:: SPPOL_2 semantic presentation

REAL is V172() V173() V174() V178() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V32() V37() V38() V172() V173() V174() V175() V176() V177() V178() Element of bool REAL
bool REAL is set
omega is non empty epsilon-transitive epsilon-connected ordinal V32() V37() V38() V172() V173() V174() V175() V176() V177() V178() set
bool omega is V32() set
bool NAT is V32() set
COMPLEX is V172() V178() set
RAT is V172() V173() V174() V175() V178() set
INT is V172() V173() V174() V175() V176() V178() set
[:COMPLEX,COMPLEX:] is V15() set
bool [:COMPLEX,COMPLEX:] is set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is V15() set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:REAL,REAL:] is V15() set
bool [:REAL,REAL:] is set
[:[:REAL,REAL:],REAL:] is V15() set
bool [:[:REAL,REAL:],REAL:] is set
[:RAT,RAT:] is V15() set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is V15() set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is V15() set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is V15() set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is V15() V32() set
[:[:NAT,NAT:],NAT:] is V15() V32() set
bool [:[:NAT,NAT:],NAT:] is V32() set
K266() is set
1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
I[01] is TopStruct
the carrier of I[01] is set
[:1,1:] is V15() set
bool [:1,1:] is set
[:[:1,1:],1:] is V15() set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is V15() set
bool [:[:1,1:],REAL:] is set
2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
[:2,2:] is V15() set
[:[:2,2:],REAL:] is V15() set
bool [:[:2,2:],REAL:] is set
K408() is V111() L7()
K418() is TopSpace-like TopStruct
TOP-REAL 2 is non empty TopSpace-like T_0 T_1 T_2 V138() V184() V185() V186() V187() V188() V189() V190() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty functional set
bool the carrier of (TOP-REAL 2) is set
{} is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set
the ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set
3 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
0 is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V45() V172() V173() V174() V175() V176() V177() V178() Element of NAT
K419(0,1) is non empty strict TopSpace-like SubSpace of K418()
K420() is TopSpace-like SubSpace of K418()
the carrier of K420() is set
K75({}) is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set
rng {} is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set
len {} is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() set
P is ext-real V14() real set
p1 is ext-real V14() real set
|[P,p1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real V14() real set
f1 is ext-real V14() real set
|[p2,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
LSeg (P,p1) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((Rev P),p2) is Element of bool the carrier of (TOP-REAL 2)
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
dom (Rev P) is V172() V173() V174() V175() V176() V177() Element of bool NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p1 + 1) + p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p1),(P /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(Rev P) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((Rev P) /. (p2 + 1)),(P /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(Rev P) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((Rev P) /. p2),((Rev P) /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
P | p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P | p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P | p2),p1) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p1) is Element of bool the carrier of (TOP-REAL 2)
dom (P | p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P | p2) /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P | p2) /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. p1),((P | p2) /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p1),((P | p2) /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p1),(P /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg ((P /^ p2),p1) is Element of bool the carrier of (TOP-REAL 2)
p2 + p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
LSeg (P,(p2 + p1)) is Element of bool the carrier of (TOP-REAL 2)
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
1 + p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P /^ p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
(p1 + 1) + p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
(P /^ p2) /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /^ p2) /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P /^ p2) /. p1),((P /^ p2) /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. (p1 + p2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p1 + p2)),((P /^ p2) /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. ((p1 + 1) + p2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p1 + p2)),(P /. ((p1 + 1) + p2))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(p1 + p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. ((p1 + p2) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p1 + p2)),(P /. ((p1 + p2) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
p2 + (p1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p2 + p1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
(len P) - p2 is ext-real V14() real V44() set
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg ((P /^ p2),p1) is Element of bool the carrier of (TOP-REAL 2)
p2 + p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
LSeg (P,(p2 + p1)) is Element of bool the carrier of (TOP-REAL 2)
(p1 + 1) + p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P ^ p1) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P ^ p1) /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P ^ p1) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P ^ p1) /. p2),((P ^ p1) /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
