1() Function-like set
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(X_axis f) . O is V28() real ext-real Element of REAL
(f /. O) `1 is V28() real ext-real Element of REAL
(f /. O) . 1 is V28() real ext-real Element of REAL
(a /. (len a)) `1 is V28() real ext-real Element of REAL
(a /. (len a)) . 1 is V28() real ext-real Element of REAL
(a /. 1) `1 is V28() real ext-real Element of REAL
(a /. 1) . 1 is V28() real ext-real Element of REAL
dom a is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
a /. c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a /. (c + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a . c is V1() Function-like set
a . (c + 1) is V1() Function-like set
(L~ a) /\ (L~ b) is functional Element of bool the carrier of (TOP-REAL 2)
(L~ f) /\ (L~ g) is functional Element of bool the carrier of (TOP-REAL 2)
f is V28() real ext-real Element of REAL
a is V28() real ext-real Element of REAL
g is V28() real ext-real Element of REAL
b is V28() real ext-real Element of REAL
a - b is V28() real ext-real Element of REAL
abs (a - b) is V28() real ext-real Element of REAL
g - f is V28() real ext-real Element of REAL
g - b is V28() real ext-real Element of REAL
- (a - b) is V28() real ext-real Element of REAL
b - a is V28() real ext-real Element of REAL
g - a is V28() real ext-real Element of REAL
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
TOP-REAL f is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL f) is functional non empty set
Euclid f is non empty strict Reflexive discerning V105() triangle Discerning MetrStruct
REAL f is functional non empty FinSequence-membered M9( REAL )
K303(f,REAL) is functional FinSequence-membered M9( REAL )
Pitag_dist f is V1() V4([:(REAL f),(REAL f):]) V5( REAL ) Function-like V18([:(REAL f),(REAL f):], REAL ) complex-yielding V172() V173() Element of bool [:[:(REAL f),(REAL f):],REAL:]
[:(REAL f),(REAL f):] is V1() set
[:[:(REAL f),(REAL f):],REAL:] is V1() complex-yielding V172() V173() set
bool [:[:(REAL f),(REAL f):],REAL:] is set
MetrStruct(# (REAL f),(Pitag_dist f) #) is strict MetrStruct
the carrier of (Euclid f) is non empty set
g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
g - a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),g,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) is V1() V4([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):]) V5( the carrier of (TOP-REAL f)) Function-like total V18([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f)) Element of bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):]
[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):] is V1() set
[:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is V1() set
bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is set
the U7 of (TOP-REAL f) . (g,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[g,(- a)] is set
{g,(- a)} is functional finite V45() set
{g} is functional non empty trivial finite V45() 1 -element set
{{g,(- a)},{g}} is finite V45() set
the U7 of (TOP-REAL f) . [g,(- a)] is V1() Function-like set
g + (- a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
g - a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(g - a).| is V28() real ext-real non negative Element of REAL
sqr (g - a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (g - a)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (g - a))) is V28() real ext-real Element of REAL
b is Element of the carrier of (Euclid f)
c is Element of the carrier of (Euclid f)
dist (b,c) is V28() real ext-real Element of REAL
d is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like Element of REAL f
O is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like Element of REAL f
(Pitag_dist f) . (d,O) is V28() real ext-real Element of REAL
[d,O] is set
{d,O} is functional finite V45() set
{d} is functional non empty trivial finite V45() 1 -element set
{{d,O},{d}} is finite V45() set
(Pitag_dist f) . [d,O] is V28() real ext-real set
d - O is V1() V4( NAT ) V5( REAL ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() M10( REAL , REAL f)
|.(d - O).| is V28() real ext-real non negative Element of REAL
sqr (d - O) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (d - O)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (d - O))) is V28() real ext-real Element of REAL
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|.f.| is V28() real ext-real non negative Element of REAL
sqr f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr f) is V28() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V28() real ext-real Element of REAL
|.f.| ^2 is V28() real ext-real Element of REAL
|.f.| * |.f.| is V28() real ext-real non negative set
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
(f `1) ^2 is V28() real ext-real Element of REAL
(f `1) * (f `1) is V28() real ext-real set
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
(f `2) ^2 is V28() real ext-real Element of REAL
(f `2) * (f `2) is V28() real ext-real set
((f `1) ^2) + ((f `2) ^2) is V28() real ext-real Element of REAL
REAL 2 is functional non empty FinSequence-membered M9( REAL )
K303(2,REAL) is functional FinSequence-membered M9( REAL )
g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like Element of REAL 2
sqr g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() M10( REAL ,K303(2,REAL))
(sqr g) . 2 is V28() real ext-real Element of REAL
Sum (sqr g) is V28() real ext-real Element of REAL
len (sqr g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(sqr g) . 1 is V28() real ext-real Element of REAL
<*((f `1) ^2),((f `2) ^2)*> is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like set
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|.f.| is V28() real ext-real non negative Element of REAL
sqr f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr f) is V28() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
(f `1) ^2 is V28() real ext-real Element of REAL
(f `1) * (f `1) is V28() real ext-real set
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
(f `2) ^2 is V28() real ext-real Element of REAL
(f `2) * (f `2) is V28() real ext-real set
((f `1) ^2) + ((f `2) ^2) is V28() real ext-real Element of REAL
sqrt (((f `1) ^2) + ((f `2) ^2)) is V28() real ext-real Element of REAL
|.f.| ^2 is V28() real ext-real Element of REAL
|.f.| * |.f.| is V28() real ext-real non negative set
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|.f.| is V28() real ext-real non negative Element of REAL
sqr f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr f) is V28() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
abs (f `1) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
abs (f `2) is V28() real ext-real Element of REAL
(abs (f `1)) + (abs (f `2)) is V28() real ext-real Element of REAL
|.f.| ^2 is V28() real ext-real Element of REAL
|.f.| * |.f.| is V28() real ext-real non negative set
(f `1) ^2 is V28() real ext-real Element of REAL
(f `1) * (f `1) is V28() real ext-real set
(f `2) ^2 is V28() real ext-real Element of REAL
(f `2) * (f `2) is V28() real ext-real set
((f `1) ^2) + ((f `2) ^2) is V28() real ext-real Element of REAL
sqrt (((f `1) ^2) + ((f `2) ^2)) is V28() real ext-real Element of REAL
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f - g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),f,(- g)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . (f,(- g)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[f,(- g)] is set
{f,(- g)} is functional finite V45() set
{f} is functional non empty trivial finite V45() 1 -element set
{{f,(- g)},{f}} is finite V45() set
the U7 of (TOP-REAL 2) . [f,(- g)] is V1() Function-like set
f + (- g) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
f - g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(f - g).| is V28() real ext-real non negative Element of REAL
sqr (f - g) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (f - g)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (f - g))) is V28() real ext-real Element of REAL
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
g `1 is V28() real ext-real Element of REAL
g . 1 is V28() real ext-real Element of REAL
(f `1) - (g `1) is V28() real ext-real Element of REAL
abs ((f `1) - (g `1)) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
g `2 is V28() real ext-real Element of REAL
g . 2 is V28() real ext-real Element of REAL
(f `2) - (g `2) is V28() real ext-real Element of REAL
abs ((f `2) - (g `2)) is V28() real ext-real Element of REAL
(abs ((f `1) - (g `1))) + (abs ((f `2) - (g `2))) is V28() real ext-real Element of REAL
(f - g) `1 is V28() real ext-real Element of REAL
(f - g) . 1 is V28() real ext-real Element of REAL
(f - g) `2 is V28() real ext-real Element of REAL
(f - g) . 2 is V28() real ext-real Element of REAL
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
abs (f `1) is V28() real ext-real Element of REAL
|.f.| is V28() real ext-real non negative Element of REAL
sqr f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr f) is V28() real ext-real Element of REAL
sqrt (Sum (sqr f)) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
abs (f `2) is V28() real ext-real Element of REAL
(f `1) ^2 is V28() real ext-real Element of REAL
(f `1) * (f `1) is V28() real ext-real set
(f `2) ^2 is V28() real ext-real Element of REAL
(f `2) * (f `2) is V28() real ext-real set
((f `1) ^2) + ((f `2) ^2) is V28() real ext-real Element of REAL
sqrt (((f `1) ^2) + ((f `2) ^2)) is V28() real ext-real Element of REAL
f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f `1 is V28() real ext-real Element of REAL
f . 1 is V28() real ext-real Element of REAL
g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g `1 is V28() real ext-real Element of REAL
g . 1 is V28() real ext-real Element of REAL
(f `1) - (g `1) is V28() real ext-real Element of REAL
abs ((f `1) - (g `1)) is V28() real ext-real Element of REAL
f - g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- g is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),f,(- g)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . (f,(- g)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[f,(- g)] is set
{f,(- g)} is functional finite V45() set
{f} is functional non empty trivial finite V45() 1 -element set
{{f,(- g)},{f}} is finite V45() set
the U7 of (TOP-REAL 2) . [f,(- g)] is V1() Function-like set
f + (- g) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
f - g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(f - g).| is V28() real ext-real non negative Element of REAL
sqr (f - g) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (f - g)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (f - g))) is V28() real ext-real Element of REAL
f `2 is V28() real ext-real Element of REAL
f . 2 is V28() real ext-real Element of REAL
g `2 is V28() real ext-real Element of REAL
g . 2 is V28() real ext-real Element of REAL
(f `2) - (g `2) is V28() real ext-real Element of REAL
abs ((f `2) - (g `2)) is V28() real ext-real Element of REAL
(f - g) `1 is V28() real ext-real Element of REAL
(f - g) . 1 is V28() real ext-real Element of REAL
(f - g) `2 is V28() real ext-real Element of REAL
(f - g) . 2 is V28() real ext-real Element of REAL
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
TOP-REAL f is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL f) is functional non empty set
g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
LSeg (a,b) is functional Element of bool the carrier of (TOP-REAL f)
bool the carrier of (TOP-REAL f) is set
{ (((1 - b₁) * a) + (b₁ * b)) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
c is V28() real ext-real Element of REAL
1 - c is V28() real ext-real Element of REAL
(1 - c) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - c) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
c * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
c * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) + (c * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) is V1() V4([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):]) V5( the carrier of (TOP-REAL f)) Function-like total V18([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f)) Element of bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):]
[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):] is V1() set
[:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is V1() set
bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is set
the U7 of (TOP-REAL f) . (((1 - c) * a),(c * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - c) * a),(c * b)] is set
{((1 - c) * a),(c * b)} is functional finite V45() set
{((1 - c) * a)} is functional non empty trivial finite V45() 1 -element set
{{((1 - c) * a),(c * b)},{((1 - c) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - c) * a),(c * b)] is V1() Function-like set
((1 - c) * a) + (c * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
TOP-REAL f is non empty TopSpace-like T_0 T_1 T_2 V128() V194() V211() V212() V213() V214() V215() V216() V217() strict RLTopStruct
the carrier of (TOP-REAL f) is functional non empty set
g is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
g - a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),g,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) is V1() V4([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):]) V5( the carrier of (TOP-REAL f)) Function-like total V18([: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f)) Element of bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):]
[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):] is V1() set
[:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is V1() set
bool [:[: the carrier of (TOP-REAL f), the carrier of (TOP-REAL f):], the carrier of (TOP-REAL f):] is set
the U7 of (TOP-REAL f) . (g,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[g,(- a)] is set
{g,(- a)} is functional finite V45() set
{g} is functional non empty trivial finite V45() 1 -element set
{{g,(- a)},{g}} is finite V45() set
the U7 of (TOP-REAL f) . [g,(- a)] is V1() Function-like set
g + (- a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
g - a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(g - a).| is V28() real ext-real non negative Element of REAL
sqr (g - a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (g - a)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (g - a))) is V28() real ext-real Element of REAL
b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
LSeg (a,b) is functional Element of bool the carrier of (TOP-REAL f)
bool the carrier of (TOP-REAL f) is set
{ (((1 - b₁) * a) + (b₁ * b)) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
a - b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),a,(- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (a,(- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[a,(- b)] is set
{a,(- b)} is functional finite V45() set
{a} is functional non empty trivial finite V45() 1 -element set