(len P) + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),((len P) + p2)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,p2) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((len P) + p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((p1 /. p2),(p1 /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P ^ p1) /. ((len P) + p2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P ^ p1) /. ((len P) + p2)),(p1 /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P ^ p1) /. ((len P) + (p2 + 1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P ^ p1) /. ((len P) + p2)),((P ^ p1) /. ((len P) + (p2 + 1)))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((len P) + p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg ((P ^ p1),(len P)) is closed Element of bool the carrier of (TOP-REAL 2)
p1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),(p1 /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(P ^ p1) /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P ^ p1) /. ((len P) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P ^ p1) /. (len P)),((P ^ p1) /. ((len P) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),((P ^ p1) /. ((len P) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P -: p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P -: p1),p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P :- p1),(p2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
p2 + (p1 .. P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p2 + (p1 .. P))) is closed Element of bool the carrier of (TOP-REAL 2)
len (P :- p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 .. P) is ext-real V14() real V44() set
((len P) - (p1 .. P)) + 1 is ext-real V14() real V44() set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p2 + 1) + (p1 .. P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P :- p1) is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
(P :- p1) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P :- p1) /. ((p2 + 1) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P :- p1) /. (p2 + 1)),((P :- p1) /. ((p2 + 1) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. (p2 + (p1 .. P)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p2 + (p1 .. P))),((P :- p1) /. ((p2 + 1) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P /. ((p2 + 1) + (p1 .. P)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p2 + (p1 .. P))),(P /. ((p2 + 1) + (p1 .. P)))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(p2 + (p1 .. P)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. ((p2 + (p1 .. P)) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (p2 + (p1 .. P))),(P /. ((p2 + (p1 .. P)) + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p1 .. P) + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p2 + (p1 .. P)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*> the carrier of (TOP-REAL 2) is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like functional V32() V37() V39( {} ) FinSequence-like FinSubsequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() FinSequence of the carrier of (TOP-REAL 2)
L~ (<*> the carrier of (TOP-REAL 2)) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*> the carrier of (TOP-REAL 2)) is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V45() V172() V173() V174() V175() V176() V177() V178() Element of NAT
{ (LSeg ((<*> the carrier of (TOP-REAL 2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*> the carrier of (TOP-REAL 2)) ) } is set
union { (LSeg ((<*> the carrier of (TOP-REAL 2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*> the carrier of (TOP-REAL 2)) ) } is set
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*P*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*P*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*P*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P*> ) } is set
union { (LSeg (<*P*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P*> ) } is set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p1),(P /. (p1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p1) is closed Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
rng P is set
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is set
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (f2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. f2),(P /. (f2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P ^ <*p1*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (P ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*p1*>) ) } is set
union { (LSeg ((P ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*p1*>) ) } is set
LSeg ((P /. (len P)),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ P) \/ (LSeg ((P /. (len P)),p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P ^ <*p1*>) is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
(P ^ <*p1*>) /. ((len P) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P ^ <*p1*>) | ((len P) + 1) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(P ^ <*p1*>) | (len P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P ^ <*p1*>) /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> ^ P is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*p1*> ^ P) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*p1*> ^ P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*p1*> ^ P),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*p1*> ^ P) ) } is set
union { (LSeg ((<*p1*> ^ P),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*p1*> ^ P) ) } is set
LSeg (p1,(P /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,(P /. 1))) \/ (L~ P) is non empty Element of bool the carrier of (TOP-REAL 2)
len <*p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + (len P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is set
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(<*p1*> ^ P) /. P1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*p1*> ^ P) /. (P1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((<*p1*> ^ P) /. P1),((<*p1*> ^ P) /. (P1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