{{a,(- b)},{a}} is finite V45() set
the U7 of (TOP-REAL f) . [a,(- b)] is V1() Function-like set
a + (- b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
a - b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(a - b).| is V28() real ext-real non negative Element of REAL
sqr (a - b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (a - b)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (a - b))) is V28() real ext-real Element of REAL
g - b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
K385((TOP-REAL f),g,(- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (g,(- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[g,(- b)] is set
{g,(- b)} is functional finite V45() set
{{g,(- b)},{g}} is finite V45() set
the U7 of (TOP-REAL f) . [g,(- b)] is V1() Function-like set
g + (- b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
g - b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(g - b).| is V28() real ext-real non negative Element of REAL
sqr (g - b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (g - b)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (g - b))) is V28() real ext-real Element of REAL
c is V28() real ext-real Element of REAL
1 - c is V28() real ext-real Element of REAL
(1 - c) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - c) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
c * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
c * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) + (c * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - c) * a),(c * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - c) * a),(c * b)] is set
{((1 - c) * a),(c * b)} is functional finite V45() set
{((1 - c) * a)} is functional non empty trivial finite V45() 1 -element set
{{((1 - c) * a),(c * b)},{((1 - c) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - c) * a),(c * b)] is V1() Function-like set
((1 - c) * a) + (c * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) - a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
K385((TOP-REAL f),((1 - c) * a),(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - c) * a),(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - c) * a),(- a)] is set
{((1 - c) * a),(- a)} is functional finite V45() set
{{((1 - c) * a),(- a)},{((1 - c) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - c) * a),(- a)] is V1() Function-like set
((1 - c) * a) + (- a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) - a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - c) * a) - a) + (c * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - c) * a) - a),(c * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - c) * a) - a),(c * b)] is set
{(((1 - c) * a) - a),(c * b)} is functional finite V45() set
{(((1 - c) * a) - a)} is functional non empty trivial finite V45() 1 -element set
{{(((1 - c) * a) - a),(c * b)},{(((1 - c) * a) - a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - c) * a) - a),(c * b)] is V1() Function-like set
(((1 - c) * a) - a) + (c * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) - (1 * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (1 * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (1 * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),((1 - c) * a),(- (1 * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - c) * a),(- (1 * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - c) * a),(- (1 * a))] is set
{((1 - c) * a),(- (1 * a))} is functional finite V45() set
{{((1 - c) * a),(- (1 * a))},{((1 - c) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - c) * a),(- (1 * a))] is V1() Function-like set
((1 - c) * a) + (- (1 * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - c) * a) - (1 * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - c) * a) - (1 * a)) + (c * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - c) * a) - (1 * a)),(c * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - c) * a) - (1 * a)),(c * b)] is set
{(((1 - c) * a) - (1 * a)),(c * b)} is functional finite V45() set
{(((1 - c) * a) - (1 * a))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - c) * a) - (1 * a)),(c * b)},{(((1 - c) * a) - (1 * a))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - c) * a) - (1 * a)),(c * b)] is V1() Function-like set
(((1 - c) * a) - (1 * a)) + (c * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
- c is V28() real ext-real Element of REAL
1 + (- c) is V28() real ext-real Element of REAL
(1 + (- c)) - 1 is V28() real ext-real Element of REAL
((1 + (- c)) - 1) * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 + (- c)) - 1) * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 + (- c)) - 1) * a) + (c * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 + (- c)) - 1) * a),(c * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 + (- c)) - 1) * a),(c * b)] is set
{(((1 + (- c)) - 1) * a),(c * b)} is functional finite V45() set
{(((1 + (- c)) - 1) * a)} is functional non empty trivial finite V45() 1 -element set
{{(((1 + (- c)) - 1) * a),(c * b)},{(((1 + (- c)) - 1) * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 + (- c)) - 1) * a),(c * b)] is V1() Function-like set
(((1 + (- c)) - 1) * a) + (c * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
c * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
c * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
- (c * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (c * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(c * b) + (- (c * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((c * b),(- (c * a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(c * b),(- (c * a))] is set
{(c * b),(- (c * a))} is functional finite V45() set
{(c * b)} is functional non empty trivial finite V45() 1 -element set
{{(c * b),(- (c * a))},{(c * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [(c * b),(- (c * a))] is V1() Function-like set
(c * b) + (- (c * a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
c * (- a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
c * (- a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(c * b) + (c * (- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((c * b),(c * (- a))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(c * b),(c * (- a))] is set
{(c * b),(c * (- a))} is functional finite V45() set
{{(c * b),(c * (- a))},{(c * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [(c * b),(c * (- a))] is V1() Function-like set
(c * b) + (c * (- a)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
b - a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
K385((TOP-REAL f),b,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (b,(- a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[b,(- a)] is set
{b,(- a)} is functional finite V45() set
{b} is functional non empty trivial finite V45() 1 -element set
{{b,(- a)},{b}} is finite V45() set
the U7 of (TOP-REAL f) . [b,(- a)] is V1() Function-like set
b + (- a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
b - a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
c * (b - a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
c * (b - a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
abs c is V28() real ext-real Element of REAL
|.(b - a).| is V28() real ext-real non negative Element of REAL
sqr (b - a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (b - a)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (b - a))) is V28() real ext-real Element of REAL
(abs c) * |.(b - a).| is V28() real ext-real Element of REAL
(abs c) * |.(a - b).| is V28() real ext-real Element of REAL
c * |.(a - b).| is V28() real ext-real Element of REAL
|.(a - b).| - |.(g - a).| is V28() real ext-real Element of REAL
(1 - c) * |.(a - b).| is V28() real ext-real Element of REAL
d is V28() real ext-real Element of REAL
1 - d is V28() real ext-real Element of REAL
(1 - d) * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
(1 - d) * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
d * a is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
d * a is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - d) * b) + (d * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - d) * b),(d * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - d) * b),(d * a)] is set
{((1 - d) * b),(d * a)} is functional finite V45() set
{((1 - d) * b)} is functional non empty trivial finite V45() 1 -element set
{{((1 - d) * b),(d * a)},{((1 - d) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - d) * b),(d * a)] is V1() Function-like set
((1 - d) * b) + (d * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - d) * b) + (- b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - d) * b),(- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - d) * b),(- b)] is set
{((1 - d) * b),(- b)} is functional finite V45() set
{{((1 - d) * b),(- b)},{((1 - d) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - d) * b),(- b)] is V1() Function-like set
((1 - d) * b) + (- b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - d) * b) + (- b)) + (d * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - d) * b) + (- b)),(d * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - d) * b) + (- b)),(d * a)] is set
{(((1 - d) * b) + (- b)),(d * a)} is functional finite V45() set
{(((1 - d) * b) + (- b))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - d) * b) + (- b)),(d * a)},{(((1 - d) * b) + (- b))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - d) * b) + (- b)),(d * a)] is V1() Function-like set
(((1 - d) * b) + (- b)) + (d * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
1 * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
1 * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - d) * b) - (1 * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (1 * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (1 * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL f),((1 - d) * b),(- (1 * b))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . (((1 - d) * b),(- (1 * b))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[((1 - d) * b),(- (1 * b))] is set
{((1 - d) * b),(- (1 * b))} is functional finite V45() set
{{((1 - d) * b),(- (1 * b))},{((1 - d) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [((1 - d) * b),(- (1 * b))] is V1() Function-like set
((1 - d) * b) + (- (1 * b)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((1 - d) * b) - (1 * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 - d) * b) - (1 * b)) + (d * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 - d) * b) - (1 * b)),(d * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 - d) * b) - (1 * b)),(d * a)] is set
{(((1 - d) * b) - (1 * b)),(d * a)} is functional finite V45() set
{(((1 - d) * b) - (1 * b))} is functional non empty trivial finite V45() 1 -element set
{{(((1 - d) * b) - (1 * b)),(d * a)},{(((1 - d) * b) - (1 * b))}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 - d) * b) - (1 * b)),(d * a)] is V1() Function-like set
(((1 - d) * b) - (1 * b)) + (d * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
- d is V28() real ext-real Element of REAL
1 + (- d) is V28() real ext-real Element of REAL
(1 + (- d)) - 1 is V28() real ext-real Element of REAL
((1 + (- d)) - 1) * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
((1 + (- d)) - 1) * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(((1 + (- d)) - 1) * b) + (d * a) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((((1 + (- d)) - 1) * b),(d * a)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(((1 + (- d)) - 1) * b),(d * a)] is set
{(((1 + (- d)) - 1) * b),(d * a)} is functional finite V45() set
{(((1 + (- d)) - 1) * b)} is functional non empty trivial finite V45() 1 -element set
{{(((1 + (- d)) - 1) * b),(d * a)},{(((1 + (- d)) - 1) * b)}} is finite V45() set
the U7 of (TOP-REAL f) . [(((1 + (- d)) - 1) * b),(d * a)] is V1() Function-like set
(((1 + (- d)) - 1) * b) + (d * a) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
d * b is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
d * b is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
- (d * b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
- (d * b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d * a) + (- (d * b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((d * a),(- (d * b))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(d * a),(- (d * b))] is set
{(d * a),(- (d * b))} is functional finite V45() set
{(d * a)} is functional non empty trivial finite V45() 1 -element set
{{(d * a),(- (d * b))},{(d * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(d * a),(- (d * b))] is V1() Function-like set
(d * a) + (- (d * b)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
d * (- b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
d * (- b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d * a) + (d * (- b)) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
the U7 of (TOP-REAL f) . ((d * a),(d * (- b))) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
[(d * a),(d * (- b))] is set
{(d * a),(d * (- b))} is functional finite V45() set
{{(d * a),(d * (- b))},{(d * a)}} is finite V45() set
the U7 of (TOP-REAL f) . [(d * a),(d * (- b))] is V1() Function-like set
(d * a) + (d * (- b)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
d * (a - b) is V1() V4( NAT ) Function-like finite f -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL f)
d * (a - b) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
abs d is V28() real ext-real Element of REAL
(abs d) * |.(a - b).| is V28() real ext-real Element of REAL
d * |.(a - b).| is V28() real ext-real Element of REAL
|.(a - b).| - |.(g - b).| is V28() real ext-real Element of REAL
(1 - d) * |.(a - b).| is V28() real ext-real Element of REAL
f is non empty Reflexive discerning V105() triangle Discerning MetrStruct
TopSpaceMetr f is TopStruct
the carrier of (TopSpaceMetr f) is set
bool the carrier of (TopSpaceMetr f) is set
g is Element of bool the carrier of (TopSpaceMetr f)
a is Element of bool the carrier of (TopSpaceMetr f)
min_dist_min (g,a) is V28() real ext-real Element of REAL
the carrier of f is non empty set
b is Element of the carrier of f
c is Element of the carrier of f
dist (b,c) is V28() real ext-real Element of REAL
f is non empty Reflexive discerning V105() triangle Discerning MetrStruct
TopSpaceMetr f is TopStruct
the carrier of (TopSpaceMetr f) is set
bool the carrier of (TopSpaceMetr f) is set
g is Element of bool the carrier of (TopSpaceMetr f)
a is Element of bool the carrier of (TopSpaceMetr f)
min_dist_min (g,a) is V28() real ext-real Element of REAL
g /\ a is Element of bool the carrier of (TopSpaceMetr f)
the Element of g /\ a is Element of g /\ a
the carrier of f is non empty set
c is Element of the carrier of (TopSpaceMetr f)
the distance of f is V1() V4([: the carrier of f, the carrier of f:]) V5( REAL ) Function-like V18([: the carrier of f, the carrier of f:], REAL ) complex-yielding V172() V173() Element of bool [:[: the carrier of f, the carrier of f:],REAL:]