P2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. (p4 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. p4 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is set
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(<*p1*> ^ P) /. (1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*p1*> ^ P) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. P1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (P1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. P1),(P /. (P1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(<*p1*> ^ P) /. (P1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(<*p1*> ^ P) /. ((P1 + 1) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*P,p1*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*P,p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*P,p1*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P,p1*> ) } is set
union { (LSeg (<*P,p1*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P,p1*> ) } is set
LSeg (P,p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
<*P*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*P*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*P*> ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1 + 1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
L~ (<*P*> ^ <*p1*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*P*> ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*P*> ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*P*> ^ <*p1*>) ) } is set
union { (LSeg ((<*P*> ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*P*> ^ <*p1*>) ) } is set
L~ <*P*> is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (<*P*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P*> ) } is set
union { (LSeg (<*P*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*P*> ) } is set
<*P*> /. (len <*P*>) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((<*P*> /. (len <*P*>)),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ <*P*>) \/ (LSeg ((<*P*> /. (len <*P*>)),p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ <*P*>) \/ (LSeg (P,p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
{} \/ (LSeg (P,p1)) is non empty set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Rev P) is closed Element of bool the carrier of (TOP-REAL 2)
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((Rev P),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev P) ) } is set
union { (LSeg ((Rev P),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev P) ) } is set
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ p1 is closed Element of bool the carrier of (TOP-REAL 2)
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
union { (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
Rev p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Rev p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (Rev p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((Rev p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev p1) ) } is set
union { (LSeg ((Rev p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev p1) ) } is set
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*p2*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 ^ <*p2*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (p1 ^ <*p2*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (p1 ^ <*p2*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((p1 ^ <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (p1 ^ <*p2*>) ) } is set
union { (LSeg ((p1 ^ <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (p1 ^ <*p2*>) ) } is set
Rev (p1 ^ <*p2*>) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Rev (p1 ^ <*p2*>)) is closed Element of bool the carrier of (TOP-REAL 2)
len (Rev (p1 ^ <*p2*>)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((Rev (p1 ^ <*p2*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (p1 ^ <*p2*>)) ) } is set
union { (LSeg ((Rev (p1 ^ <*p2*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (p1 ^ <*p2*>)) ) } is set
L~ <*p2*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*p2*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*p2*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*p2*> ) } is set
union { (LSeg (<*p2*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*p2*> ) } is set
Rev <*p2*> is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Rev <*p2*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (Rev <*p2*>) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((Rev <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev <*p2*>) ) } is set
union { (LSeg ((Rev <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev <*p2*>) ) } is set
(Rev p1) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 /. (len p1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (p2,((Rev p1) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (p2,((Rev p1) /. 1))) \/ (L~ (Rev p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
<*p2*> ^ (Rev p1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*p2*> ^ (Rev p1)) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*p2*> ^ (Rev p1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*p2*> ^ (Rev p1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*p2*> ^ (Rev p1)) ) } is set
union { (LSeg ((<*p2*> ^ (Rev p1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*p2*> ^ (Rev p1)) ) } is set
Rev (<*> the carrier of (TOP-REAL 2)) is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like functional V32() V37() V39( {} ) FinSequence-like FinSubsequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() FinSequence of the carrier of (TOP-REAL 2)
L~ (Rev (<*> the carrier of (TOP-REAL 2))) is closed Element of bool the carrier of (TOP-REAL 2)
len (Rev (<*> the carrier of (TOP-REAL 2))) is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding functional V32() V37() V39( {} ) FinSequence-like FinSequence-membered real V44() V45() V172() V173() V174() V175() V176() V177() V178() Element of NAT