[: the carrier of f, the carrier of f:] is V1() set
[:[: the carrier of f, the carrier of f:],REAL:] is V1() complex-yielding V172() V173() set
bool [:[: the carrier of f, the carrier of f:],REAL:] is set
d is Element of the carrier of f
the distance of f . (d,d) is V28() real ext-real Element of REAL
[d,d] is set
{d,d} is finite set
{d} is non empty trivial finite 1 -element set
{{d,d},{d}} is finite V45() set
the distance of f . [d,d] is V28() real ext-real set
dist (d,d) is V28() real ext-real Element of REAL
b is Element of the carrier of f
c is Element of the carrier of f
dist (b,c) is V28() real ext-real Element of REAL
the distance of f . (b,c) is V28() real ext-real Element of REAL
[b,c] is set
{b,c} is finite set
{b} is non empty trivial finite 1 -element set
{{b,c},{b}} is finite V45() set
the distance of f . [b,c] is V28() real ext-real set
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
X_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(X_axis f) . 1 is V28() real ext-real Element of REAL
(X_axis f) . (len f) is V28() real ext-real Element of REAL
Y_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
f . 1 is V1() Function-like set
f . (len f) is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a is V28() real ext-real Element of REAL
b is V28() real ext-real Element of REAL
g is V28() real ext-real Element of REAL
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
2 * (len f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (len f)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg ((2 * (len f)) -' 1) is finite (2 * (len f)) -' 1 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative finite cardinal set
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative finite cardinal set
2 * d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * d) + (c mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. d) `1 is V28() real ext-real Element of REAL
(f /. d) . 1 is V28() real ext-real Element of REAL
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (d + 1)) `2 is V28() real ext-real Element of REAL
(f /. (d + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. d) `1),((f /. (d + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * O) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. O) `1 is V28() real ext-real Element of REAL
(f /. O) . 1 is V28() real ext-real Element of REAL
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (O + 1)) `2 is V28() real ext-real Element of REAL
(f /. (O + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. O) `1),((f /. (O + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
0 - 1 is V28() real ext-real Element of REAL
0 -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O - 1 is V28() real ext-real Element of REAL
2 * (O - 1) is V28() real ext-real Element of REAL
(2 * (O - 1)) + (1 + 1) is V28() real ext-real Element of REAL
((2 * (O - 1)) + (1 + 1)) - 1 is V28() real ext-real Element of REAL
(2 * (O - 1)) + 1 is V28() real ext-real Element of REAL
O -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * (O -' 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (O -' 1)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative finite cardinal set
2 * d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * d) + (c mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * O) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. O) `1 is V28() real ext-real Element of REAL
(f /. O) . 1 is V28() real ext-real Element of REAL
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (O + 1)) `2 is V28() real ext-real Element of REAL
(f /. (O + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. O) `1),((f /. (O + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O - 1 is V28() real ext-real Element of REAL
2 * (O - 1) is V28() real ext-real Element of REAL
(2 * (O - 1)) + (1 + 1) is V28() real ext-real Element of REAL
((2 * (O - 1)) + (1 + 1)) - 1 is V28() real ext-real Element of REAL
(2 * (O - 1)) + 1 is V28() real ext-real Element of REAL
(2 * O) - 1 is V28() real ext-real Element of REAL
O - d is V28() real ext-real set
2 * (O - d) is V28() real ext-real Element of REAL
O -' d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom c is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom c is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng c is finite set
d is set
O is set
c . O is set
len c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len c) is finite len c -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative finite cardinal set
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + (I mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c . I is set
f1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. f1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. f1) `1 is V28() real ext-real Element of REAL
(f /. f1) . 1 is V28() real ext-real Element of REAL
f1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (f1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (f1 + 1)) `2 is V28() real ext-real Element of REAL
(f /. (f1 + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. f1) `1),((f /. (f1 + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative finite cardinal set
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + (I mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (f1 + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (f1 + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (f1 + 1)) - 1 is V28() real ext-real Element of REAL
c . I is set
f /. (f1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
O is ordinal natural V28() real ext-real non negative finite cardinal set
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
d /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
d . O is V1() Function-like set
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d . (O + 1) is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
1 + O is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
(P + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. ((P + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. ((P + 1) + 1)) `2 is V28() real ext-real Element of REAL
(f /. ((P + 1) + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. (P + 1)) `1),((f /. ((P + 1) + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (len f)) - 1 is V28() real ext-real Element of REAL
Y_axis d is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (Y_axis d) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis d) . O is V28() real ext-real Element of REAL
len (Y_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (Y_axis d) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (Y_axis d)) is finite len (Y_axis d) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . O is V1() Function-like set
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
X_axis d is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (X_axis d) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis d) . O is V28() real ext-real Element of REAL
len (X_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (X_axis d) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (X_axis d)) is finite len (X_axis d) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . O is V1() Function-like set
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis f) . P is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(len f) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) + (len f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len f) + 1) - 1 is V28() real ext-real Element of REAL
(2 * 1) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(1 + 1) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(1 + 1) - 1 is V28() real ext-real Element of REAL
c . 1 is set
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) - (d /. (O + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (d /. (O + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (d /. (O + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (d /. (O + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (d /. (O + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (d /. (O + 1)))] is set
{(d /. O),(- (d /. (O + 1)))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (d /. (O + 1)))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (d /. (O + 1)))] is V1() Function-like set
(d /. O) + (- (d /. (O + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (d /. (O + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((d /. O) - (d /. (O + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (d /. (O + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (d /. (O + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (d /. (O + 1))))) is V28() real ext-real Element of REAL
d . (O + 1) is V1() Function-like set
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d . O is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
1 + O is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
((d /. O) `1) - ((d /. (O + 1)) `1) is V28() real ext-real Element of REAL
((d /. O) `2) - ((d /. (O + 1)) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((d /. (O + 1)) `1)),(((d /. O) `2) - ((d /. (O + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((f /. P) `1) - ((f /. (P + 1)) `1) is V28() real ext-real Element of REAL
|[(((f /. P) `1) - ((f /. (P + 1)) `1)),0]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (d /. (O + 1))) `1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 1 is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
(((d /. O) - (d /. (O + 1))) `1) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `1) * (((d /. O) - (d /. (O + 1))) `1) is V28() real ext-real set
((d /. O) - (d /. (O + 1))) `2 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `2) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `2) * (((d /. O) - (d /. (O + 1))) `2) is V28() real ext-real set
((((d /. O) - (d /. (O + 1))) `1) ^2) + ((((d /. O) - (d /. (O + 1))) `2) ^2) is V28() real ext-real Element of REAL
sqrt (((((d /. O) - (d /. (O + 1))) `1) ^2) + ((((d /. O) - (d /. (O + 1))) `2) ^2)) is V28() real ext-real Element of REAL
(((f /. P) `1) - ((f /. (P + 1)) `1)) ^2 is V28() real ext-real Element of REAL
(((f /. P) `1) - ((f /. (P + 1)) `1)) * (((f /. P) `1) - ((f /. (P + 1)) `1)) is V28() real ext-real set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is ordinal natural V28() real ext-real non negative finite cardinal set
((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt ((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) is V28() real ext-real Element of REAL
abs (((f /. P) `1) - ((f /. (P + 1)) `1)) is V28() real ext-real Element of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. P),(- (f /. (P + 1)))] is set
{(f /. P),(- (f /. (P + 1)))} is functional finite V45() set
{(f /. P)} is functional non empty trivial finite V45() 1 -element set
{{(f /. P),(- (f /. (P + 1)))},{(f /. P)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. P),(- (f /. (P + 1)))] is V1() Function-like set
(f /. P) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. P) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. P) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. P) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. P) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
(P + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. ((P + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. ((P + 1) + 1)) `2 is V28() real ext-real Element of REAL
(f /. ((P + 1) + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. (P + 1)) `1),((f /. ((P + 1) + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
((d /. O) `1) - ((d /. (O + 1)) `1) is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
((d /. O) `2) - ((d /. (O + 1)) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((d /. (O + 1)) `1)),(((d /. O) `2) - ((d /. (O + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2) is V28() real ext-real Element of REAL
|[0,(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (d /. (O + 1))) `1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 1 is V28() real ext-real Element of REAL
(2 * (P + 1)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * (P + 1)) / 2 is V28() real ext-real non negative Element of REAL
(f /. (P + 1)) - (f /. ((P + 1) + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. ((P + 1) + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. ((P + 1) + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. (P + 1)),(- (f /. ((P + 1) + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. (P + 1)),(- (f /. ((P + 1) + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. (P + 1)),(- (f /. ((P + 1) + 1)))] is set
{(f /. (P + 1)),(- (f /. ((P + 1) + 1)))} is functional finite V45() set
{(f /. (P + 1))} is functional non empty trivial finite V45() 1 -element set
{{(f /. (P + 1)),(- (f /. ((P + 1) + 1)))},{(f /. (P + 1))}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. (P + 1)),(- (f /. ((P + 1) + 1)))] is V1() Function-like set
(f /. (P + 1)) + (- (f /. ((P + 1) + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. (P + 1)) - (f /. ((P + 1) + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. (P + 1)) - (f /. ((P + 1) + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1))))) is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `1) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `1) * (((d /. O) - (d /. (O + 1))) `1) is V28() real ext-real set
((d /. O) - (d /. (O + 1))) `2 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `2) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (d /. (O + 1))) `2) * (((d /. O) - (d /. (O + 1))) `2) is V28() real ext-real set
((((d /. O) - (d /. (O + 1))) `1) ^2) + ((((d /. O) - (d /. (O + 1))) `2) ^2) is V28() real ext-real Element of REAL
sqrt (((((d /. O) - (d /. (O + 1))) `1) ^2) + ((((d /. O) - (d /. (O + 1))) `2) ^2)) is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2 is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) * (((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) is V28() real ext-real set
sqrt ((((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2) is V28() real ext-real Element of REAL
abs (((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom d is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d . O is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(d /. O) - (f /. P) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. P) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. P) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (f /. P))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (f /. P))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (f /. P))] is set
{(d /. O),(- (f /. P))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (f /. P))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (f /. P))] is V1() Function-like set
(d /. O) + (- (f /. P)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (f /. P) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((d /. O) `1) - ((f /. P) `1) is V28() real ext-real Element of REAL
(f /. P) `2 is V28() real ext-real Element of REAL
(f /. P) . 2 is V28() real ext-real Element of REAL
((d /. O) `2) - ((f /. P) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((f /. P) `1)),(((d /. O) `2) - ((f /. P) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|[0,(((d /. O) `2) - ((f /. P) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (f /. P)) `2 is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) . 2 is V28() real ext-real Element of REAL
|.((d /. O) - (f /. P)).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (f /. P)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (f /. P))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (f /. P)))) is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) `1 is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) . 1 is V28() real ext-real Element of REAL
(((d /. O) - (f /. P)) `1) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (f /. P)) `1) * (((d /. O) - (f /. P)) `1) is V28() real ext-real set
(((d /. O) `2) - ((f /. P) `2)) ^2 is V28() real ext-real Element of REAL
(((d /. O) `2) - ((f /. P) `2)) * (((d /. O) `2) - ((f /. P) `2)) is V28() real ext-real set
((((d /. O) - (f /. P)) `1) ^2) + ((((d /. O) `2) - ((f /. P) `2)) ^2) is V28() real ext-real Element of REAL
sqrt (((((d /. O) - (f /. P)) `1) ^2) + ((((d /. O) `2) - ((f /. P) `2)) ^2)) is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is ordinal natural V28() real ext-real non negative finite cardinal set
((f /. (P + 1)) `2) - ((f /. P) `2) is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. P) `2)) ^2 is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. P) `2)) * (((f /. (P + 1)) `2) - ((f /. P) `2)) is V28() real ext-real set
(0 ^2) + ((((f /. (P + 1)) `2) - ((f /. P) `2)) ^2) is V28() real ext-real Element of REAL
sqrt ((0 ^2) + ((((f /. (P + 1)) `2) - ((f /. P) `2)) ^2)) is V28() real ext-real Element of REAL
sqrt ((((f /. (P + 1)) `2) - ((f /. P) `2)) ^2) is V28() real ext-real Element of REAL
abs (((f /. (P + 1)) `2) - ((f /. P) `2)) is V28() real ext-real Element of REAL
((f /. P) `2) - ((f /. (P + 1)) `2) is V28() real ext-real Element of REAL
abs (((f /. P) `2) - ((f /. (P + 1)) `2)) is V28() real ext-real Element of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. P),(- (f /. (P + 1)))] is set
{(f /. P),(- (f /. (P + 1)))} is functional finite V45() set
{(f /. P)} is functional non empty trivial finite V45() 1 -element set
{{(f /. P),(- (f /. (P + 1)))},{(f /. P)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. P),(- (f /. (P + 1)))] is V1() Function-like set
(f /. P) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. P) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. P) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. P) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. P) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (f /. (P + 1)))] is set
{(d /. O),(- (f /. (P + 1)))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (f /. (P + 1)))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (f /. (P + 1)))] is V1() Function-like set
(d /. O) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((d /. O) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
0. (TOP-REAL 2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like V71( TOP-REAL 2) complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|.(0. (TOP-REAL 2)).| is V28() real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (0. (TOP-REAL 2))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (0. (TOP-REAL 2)))) is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * P) + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d . (len d) is V1() Function-like set
2 * 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * 1) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(1 + 1) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Y_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(Y_axis f) . 1 is V28() real ext-real Element of REAL
(Y_axis f) . (len f) is V28() real ext-real Element of REAL
X_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
f . 1 is V1() Function-like set
f . (len f) is V1() Function-like set
dom f is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
a is V28() real ext-real Element of REAL
b is V28() real ext-real Element of REAL
g is V28() real ext-real Element of REAL
(len f) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
(len f) + (len f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
((len f) + 1) - 1 is V28() real ext-real Element of REAL
2 * (len f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (len f)) - 1 is V28() real ext-real Element of REAL
(2 * (len f)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg ((2 * (len f)) -' 1) is finite (2 * (len f)) -' 1 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is ordinal natural V28() real ext-real non negative finite cardinal set
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative finite cardinal set
2 * d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * d) + (c mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. d) `1 is V28() real ext-real Element of REAL
(f /. d) . 1 is V28() real ext-real Element of REAL
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (d + 1)) `2 is V28() real ext-real Element of REAL
(f /. (d + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. d) `1),((f /. (d + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * O) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. O) `1 is V28() real ext-real Element of REAL
(f /. O) . 1 is V28() real ext-real Element of REAL
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (O + 1)) `2 is V28() real ext-real Element of REAL
(f /. (O + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. O) `1),((f /. (O + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
0 - 1 is V28() real ext-real Element of REAL
0 -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O - 1 is V28() real ext-real Element of REAL
2 * (O - 1) is V28() real ext-real Element of REAL
(2 * (O - 1)) + (1 + 1) is V28() real ext-real Element of REAL
((2 * (O - 1)) + (1 + 1)) - 1 is V28() real ext-real Element of REAL
(2 * (O - 1)) + 1 is V28() real ext-real Element of REAL
O -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * (O -' 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (O -' 1)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is ordinal natural V28() real ext-real non negative finite cardinal set
2 * d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * d) + (c mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (d + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
2 * O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * O) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. O) `1 is V28() real ext-real Element of REAL
(f /. O) . 1 is V28() real ext-real Element of REAL
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (O + 1)) `2 is V28() real ext-real Element of REAL
(f /. (O + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. O) `1),((f /. (O + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O - 1 is V28() real ext-real Element of REAL
2 * (O - 1) is V28() real ext-real Element of REAL
(2 * (O - 1)) + (1 + 1) is V28() real ext-real Element of REAL
((2 * (O - 1)) + (1 + 1)) - 1 is V28() real ext-real Element of REAL
(2 * (O - 1)) + 1 is V28() real ext-real Element of REAL
(2 * O) - 1 is V28() real ext-real Element of REAL
O - d is V28() real ext-real set
2 * (O - d) is V28() real ext-real Element of REAL
O -' d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
c mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom c is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
c is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
dom c is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng c is finite set
d is set
O is set
c . O is set
len c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len c) is finite len c -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative finite cardinal set
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + (I mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c . I is set
f1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. f1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. f1) `1 is V28() real ext-real Element of REAL
(f /. f1) . 1 is V28() real ext-real Element of REAL
f1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (f1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (f1 + 1)) `2 is V28() real ext-real Element of REAL
(f /. (f1 + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. f1) `1),((f /. (f1 + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative finite cardinal set
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + (I mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f1 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (f1 + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (f1 + 1)) - 1 is V28() real ext-real Element of REAL
(2 * (f1 + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c . I is set
f /. (f1 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
I mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len c is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len d is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
O is ordinal natural V28() real ext-real non negative finite cardinal set
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
d /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d . (O + 1) is V1() Function-like set
d . O is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
1 + O is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
(P + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. ((P + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. ((P + 1) + 1)) `2 is V28() real ext-real Element of REAL
(f /. ((P + 1) + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. (P + 1)) `1),((f /. ((P + 1) + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Y_axis d is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (Y_axis d) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis d) . O is V28() real ext-real Element of REAL
len (Y_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (Y_axis d) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (Y_axis d)) is finite len (Y_axis d) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . O is V1() Function-like set
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(1 + 1) - 1 is V28() real ext-real Element of REAL
c . 1 is set
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . 1 is V1() Function-like set
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
O + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d /. (O + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) - (d /. (O + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (d /. (O + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (d /. (O + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (d /. (O + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (d /. (O + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (d /. (O + 1)))] is set
{(d /. O),(- (d /. (O + 1)))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (d /. (O + 1)))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (d /. (O + 1)))] is V1() Function-like set
(d /. O) + (- (d /. (O + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (d /. (O + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((d /. O) - (d /. (O + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (d /. (O + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (d /. (O + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (d /. (O + 1))))) is V28() real ext-real Element of REAL
d . (O + 1) is V1() Function-like set
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d . O is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
1 + O is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
((d /. O) `1) - ((d /. (O + 1)) `1) is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
((d /. O) `2) - ((d /. (O + 1)) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((d /. (O + 1)) `1)),(((d /. O) `2) - ((d /. (O + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
((f /. P) `1) - ((f /. (P + 1)) `1) is V28() real ext-real Element of REAL
|[(((f /. P) `1) - ((f /. (P + 1)) `1)),0]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (d /. (O + 1))) `1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) `2 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 2 is V28() real ext-real Element of REAL
(((f /. P) `1) - ((f /. (P + 1)) `1)) ^2 is V28() real ext-real Element of REAL
(((f /. P) `1) - ((f /. (P + 1)) `1)) * (((f /. P) `1) - ((f /. (P + 1)) `1)) is V28() real ext-real set
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is ordinal natural V28() real ext-real non negative finite cardinal set
((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) + (0 ^2) is V28() real ext-real Element of REAL
sqrt (((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) + (0 ^2)) is V28() real ext-real Element of REAL
sqrt ((((f /. P) `1) - ((f /. (P + 1)) `1)) ^2) is V28() real ext-real Element of REAL
abs (((f /. P) `1) - ((f /. (P + 1)) `1)) is V28() real ext-real Element of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. P),(- (f /. (P + 1)))] is set
{(f /. P),(- (f /. (P + 1)))} is functional finite V45() set
{(f /. P)} is functional non empty trivial finite V45() 1 -element set
{{(f /. P),(- (f /. (P + 1)))},{(f /. P)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. P),(- (f /. (P + 1)))] is V1() Function-like set
(f /. P) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. P) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. P) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. P) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. P) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
(P + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. ((P + 1) + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. ((P + 1) + 1)) `2 is V28() real ext-real Element of REAL
(f /. ((P + 1) + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. (P + 1)) `1),((f /. ((P + 1) + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. (O + 1)) `1 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 1 is V28() real ext-real Element of REAL
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
((d /. O) `1) - ((d /. (O + 1)) `1) is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(d /. (O + 1)) `2 is V28() real ext-real Element of REAL
(d /. (O + 1)) . 2 is V28() real ext-real Element of REAL
((d /. O) `2) - ((d /. (O + 1)) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((d /. (O + 1)) `1)),(((d /. O) `2) - ((d /. (O + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2) is V28() real ext-real Element of REAL
|[0,(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (d /. (O + 1))) `1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 1 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) `2 is V28() real ext-real Element of REAL
((d /. O) - (d /. (O + 1))) . 2 is V28() real ext-real Element of REAL
0 ^2 is V28() real ext-real Element of REAL
0 * 0 is ordinal natural V28() real ext-real non negative finite cardinal set
(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2 is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) * (((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) is V28() real ext-real set
(0 ^2) + ((((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2) is V28() real ext-real Element of REAL
sqrt ((0 ^2) + ((((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2)) is V28() real ext-real Element of REAL
sqrt ((((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) ^2) is V28() real ext-real Element of REAL
abs (((f /. (P + 1)) `2) - ((f /. ((P + 1) + 1)) `2)) is V28() real ext-real Element of REAL
(f /. (P + 1)) - (f /. ((P + 1) + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. ((P + 1) + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. ((P + 1) + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. (P + 1)),(- (f /. ((P + 1) + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. (P + 1)),(- (f /. ((P + 1) + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. (P + 1)),(- (f /. ((P + 1) + 1)))] is set
{(f /. (P + 1)),(- (f /. ((P + 1) + 1)))} is functional finite V45() set
{(f /. (P + 1))} is functional non empty trivial finite V45() 1 -element set
{{(f /. (P + 1)),(- (f /. ((P + 1) + 1)))},{(f /. (P + 1))}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. (P + 1)),(- (f /. ((P + 1) + 1)))] is V1() Function-like set
(f /. (P + 1)) + (- (f /. ((P + 1) + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. (P + 1)) - (f /. ((P + 1) + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. (P + 1)) - (f /. ((P + 1) + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. (P + 1)) - (f /. ((P + 1) + 1))))) is V28() real ext-real Element of REAL
(2 * (P + 1)) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * (P + 1)) / 2 is V28() real ext-real non negative Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom d is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . O is V1() Function-like set
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
(d /. O) - (f /. P) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. P) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. P) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (f /. P))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (f /. P))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (f /. P))] is set
{(d /. O),(- (f /. P))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (f /. P))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (f /. P))] is V1() Function-like set
(d /. O) + (- (f /. P)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (f /. P) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
((d /. O) `1) - ((f /. P) `1) is V28() real ext-real Element of REAL
(d /. O) `2 is V28() real ext-real Element of REAL
(d /. O) . 2 is V28() real ext-real Element of REAL
(f /. P) `2 is V28() real ext-real Element of REAL
(f /. P) . 2 is V28() real ext-real Element of REAL
((d /. O) `2) - ((f /. P) `2) is V28() real ext-real Element of REAL
|[(((d /. O) `1) - ((f /. P) `1)),(((d /. O) `2) - ((f /. P) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|[0,(((d /. O) `2) - ((f /. P) `2))]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
((d /. O) - (f /. P)) `1 is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) . 1 is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) `2 is V28() real ext-real Element of REAL
((d /. O) - (f /. P)) . 2 is V28() real ext-real Element of REAL
|.((d /. O) - (f /. P)).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (f /. P)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (f /. P))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (f /. P)))) is V28() real ext-real Element of REAL
(((d /. O) - (f /. P)) `1) ^2 is V28() real ext-real Element of REAL
(((d /. O) - (f /. P)) `1) * (((d /. O) - (f /. P)) `1) is V28() real ext-real set
(((d /. O) `2) - ((f /. P) `2)) ^2 is V28() real ext-real Element of REAL
(((d /. O) `2) - ((f /. P) `2)) * (((d /. O) `2) - ((f /. P) `2)) is V28() real ext-real set
((((d /. O) - (f /. P)) `1) ^2) + ((((d /. O) `2) - ((f /. P) `2)) ^2) is V28() real ext-real Element of REAL
sqrt (((((d /. O) - (f /. P)) `1) ^2) + ((((d /. O) `2) - ((f /. P) `2)) ^2)) is V28() real ext-real Element of REAL
((f /. (P + 1)) `2) - ((f /. P) `2) is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. P) `2)) ^2 is V28() real ext-real Element of REAL
(((f /. (P + 1)) `2) - ((f /. P) `2)) * (((f /. (P + 1)) `2) - ((f /. P) `2)) is V28() real ext-real set
sqrt ((((f /. (P + 1)) `2) - ((f /. P) `2)) ^2) is V28() real ext-real Element of REAL
abs (((f /. (P + 1)) `2) - ((f /. P) `2)) is V28() real ext-real Element of REAL
((f /. P) `2) - ((f /. (P + 1)) `2) is V28() real ext-real Element of REAL
abs (((f /. P) `2) - ((f /. (P + 1)) `2)) is V28() real ext-real Element of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f /. P),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f /. P),(- (f /. (P + 1)))] is set
{(f /. P),(- (f /. (P + 1)))} is functional finite V45() set
{(f /. P)} is functional non empty trivial finite V45() 1 -element set
{{(f /. P),(- (f /. (P + 1)))},{(f /. P)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f /. P),(- (f /. (P + 1)))] is V1() Function-like set
(f /. P) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f /. P) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f /. P) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f /. P) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f /. P) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f /. P) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(d /. O) - (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(d /. O),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((d /. O),(- (f /. (P + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(d /. O),(- (f /. (P + 1)))] is set
{(d /. O),(- (f /. (P + 1)))} is functional finite V45() set
{(d /. O)} is functional non empty trivial finite V45() 1 -element set
{{(d /. O),(- (f /. (P + 1)))},{(d /. O)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(d /. O),(- (f /. (P + 1)))] is V1() Function-like set
(d /. O) + (- (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(d /. O) - (f /. (P + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((d /. O) - (f /. (P + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((d /. O) - (f /. (P + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((d /. O) - (f /. (P + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((d /. O) - (f /. (P + 1))))) is V28() real ext-real Element of REAL
0. (TOP-REAL 2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like V71( TOP-REAL 2) complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
|.(0. (TOP-REAL 2)).| is V28() real ext-real non negative Element of REAL
sqr (0. (TOP-REAL 2)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (0. (TOP-REAL 2))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (0. (TOP-REAL 2)))) is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * P) + 1) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
X_axis d is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (X_axis d) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
O is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis d) . O is V28() real ext-real Element of REAL
len (X_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len (X_axis d) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (X_axis d)) is finite len (X_axis d) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len d) is finite len d -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
d /. O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d . O is V1() Function-like set
(d /. O) `1 is V28() real ext-real Element of REAL
(d /. O) . 1 is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f /. P is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. P) `1 is V28() real ext-real Element of REAL
(f /. P) . 1 is V28() real ext-real Element of REAL
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `2 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 2 is V28() real ext-real Element of REAL
|[((f /. P) `1),((f /. (P + 1)) `2)]| is V1() V4( NAT ) Function-like non empty finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
0 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis f) . P is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
I is ordinal natural V28() real ext-real non negative finite cardinal set
2 * I is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * I) + (O mod 2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
P + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
2 * (P + 1) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) -' 1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * (P + 1)) - 1 is V28() real ext-real Element of REAL
f /. (P + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (P + 1)) `1 is V28() real ext-real Element of REAL
(f /. (P + 1)) . 1 is V28() real ext-real Element of REAL
2 * P is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(2 * P) + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
((2 * (len f)) - 1) + 1 is V28() real ext-real Element of REAL
(2 * (len f)) / 2 is V28() real ext-real non negative Element of REAL
(2 * P) / 2 is V28() real ext-real non negative Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis f) . (P + 1) is V28() real ext-real Element of REAL
O mod 2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
c . ((2 * (len f)) -' 1) is set
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
X_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
len (X_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis f) . 1 is V28() real ext-real Element of REAL
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. 1) `1 is V28() real ext-real Element of REAL
(f /. 1) . 1 is V28() real ext-real Element of REAL
(X_axis f) . (len f) is V28() real ext-real Element of REAL
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (len f)) `1 is V28() real ext-real Element of REAL
(f /. (len f)) . 1 is V28() real ext-real Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (X_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Y_axis f is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
len (Y_axis f) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis f) . 1 is V28() real ext-real Element of REAL
f /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. 1) `2 is V28() real ext-real Element of REAL
(f /. 1) . 2 is V28() real ext-real Element of REAL
(Y_axis f) . (len f) is V28() real ext-real Element of REAL
f /. (len f) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f /. (len f)) `2 is V28() real ext-real Element of REAL
(f /. (len f)) . 2 is V28() real ext-real Element of REAL
Seg (len f) is finite len f -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom (Y_axis f) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom g is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
X_axis g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(X_axis g) . f is V28() real ext-real Element of REAL
g /. f is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g /. f) `1 is V28() real ext-real Element of REAL
(g /. f) . 1 is V28() real ext-real Element of REAL
Y_axis g is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(Y_axis g) . f is V28() real ext-real Element of REAL
(g /. f) `2 is V28() real ext-real Element of REAL
(g /. f) . 2 is V28() real ext-real Element of REAL
len (X_axis g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
len g is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom (X_axis g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
len (Y_axis g) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom (Y_axis g) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f is functional non empty Element of bool the carrier of (TOP-REAL 2)
g is functional non empty Element of bool the carrier of (TOP-REAL 2)
a is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
b is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
c is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
d is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
a `1 is V28() real ext-real Element of REAL
a . 1 is V28() real ext-real Element of REAL
b `1 is V28() real ext-real Element of REAL
b . 1 is V28() real ext-real Element of REAL
c `2 is V28() real ext-real Element of REAL
c . 2 is V28() real ext-real Element of REAL
d `2 is V28() real ext-real Element of REAL
d . 2 is V28() real ext-real Element of REAL
(TOP-REAL 2) | g is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | g) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | g):] is V1() set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | g):] is set
O is V1() V4( the carrier of I[01]) V5( the carrier of ((TOP-REAL 2) | g)) Function-like non empty total V18( the carrier of I[01], the carrier of ((TOP-REAL 2) | g)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | g):]
O . 0 is set
O . 1 is set
the topology of (TOP-REAL 2) is non empty Element of bool (bool the carrier of (TOP-REAL 2))
bool (bool the carrier of (TOP-REAL 2)) is set
TopStruct(# the carrier of (TOP-REAL 2), the topology of (TOP-REAL 2) #) is non empty strict TopSpace-like TopStruct
Euclid 2 is non empty strict Reflexive discerning V105() triangle Discerning MetrStruct
REAL 2 is functional non empty FinSequence-membered M9( REAL )
K303(2,REAL) is functional FinSequence-membered M9( REAL )
Pitag_dist 2 is V1() V4([:(REAL 2),(REAL 2):]) V5( REAL ) Function-like V18([:(REAL 2),(REAL 2):], REAL ) complex-yielding V172() V173() Element of bool [:[:(REAL 2),(REAL 2):],REAL:]
[:(REAL 2),(REAL 2):] is V1() set
[:[:(REAL 2),(REAL 2):],REAL:] is V1() complex-yielding V172() V173() set
bool [:[:(REAL 2),(REAL 2):],REAL:] is set
MetrStruct(# (REAL 2),(Pitag_dist 2) #) is strict MetrStruct
TopSpaceMetr (Euclid 2) is TopStruct
the carrier of (TopSpaceMetr (Euclid 2)) is set
bool the carrier of (TopSpaceMetr (Euclid 2)) is set
I is Element of bool the carrier of (TopSpaceMetr (Euclid 2))
P is Element of bool the carrier of (TopSpaceMetr (Euclid 2))
min_dist_min (I,P) is V28() real ext-real Element of REAL
(min_dist_min (I,P)) / 5 is V28() real ext-real Element of REAL
(TOP-REAL 2) | f is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | f) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | f):] is V1() set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | f):] is set
Q is V1() V4( the carrier of I[01]) V5( the carrier of ((TOP-REAL 2) | f)) Function-like non empty total V18( the carrier of I[01], the carrier of ((TOP-REAL 2) | f)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | f):]
Q . 0 is set
Q . 1 is set
[: the carrier of I[01], the carrier of (TOP-REAL 2):] is V1() set
bool [: the carrier of I[01], the carrier of (TOP-REAL 2):] is set
g1 is V1() V4( the carrier of I[01]) V5( the carrier of (TOP-REAL 2)) Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
q2 is V1() V4( the carrier of I[01]) V5( the carrier of (TOP-REAL 2)) Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
f /\ g is functional Element of bool the carrier of (TOP-REAL 2)
0 / 5 is V28() real ext-real non negative Element of REAL
the carrier of (Euclid 2) is non empty set
bool the carrier of (Euclid 2) is set
q1 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
q1 . 1 is V28() real ext-real Element of REAL
len q1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
q1 . (len q1) is V28() real ext-real Element of REAL
rng q1 is finite V181() V182() V183() V283() V284() V285() Element of bool REAL
p2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
p2 . 1 is V28() real ext-real Element of REAL
len p2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
p2 . (len p2) is V28() real ext-real Element of REAL
rng p2 is finite V181() V182() V183() V283() V284() V285() Element of bool REAL
p1 is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len p1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom p1 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p1 is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len p1 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom p1 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom q2 is non empty Element of bool the carrier of I[01]
[#] I[01] is non empty non proper closed Element of bool the carrier of I[01]
rng p1 is finite set
p is set
f2 is set
p1 . f2 is set
Seg (len p1) is finite len p1 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
h29 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom p2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p2 . h29 is V28() real ext-real Element of REAL
dom g1 is non empty Element of bool the carrier of I[01]
rng Q is non empty Element of bool the carrier of ((TOP-REAL 2) | f)
bool the carrier of ((TOP-REAL 2) | f) is set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | f)
p1 . h29 is set
g1 . (p2 . h29) is V1() Function-like set
p is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len p is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
p . 1 is V1() Function-like set
p /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
h2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
h2 + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
p /. h2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p /. (h2 + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. h2) - (p /. (h2 + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (p /. (h2 + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (p /. (h2 + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(p /. h2),(- (p /. (h2 + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((p /. h2),(- (p /. (h2 + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(p /. h2),(- (p /. (h2 + 1)))] is set
{(p /. h2),(- (p /. (h2 + 1)))} is functional finite V45() set
{(p /. h2)} is functional non empty trivial finite V45() 1 -element set
{{(p /. h2),(- (p /. (h2 + 1)))},{(p /. h2)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(p /. h2),(- (p /. (h2 + 1)))] is V1() Function-like set
(p /. h2) + (- (p /. (h2 + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(p /. h2) - (p /. (h2 + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((p /. h2) - (p /. (h2 + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((p /. h2) - (p /. (h2 + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((p /. h2) - (p /. (h2 + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((p /. h2) - (p /. (h2 + 1))))) is V28() real ext-real Element of REAL
p2 . (h2 + 1) is V28() real ext-real Element of REAL
p2 /. (h2 + 1) is V28() real ext-real Element of REAL
p1 . (h2 + 1) is set
g1 . (p2 . (h2 + 1)) is V1() Function-like set
p2 . h2 is V28() real ext-real Element of REAL
p2 /. h2 is V28() real ext-real Element of REAL
dom p2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
[.(p2 /. h2),(p2 /. (h2 + 1)).] is V181() V182() V183() V286() Element of bool REAL
g2 is Element of bool the carrier of I[01]
g1 .: g2 is functional Element of bool the carrier of (TOP-REAL 2)
f2 is functional Element of bool the carrier of (TOP-REAL 2)
rng Q is non empty Element of bool the carrier of ((TOP-REAL 2) | f)
bool the carrier of ((TOP-REAL 2) | f) is set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | f)
ps is functional non empty Element of bool the carrier of (TOP-REAL 2)
E-bound ps is V28() real ext-real Element of REAL
W-bound ps is V28() real ext-real Element of REAL
(E-bound ps) - (W-bound ps) is V28() real ext-real Element of REAL
N-bound ps is V28() real ext-real Element of REAL
S-bound ps is V28() real ext-real Element of REAL
(N-bound ps) - (S-bound ps) is V28() real ext-real Element of REAL
((E-bound ps) - (W-bound ps)) + ((N-bound ps) - (S-bound ps)) is V28() real ext-real Element of REAL
(((E-bound ps) - (W-bound ps)) + ((N-bound ps) - (S-bound ps))) + 1 is V28() real ext-real Element of REAL
h29 is Element of bool the carrier of (Euclid 2)
x is Element of the carrier of (Euclid 2)
i is Element of the carrier of (Euclid 2)
dist (x,i) is V28() real ext-real Element of REAL
p11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p11 `2 is V28() real ext-real Element of REAL
p11 . 2 is V28() real ext-real Element of REAL
k is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
k `2 is V28() real ext-real Element of REAL
k . 2 is V28() real ext-real Element of REAL
(k `2) - (p11 `2) is V28() real ext-real Element of REAL
abs ((k `2) - (p11 `2)) is V28() real ext-real Element of REAL
p11 `1 is V28() real ext-real Element of REAL
p11 . 1 is V28() real ext-real Element of REAL
k `1 is V28() real ext-real Element of REAL
k . 1 is V28() real ext-real Element of REAL
(k `1) - (p11 `1) is V28() real ext-real Element of REAL
abs ((k `1) - (p11 `1)) is V28() real ext-real Element of REAL
(abs ((k `1) - (p11 `1))) + (abs ((k `2) - (p11 `2))) is V28() real ext-real Element of REAL
k - p11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- p11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- p11 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),k,(- p11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (k,(- p11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[k,(- p11)] is set
{k,(- p11)} is functional finite V45() set
{k} is functional non empty trivial finite V45() 1 -element set
{{k,(- p11)},{k}} is finite V45() set
the U7 of (TOP-REAL 2) . [k,(- p11)] is V1() Function-like set
k + (- p11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
k - p11 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(k - p11).| is V28() real ext-real non negative Element of REAL
sqr (k - p11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (k - p11)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (k - p11))) is V28() real ext-real Element of REAL
a `2 is V28() real ext-real Element of REAL
a . 2 is V28() real ext-real Element of REAL
dom g1 is non empty Element of bool the carrier of I[01]
p1 . h2 is set
g1 . (p2 . h2) is V1() Function-like set
x is Element of the carrier of (Euclid 2)
i is Element of the carrier of (Euclid 2)
g1 .: [.0,1.] is functional Element of bool the carrier of (TOP-REAL 2)
s is Element of bool the carrier of (Euclid 2)
dist (x,i) is V28() real ext-real Element of REAL
diameter s is V28() real ext-real Element of REAL
dom p is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(p /. 1) `1 is V28() real ext-real Element of REAL
(p /. 1) . 1 is V28() real ext-real Element of REAL
p /. (len p) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. (len p)) `1 is V28() real ext-real Element of REAL
(p /. (len p)) . 1 is V28() real ext-real Element of REAL
p . (len p) is V1() Function-like set
g1 . (p2 . (len p2)) is V1() Function-like set
f2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
p /. f2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. f2) `1 is V28() real ext-real Element of REAL
(p /. f2) . 1 is V28() real ext-real Element of REAL
p . f2 is V1() Function-like set
p2 . f2 is V28() real ext-real Element of REAL
g1 . (p2 . f2) is V1() Function-like set
Seg (len p2) is finite len p2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom p2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom g1 is non empty Element of bool the carrier of I[01]
rng Q is non empty Element of bool the carrier of ((TOP-REAL 2) | f)
bool the carrier of ((TOP-REAL 2) | f) is set
g1 . (p2 . 1) is V1() Function-like set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | f)
X_axis p is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (X_axis p) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(X_axis p) . 1 is V28() real ext-real Element of REAL
(X_axis p) . (len p) is V28() real ext-real Element of REAL
f2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis p) . f2 is V28() real ext-real Element of REAL
len (X_axis p) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (X_axis p)) is finite len (X_axis p) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len p) is finite len p -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p /. f2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. f2) `1 is V28() real ext-real Element of REAL
(p /. f2) . 1 is V28() real ext-real Element of REAL
f2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
p /. f2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. f2) `2 is V28() real ext-real Element of REAL
(p /. f2) . 2 is V28() real ext-real Element of REAL
rng Q is non empty Element of bool the carrier of ((TOP-REAL 2) | f)
bool the carrier of ((TOP-REAL 2) | f) is set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | f)
p . f2 is V1() Function-like set
p2 . f2 is V28() real ext-real Element of REAL
g1 . (p2 . f2) is V1() Function-like set
Seg (len p) is finite len p -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom p2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom g1 is non empty Element of bool the carrier of I[01]
Y_axis p is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (Y_axis p) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis p) . f2 is V28() real ext-real Element of REAL
len (Y_axis p) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (Y_axis p)) is finite len (Y_axis p) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len p) is finite len p -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p /. f2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(p /. f2) `2 is V28() real ext-real Element of REAL
(p /. f2) . 2 is V28() real ext-real Element of REAL
p . (len p) is V1() Function-like set
f2 is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f2 . 1 is V1() Function-like set
len f2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
f2 . (len f2) is V1() Function-like set
X_axis f2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Y_axis f2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom f2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
f2 /. (len f2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
h29 is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len h29 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom h29 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
h29 is V1() V4( NAT ) Function-like finite FinSequence-like FinSubsequence-like set
len h29 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom h29 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
rng h29 is finite set
h2 is set
g2 is set
h29 . g2 is set
Seg (len h29) is finite len h29 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
s is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
dom q1 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
q1 . s is V28() real ext-real Element of REAL
rng O is non empty Element of bool the carrier of ((TOP-REAL 2) | g)
bool the carrier of ((TOP-REAL 2) | g) is set
[#] ((TOP-REAL 2) | g) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | g)
h29 . s is set
q2 . (q1 . s) is V1() Function-like set
rng Q is non empty Element of bool the carrier of ((TOP-REAL 2) | f)
bool the carrier of ((TOP-REAL 2) | f) is set
[#] ((TOP-REAL 2) | f) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | f)
h2 is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len h2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
ps is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
ps + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
h2 /. ps is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
h2 /. (ps + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(h2 /. ps) - (h2 /. (ps + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (h2 /. (ps + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (h2 /. (ps + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(h2 /. ps),(- (h2 /. (ps + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . ((h2 /. ps),(- (h2 /. (ps + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(h2 /. ps),(- (h2 /. (ps + 1)))] is set
{(h2 /. ps),(- (h2 /. (ps + 1)))} is functional finite V45() set
{(h2 /. ps)} is functional non empty trivial finite V45() 1 -element set
{{(h2 /. ps),(- (h2 /. (ps + 1)))},{(h2 /. ps)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(h2 /. ps),(- (h2 /. (ps + 1)))] is V1() Function-like set
(h2 /. ps) + (- (h2 /. (ps + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(h2 /. ps) - (h2 /. (ps + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((h2 /. ps) - (h2 /. (ps + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((h2 /. ps) - (h2 /. (ps + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((h2 /. ps) - (h2 /. (ps + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((h2 /. ps) - (h2 /. (ps + 1))))) is V28() real ext-real Element of REAL
g2 is functional Element of bool the carrier of (TOP-REAL 2)
rng O is non empty Element of bool the carrier of ((TOP-REAL 2) | g)
bool the carrier of ((TOP-REAL 2) | g) is set
[#] ((TOP-REAL 2) | g) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | g)
y is functional non empty Element of bool the carrier of (TOP-REAL 2)
E-bound y is V28() real ext-real Element of REAL
W-bound y is V28() real ext-real Element of REAL
(E-bound y) - (W-bound y) is V28() real ext-real Element of REAL
N-bound y is V28() real ext-real Element of REAL
S-bound y is V28() real ext-real Element of REAL
(N-bound y) - (S-bound y) is V28() real ext-real Element of REAL
((E-bound y) - (W-bound y)) + ((N-bound y) - (S-bound y)) is V28() real ext-real Element of REAL
(((E-bound y) - (W-bound y)) + ((N-bound y) - (S-bound y))) + 1 is V28() real ext-real Element of REAL
s is Element of bool the carrier of (Euclid 2)
i is Element of the carrier of (Euclid 2)
k is Element of the carrier of (Euclid 2)
dist (i,k) is V28() real ext-real Element of REAL
j is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
j `2 is V28() real ext-real Element of REAL
j . 2 is V28() real ext-real Element of REAL
p11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p11 `2 is V28() real ext-real Element of REAL
p11 . 2 is V28() real ext-real Element of REAL
(p11 `2) - (j `2) is V28() real ext-real Element of REAL
abs ((p11 `2) - (j `2)) is V28() real ext-real Element of REAL
j `1 is V28() real ext-real Element of REAL
j . 1 is V28() real ext-real Element of REAL
p11 `1 is V28() real ext-real Element of REAL
p11 . 1 is V28() real ext-real Element of REAL
(p11 `1) - (j `1) is V28() real ext-real Element of REAL
abs ((p11 `1) - (j `1)) is V28() real ext-real Element of REAL
(abs ((p11 `1) - (j `1))) + (abs ((p11 `2) - (j `2))) is V28() real ext-real Element of REAL
p11 - j is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- j is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- j is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),p11,(- j)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (p11,(- j)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[p11,(- j)] is set
{p11,(- j)} is functional finite V45() set
{p11} is functional non empty trivial finite V45() 1 -element set
{{p11,(- j)},{p11}} is finite V45() set
the U7 of (TOP-REAL 2) . [p11,(- j)] is V1() Function-like set
p11 + (- j) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
p11 - j is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(p11 - j).| is V28() real ext-real non negative Element of REAL
sqr (p11 - j) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (p11 - j)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (p11 - j))) is V28() real ext-real Element of REAL
c `1 is V28() real ext-real Element of REAL
c . 1 is V28() real ext-real Element of REAL
Seg (len q1) is finite len q1 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
dom q1 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
q1 . (ps + 1) is V28() real ext-real Element of REAL
q1 . ps is V28() real ext-real Element of REAL
q1 /. ps is V28() real ext-real Element of REAL
h29 . (ps + 1) is set
q2 . (q1 . (ps + 1)) is V1() Function-like set
q1 /. (ps + 1) is V28() real ext-real Element of REAL
h29 . ps is set
q2 . (q1 . ps) is V1() Function-like set
[.(q1 /. ps),(q1 /. (ps + 1)).] is V181() V182() V183() V286() Element of bool REAL
p11 is Element of bool the carrier of I[01]
i is Element of the carrier of (Euclid 2)
q2 .: p11 is functional Element of bool the carrier of (TOP-REAL 2)
k is Element of the carrier of (Euclid 2)
q2 .: [.0,1.] is functional Element of bool the carrier of (TOP-REAL 2)
j is Element of bool the carrier of (Euclid 2)
dist (i,k) is V28() real ext-real Element of REAL
diameter j is V28() real ext-real Element of REAL
h2 . (ps + 1) is V1() Function-like set
dom q1 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
h2 . (len h2) is V1() Function-like set
h2 /. (len h2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
Seg (len q1) is finite len q1 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
h2 /. g2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
q1 . g2 is V28() real ext-real Element of REAL
q2 . (q1 . g2) is V1() Function-like set
h2 . g2 is V1() Function-like set
f2 /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g1 . (p2 . 1) is V1() Function-like set
(X_axis f2) . (len f2) is V28() real ext-real Element of REAL
h2 . 1 is V1() Function-like set
h2 /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
dom h2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(h2 /. 1) `2 is V28() real ext-real Element of REAL
(h2 /. 1) . 2 is V28() real ext-real Element of REAL
(h2 /. (len h2)) `2 is V28() real ext-real Element of REAL
(h2 /. (len h2)) . 2 is V28() real ext-real Element of REAL
g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
h2 /. g2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(h2 /. g2) `2 is V28() real ext-real Element of REAL
(h2 /. g2) . 2 is V28() real ext-real Element of REAL
Seg (len h2) is finite len h2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
q1 . g2 is V28() real ext-real Element of REAL
q2 . (q1 . g2) is V1() Function-like set
rng O is non empty Element of bool the carrier of ((TOP-REAL 2) | g)
bool the carrier of ((TOP-REAL 2) | g) is set
q2 . (q1 . 1) is V1() Function-like set
q2 . (q1 . (len q1)) is V1() Function-like set
[#] ((TOP-REAL 2) | g) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | g)
Y_axis h2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (Y_axis h2) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
(Y_axis h2) . 1 is V28() real ext-real Element of REAL
(Y_axis h2) . (len h2) is V28() real ext-real Element of REAL
g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(Y_axis h2) . g2 is V28() real ext-real Element of REAL
len (Y_axis h2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (Y_axis h2)) is finite len (Y_axis h2) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len h2) is finite len h2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
h2 /. g2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(h2 /. g2) `2 is V28() real ext-real Element of REAL
(h2 /. g2) . 2 is V28() real ext-real Element of REAL
g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
h2 /. g2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(h2 /. g2) `1 is V28() real ext-real Element of REAL
(h2 /. g2) . 1 is V28() real ext-real Element of REAL
rng O is non empty Element of bool the carrier of ((TOP-REAL 2) | g)
bool the carrier of ((TOP-REAL 2) | g) is set
[#] ((TOP-REAL 2) | g) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | g)
Seg (len h2) is finite len h2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
q1 . g2 is V28() real ext-real Element of REAL
q2 . (q1 . g2) is V1() Function-like set
X_axis h2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom (X_axis h2) is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
(X_axis h2) . g2 is V28() real ext-real Element of REAL
len (X_axis h2) is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
Seg (len (X_axis h2)) is finite len (X_axis h2) -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
Seg (len h2) is finite len h2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
h2 /. g2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(h2 /. g2) `1 is V28() real ext-real Element of REAL
(h2 /. g2) . 1 is V28() real ext-real Element of REAL
g2 is V1() V4( NAT ) V5( the carrier of (TOP-REAL 2)) Function-like finite FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
g2 . 1 is V1() Function-like set
len g2 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
g2 . (len g2) is V1() Function-like set
Y_axis g2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
X_axis g2 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
dom g2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
g2 /. 1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(Y_axis g2) . 1 is V28() real ext-real Element of REAL
q2 . (q1 . 1) is V1() Function-like set
g2 /. (len g2) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(Y_axis g2) . (len g2) is V28() real ext-real Element of REAL
rng O is non empty Element of bool the carrier of ((TOP-REAL 2) | g)
bool the carrier of ((TOP-REAL 2) | g) is set
[#] ((TOP-REAL 2) | g) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | g)
(X_axis f2) . 1 is V28() real ext-real Element of REAL
L~ f2 is functional Element of bool the carrier of (TOP-REAL 2)
L~ g2 is functional Element of bool the carrier of (TOP-REAL 2)
s is set
ps is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
{ (LSeg (g2,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g2 ) } is set
union { (LSeg (g2,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len g2 ) } is set
y is set
{ (LSeg (f2,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
x is set
i is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (f2,i) is functional Element of bool the carrier of (TOP-REAL 2)
i + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
f2 /. i is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f2 /. (i + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((f2 /. i),(f2 /. (i + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (f2 /. i)) + (b₁ * (f2 /. (i + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
ps - (f2 /. i) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f2 /. i) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f2 /. i) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),ps,(- (f2 /. i))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) is V1() V4([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):]) V5( the carrier of (TOP-REAL 2)) Function-like total V18([: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2)) Element of bool [:[: the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2):], the carrier of (TOP-REAL 2):]
the U7 of (TOP-REAL 2) . (ps,(- (f2 /. i))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[ps,(- (f2 /. i))] is set
{ps,(- (f2 /. i))} is functional finite V45() set
{ps} is functional non empty trivial finite V45() 1 -element set
{{ps,(- (f2 /. i))},{ps}} is finite V45() set
the U7 of (TOP-REAL 2) . [ps,(- (f2 /. i))] is V1() Function-like set
ps + (- (f2 /. i)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
ps - (f2 /. i) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(ps - (f2 /. i)).| is V28() real ext-real non negative Element of REAL
sqr (ps - (f2 /. i)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (ps - (f2 /. i))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (ps - (f2 /. i)))) is V28() real ext-real Element of REAL
(f2 /. i) - (f2 /. (i + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f2 /. (i + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (f2 /. (i + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f2 /. i),(- (f2 /. (i + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f2 /. i),(- (f2 /. (i + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f2 /. i),(- (f2 /. (i + 1)))] is set
{(f2 /. i),(- (f2 /. (i + 1)))} is functional finite V45() set
{(f2 /. i)} is functional non empty trivial finite V45() 1 -element set
{{(f2 /. i),(- (f2 /. (i + 1)))},{(f2 /. i)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f2 /. i),(- (f2 /. (i + 1)))] is V1() Function-like set
(f2 /. i) + (- (f2 /. (i + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f2 /. i) - (f2 /. (i + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f2 /. i) - (f2 /. (i + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((f2 /. i) - (f2 /. (i + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f2 /. i) - (f2 /. (i + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f2 /. i) - (f2 /. (i + 1))))) is V28() real ext-real Element of REAL
k is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
p /. k is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f2 /. i) - (p /. k) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (p /. k) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (p /. k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(f2 /. i),(- (p /. k))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((f2 /. i),(- (p /. k))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(f2 /. i),(- (p /. k))] is set
{(f2 /. i),(- (p /. k))} is functional finite V45() set
{{(f2 /. i),(- (p /. k))},{(f2 /. i)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(f2 /. i),(- (p /. k))] is V1() Function-like set
(f2 /. i) + (- (p /. k)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(f2 /. i) - (p /. k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((f2 /. i) - (p /. k)).| is V28() real ext-real non negative Element of REAL
sqr ((f2 /. i) - (p /. k)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((f2 /. i) - (p /. k))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((f2 /. i) - (p /. k)))) is V28() real ext-real Element of REAL
dom p2 is finite V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p2 . k is V28() real ext-real Element of REAL
ps - (p /. k) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
K385((TOP-REAL 2),ps,(- (p /. k))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (ps,(- (p /. k))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[ps,(- (p /. k))] is set
{ps,(- (p /. k))} is functional finite V45() set
{{ps,(- (p /. k))},{ps}} is finite V45() set
the U7 of (TOP-REAL 2) . [ps,(- (p /. k))] is V1() Function-like set
ps + (- (p /. k)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
ps - (p /. k) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(ps - (p /. k)).| is V28() real ext-real non negative Element of REAL
sqr (ps - (p /. k)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (ps - (p /. k))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (ps - (p /. k)))) is V28() real ext-real Element of REAL
|.(ps - (f2 /. i)).| + |.((f2 /. i) - (p /. k)).| is V28() real ext-real non negative Element of REAL
((min_dist_min (I,P)) / 5) + ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
p11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p11 - ps is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- ps is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- ps is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),p11,(- ps)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (p11,(- ps)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[p11,(- ps)] is set
{p11,(- ps)} is functional finite V45() set
{p11} is functional non empty trivial finite V45() 1 -element set
{{p11,(- ps)},{p11}} is finite V45() set
the U7 of (TOP-REAL 2) . [p11,(- ps)] is V1() Function-like set
p11 + (- ps) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
p11 - ps is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(p11 - ps).| is V28() real ext-real non negative Element of REAL
sqr (p11 - ps) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (p11 - ps)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (p11 - ps))) is V28() real ext-real Element of REAL
Seg (len p) is finite len p -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
p . k is V1() Function-like set
g1 . (p2 . k) is V1() Function-like set
j is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
LSeg (g2,j) is functional Element of bool the carrier of (TOP-REAL 2)
j + 1 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
g2 /. j is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
g2 /. (j + 1) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
LSeg ((g2 /. j),(g2 /. (j + 1))) is functional Element of bool the carrier of (TOP-REAL 2)
{ (((1 - b₁) * (g2 /. j)) + (b₁ * (g2 /. (j + 1)))) where b₁ is V28() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
ps - (g2 /. j) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (g2 /. j) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (g2 /. j) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),ps,(- (g2 /. j))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (ps,(- (g2 /. j))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[ps,(- (g2 /. j))] is set
{ps,(- (g2 /. j))} is functional finite V45() set
{{ps,(- (g2 /. j))},{ps}} is finite V45() set
the U7 of (TOP-REAL 2) . [ps,(- (g2 /. j))] is V1() Function-like set
ps + (- (g2 /. j)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
ps - (g2 /. j) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(ps - (g2 /. j)).| is V28() real ext-real non negative Element of REAL
sqr (ps - (g2 /. j)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (ps - (g2 /. j))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (ps - (g2 /. j)))) is V28() real ext-real Element of REAL
(g2 /. j) - (g2 /. (j + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (g2 /. (j + 1)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (g2 /. (j + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(g2 /. j),(- (g2 /. (j + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((g2 /. j),(- (g2 /. (j + 1)))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(g2 /. j),(- (g2 /. (j + 1)))] is set
{(g2 /. j),(- (g2 /. (j + 1)))} is functional finite V45() set
{(g2 /. j)} is functional non empty trivial finite V45() 1 -element set
{{(g2 /. j),(- (g2 /. (j + 1)))},{(g2 /. j)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(g2 /. j),(- (g2 /. (j + 1)))] is V1() Function-like set
(g2 /. j) + (- (g2 /. (j + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(g2 /. j) - (g2 /. (j + 1)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((g2 /. j) - (g2 /. (j + 1))).| is V28() real ext-real non negative Element of REAL
sqr ((g2 /. j) - (g2 /. (j + 1))) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((g2 /. j) - (g2 /. (j + 1)))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((g2 /. j) - (g2 /. (j + 1))))) is V28() real ext-real Element of REAL
Seg (len g2) is finite len g2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
k9 is ordinal natural V28() real ext-real non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of NAT
h2 /. k9 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g2 /. j) - (h2 /. k9) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (h2 /. k9) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- (h2 /. k9) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),(g2 /. j),(- (h2 /. k9))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . ((g2 /. j),(- (h2 /. k9))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[(g2 /. j),(- (h2 /. k9))] is set
{(g2 /. j),(- (h2 /. k9))} is functional finite V45() set
{{(g2 /. j),(- (h2 /. k9))},{(g2 /. j)}} is finite V45() set
the U7 of (TOP-REAL 2) . [(g2 /. j),(- (h2 /. k9))] is V1() Function-like set
(g2 /. j) + (- (h2 /. k9)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
(g2 /. j) - (h2 /. k9) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.((g2 /. j) - (h2 /. k9)).| is V28() real ext-real non negative Element of REAL
sqr ((g2 /. j) - (h2 /. k9)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr ((g2 /. j) - (h2 /. k9))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr ((g2 /. j) - (h2 /. k9)))) is V28() real ext-real Element of REAL
Seg (len h2) is finite len h2 -element V181() V182() V183() V184() V185() V186() V283() V284() V285() Element of bool NAT
q1 . k9 is V28() real ext-real Element of REAL
ps - (h2 /. k9) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
K385((TOP-REAL 2),ps,(- (h2 /. k9))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (ps,(- (h2 /. k9))) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[ps,(- (h2 /. k9))] is set
{ps,(- (h2 /. k9))} is functional finite V45() set
{{ps,(- (h2 /. k9))},{ps}} is finite V45() set
the U7 of (TOP-REAL 2) . [ps,(- (h2 /. k9))] is V1() Function-like set
ps + (- (h2 /. k9)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
ps - (h2 /. k9) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(ps - (h2 /. k9)).| is V28() real ext-real non negative Element of REAL
sqr (ps - (h2 /. k9)) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (ps - (h2 /. k9))) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (ps - (h2 /. k9)))) is V28() real ext-real Element of REAL
|.(ps - (g2 /. j)).| + |.((g2 /. j) - (h2 /. k9)).| is V28() real ext-real non negative Element of REAL
q11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p11 - q11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- q11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
- q11 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
K385((TOP-REAL 2),p11,(- q11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (p11,(- q11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[p11,(- q11)] is set
{p11,(- q11)} is functional finite V45() set
{{p11,(- q11)},{p11}} is finite V45() set
the U7 of (TOP-REAL 2) . [p11,(- q11)] is V1() Function-like set
p11 + (- q11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
p11 - q11 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(p11 - q11).| is V28() real ext-real non negative Element of REAL
sqr (p11 - q11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (p11 - q11)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (p11 - q11))) is V28() real ext-real Element of REAL
ps - q11 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
K385((TOP-REAL 2),ps,(- q11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
the U7 of (TOP-REAL 2) . (ps,(- q11)) is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
[ps,(- q11)] is set
{ps,(- q11)} is functional finite V45() set
{{ps,(- q11)},{ps}} is finite V45() set
the U7 of (TOP-REAL 2) . [ps,(- q11)] is V1() Function-like set
ps + (- q11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
ps - q11 is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
|.(ps - q11).| is V28() real ext-real non negative Element of REAL
sqr (ps - q11) is V1() V4( NAT ) V5( REAL ) Function-like finite FinSequence-like FinSubsequence-like complex-yielding V172() V173() FinSequence of REAL
Sum (sqr (ps - q11)) is V28() real ext-real Element of REAL
sqrt (Sum (sqr (ps - q11))) is V28() real ext-real Element of REAL
|.(p11 - ps).| + |.(ps - q11).| is V28() real ext-real non negative Element of REAL
(((min_dist_min (I,P)) / 5) + ((min_dist_min (I,P)) / 5)) + (((min_dist_min (I,P)) / 5) + ((min_dist_min (I,P)) / 5)) is V28() real ext-real Element of REAL
(((min_dist_min (I,P)) / 5) + ((min_dist_min (I,P)) / 5)) + ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
((((min_dist_min (I,P)) / 5) + ((min_dist_min (I,P)) / 5)) + ((min_dist_min (I,P)) / 5)) + ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
q2 . (q1 . k9) is V1() Function-like set
dom g1 is non empty Element of bool the carrier of I[01]
x1 is Element of the carrier of (Euclid 2)
x2 is Element of the carrier of (Euclid 2)
dist (x1,x2) is V28() real ext-real Element of REAL
4 is non empty ordinal natural V28() real ext-real positive non negative V33() V38() finite cardinal V181() V182() V183() V184() V185() V186() V281() V282() V283() V284() V285() Element of NAT
4 * ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
5 * ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
(4 * ((min_dist_min (I,P)) / 5)) - (5 * ((min_dist_min (I,P)) / 5)) is V28() real ext-real Element of REAL
4 - 5 is V28() real ext-real Element of REAL
(4 - 5) * ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
((4 - 5) * ((min_dist_min (I,P)) / 5)) / ((min_dist_min (I,P)) / 5) is V28() real ext-real Element of REAL
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
g is non empty TopSpace-like TopStruct
the carrier of g is non empty set
[: the carrier of f, the carrier of g:] is V1() set
bool [: the carrier of f, the carrier of g:] is set
bool the carrier of g is set
a is V1() V4( the carrier of f) V5( the carrier of g) Function-like non empty total V18( the carrier of f, the carrier of g) Element of bool [: the carrier of f, the carrier of g:]
b is non empty Element of bool the carrier of g
g | b is non empty strict TopSpace-like SubSpace of g
the carrier of (g | b) is non empty set
[: the carrier of f, the carrier of (g | b):] is V1() set
bool [: the carrier of f, the carrier of (g | b):] is set
c is V1() V4( the carrier of f) V5( the carrier of (g | b)) Function-like non empty total V18( the carrier of f, the carrier of (g | b)) Element of bool [: the carrier of f, the carrier of (g | b):]
[#] g is non empty non proper closed Element of bool the carrier of g
bool the carrier of (g | b) is set
d is Element of bool the carrier of (g | b)
c " d is Element of bool the carrier of f
bool the carrier of f is set
the topology of (g | b) is non empty Element of bool (bool the carrier of (g | b))
bool (bool the carrier of (g | b)) is set
the topology of g is non empty Element of bool (bool the carrier of g)
bool (bool the carrier of g) is set
[#] (g | b) is non empty non proper closed Element of bool the carrier of (g | b)
O is Element of bool the carrier of g
O /\ ([#] (g | b)) is Element of bool the carrier of (g | b)
I is Element of bool the carrier of g
a " I is Element of bool the carrier of f
rng c is non empty Element of bool the carrier of (g | b)
(rng c) /\ I is Element of bool the carrier of g
c " ((rng c) /\ I) is Element of bool the carrier of f
b /\ I is Element of bool the carrier of g
[#] (g | b) is non empty non proper closed Element of bool the carrier of (g | b)
f is non empty TopSpace-like TopStruct
the carrier of f is non empty set
g is non empty TopSpace-like TopStruct
the carrier of g is non empty set
[: the carrier of f, the carrier of g:] is V1() set
bool [: the carrier of f, the carrier of g:] is set
bool the carrier of g is set
a is V1() V4( the carrier of f) V5( the carrier of g) Function-like non empty total V18( the carrier of f, the carrier of g) Element of bool [: the carrier of f, the carrier of g:]
rng a is non empty Element of bool the carrier of g
b is non empty Element of bool the carrier of g
g | b is non empty strict TopSpace-like SubSpace of g
the carrier of (g | b) is non empty set
[: the carrier of f, the carrier of (g | b):] is V1() set
bool [: the carrier of f, the carrier of (g | b):] is set
dom a is non empty Element of bool the carrier of f
bool the carrier of f is set
c is V1() V4( the carrier of f) V5( the carrier of (g | b)) Function-like non empty total V18( the carrier of f, the carrier of (g | b)) Element of bool [: the carrier of f, the carrier of (g | b):]
dom c is non empty Element of bool the carrier of f
[#] f is non empty non proper closed Element of bool the carrier of f
rng c is non empty Element of bool the carrier of (g | b)
bool the carrier of (g | b) is set
[#] (g | b) is non empty non proper closed Element of bool the carrier of (g | b)
[: the carrier of I[01], the carrier of (TOP-REAL 2):] is V1() set
bool [: the carrier of I[01], the carrier of (TOP-REAL 2):] is set
f is V1() V4( the carrier of I[01]) V5( the carrier of (TOP-REAL 2)) Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
g is V1() V4( the carrier of I[01]) V5( the carrier of (TOP-REAL 2)) Function-like non empty total V18( the carrier of I[01], the carrier of (TOP-REAL 2)) Element of bool [: the carrier of I[01], the carrier of (TOP-REAL 2):]
rng f is functional non empty Element of bool the carrier of (TOP-REAL 2)
rng g is functional non empty Element of bool the carrier of (TOP-REAL 2)
a is V28() real ext-real set
b is V28() real ext-real set
c is V28() real ext-real set
d is V28() real ext-real set
O is Element of the carrier of I[01]
I is Element of the carrier of I[01]
f . O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f . O) `1 is V28() real ext-real Element of REAL
(f . O) . 1 is V28() real ext-real Element of REAL
f . I is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(f . I) `1 is V28() real ext-real Element of REAL
(f . I) . 1 is V28() real ext-real Element of REAL
g . O is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g . O) `2 is V28() real ext-real Element of REAL
(g . O) . 2 is V28() real ext-real Element of REAL
g . I is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
(g . I) `2 is V28() real ext-real Element of REAL
(g . I) . 2 is V28() real ext-real Element of REAL
P is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | P is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | P) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | P):] is V1() set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | P):] is set
f1 is V1() V4( the carrier of I[01]) V5( the carrier of ((TOP-REAL 2) | P)) Function-like non empty total V18( the carrier of I[01], the carrier of ((TOP-REAL 2) | P)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | P):]
Q is functional non empty Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | Q is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | Q) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | Q):] is V1() set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | Q):] is set
g1 is V1() V4( the carrier of I[01]) V5( the carrier of ((TOP-REAL 2) | Q)) Function-like non empty total V18( the carrier of I[01], the carrier of ((TOP-REAL 2) | Q)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | Q):]
g1 . I is Element of the carrier of ((TOP-REAL 2) | Q)
g1 . O is Element of the carrier of ((TOP-REAL 2) | Q)
q1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
q2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
f1 . I is Element of the carrier of ((TOP-REAL 2) | P)
f1 . O is Element of the carrier of ((TOP-REAL 2) | P)
p1 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p1 `1 is V28() real ext-real Element of REAL
p1 . 1 is V28() real ext-real Element of REAL
p2 is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p2 `1 is V28() real ext-real Element of REAL
p2 . 1 is V28() real ext-real Element of REAL
p is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p . 1 is V28() real ext-real Element of REAL
dom f1 is non empty Element of bool the carrier of I[01]
f2 is set
f1 . f2 is set
p is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p `1 is V28() real ext-real Element of REAL
p . 1 is V28() real ext-real Element of REAL
dom g1 is non empty Element of bool the carrier of I[01]
f2 is set
g1 . f2 is set
q1 `2 is V28() real ext-real Element of REAL
q1 . 2 is V28() real ext-real Element of REAL
q2 `2 is V28() real ext-real Element of REAL
q2 . 2 is V28() real ext-real Element of REAL
p is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p . 2 is V28() real ext-real Element of REAL
dom g1 is non empty Element of bool the carrier of I[01]
f2 is set
g1 . f2 is set
p is V1() V4( NAT ) Function-like finite 2 -element FinSequence-like FinSubsequence-like complex-yielding V172() V173() Element of the carrier of (TOP-REAL 2)
p `2 is V28() real ext-real Element of REAL
p . 2 is V28() real ext-real Element of REAL
dom f1 is non empty Element of bool the carrier of I[01]
f2 is set
f1 . f2 is set