{ (LSeg ((Rev (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (<*> the carrier of (TOP-REAL 2))) ) } is set
union { (LSeg ((Rev (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (<*> the carrier of (TOP-REAL 2))) ) } is set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P ^ p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P ^ p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ p1) ) } is set
union { (LSeg ((P ^ p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ p1) ) } is set
p1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),(p1 /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ p1 is closed Element of bool the carrier of (TOP-REAL 2)
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
union { (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ p1) is non empty Element of bool the carrier of (TOP-REAL 2)
<*(p1 /. 1)*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ <*(p1 /. 1)*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P ^ <*(p1 /. 1)*>) ^ f2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P ^ <*(p1 /. 1)*>) ^ f2) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P ^ <*(p1 /. 1)*>) ^ f2) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P ^ <*(p1 /. 1)*>) ^ f2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ f2) ) } is set
union { (LSeg (((P ^ <*(p1 /. 1)*>) ^ f2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ f2) ) } is set
<*(p1 /. 1)*> ^ f2 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*(p1 /. 1)*> ^ f2) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*(p1 /. 1)*> ^ f2) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*(p1 /. 1)*> ^ f2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ f2) ) } is set
union { (LSeg ((<*(p1 /. 1)*> ^ f2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ f2) ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ (<*(p1 /. 1)*> ^ f2)) is non empty Element of bool the carrier of (TOP-REAL 2)
P1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f2 ^ <*P1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)) ) } is set
union { (LSeg (((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (f2 ^ <*P1*>)) ) } is set
<*(p1 /. 1)*> ^ (f2 ^ <*P1*>) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)) ) } is set
union { (LSeg ((<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (f2 ^ <*P1*>)) ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ (<*(p1 /. 1)*> ^ (f2 ^ <*P1*>))) is non empty Element of bool the carrier of (TOP-REAL 2)
len (P ^ <*(p1 /. 1)*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P ^ <*(p1 /. 1)*>) /. (len (P ^ <*(p1 /. 1)*>)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ (P ^ <*(p1 /. 1)*>) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P ^ <*(p1 /. 1)*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*(p1 /. 1)*>) ) } is set
union { (LSeg ((P ^ <*(p1 /. 1)*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*(p1 /. 1)*>) ) } is set
LSeg ((p1 /. 1),P1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ (P ^ <*(p1 /. 1)*>)) \/ (LSeg ((p1 /. 1),P1)) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (LSeg ((p1 /. 1),P1)) is non empty Element of bool the carrier of (TOP-REAL 2)
<*(p1 /. 1),P1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ <*(p1 /. 1),P1*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*(p1 /. 1),P1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*(p1 /. 1),P1*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(p1 /. 1),P1*> ) } is set
union { (LSeg (<*(p1 /. 1),P1*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(p1 /. 1),P1*> ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ <*(p1 /. 1),P1*>) is non empty Element of bool the carrier of (TOP-REAL 2)
len f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*f2*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f1 ^ <*f2*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(p1 /. 1)*> ^ f1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(<*(p1 /. 1)*> ^ f1) ^ <*f2*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (<*(p1 /. 1)*> ^ f1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len (<*(p1 /. 1)*> ^ f1)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(<*(p1 /. 1)*> ^ f2) /. (len (<*(p1 /. 1)*> ^ f2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P ^ <*(p1 /. 1)*>) ^ f1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P ^ <*(p1 /. 1)*>) ^ f1) ^ <*f2*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len ((P ^ <*(p1 /. 1)*>) ^ f1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len ((P ^ <*(p1 /. 1)*>) ^ f1)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P ^ <*(p1 /. 1)*>) ^ f2) /. (len ((P ^ <*(p1 /. 1)*>) ^ f2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((((P ^ <*(p1 /. 1)*>) ^ f2) /. (len ((P ^ <*(p1 /. 1)*>) ^ f2))),P1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ (<*(p1 /. 1)*> ^ f2)) \/ (LSeg ((((P ^ <*(p1 /. 1)*>) ^ f2) /. (len ((P ^ <*(p1 /. 1)*>) ^ f2))),P1)) is non empty Element of bool the carrier of (TOP-REAL 2)
(<*(p1 /. 1)*> ^ f2) ^ <*P1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((<*(p1 /. 1)*> ^ f2) ^ <*P1*>) is closed Element of bool the carrier of (TOP-REAL 2)
len ((<*(p1 /. 1)*> ^ f2) ^ <*P1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((<*(p1 /. 1)*> ^ f2) ^ <*P1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((<*(p1 /. 1)*> ^ f2) ^ <*P1*>) ) } is set
union { (LSeg (((<*(p1 /. 1)*> ^ f2) ^ <*P1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((<*(p1 /. 1)*> ^ f2) ^ <*P1*>) ) } is set
((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>) ) } is set
union { (LSeg ((((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (((P ^ <*(p1 /. 1)*>) ^ f2) ^ <*P1*>) ) } is set
(L~ ((P ^ <*(p1 /. 1)*>) ^ f2)) \/ (LSeg ((((P ^ <*(p1 /. 1)*>) ^ f2) /. (len ((P ^ <*(p1 /. 1)*>) ^ f2))),P1)) is non empty Element of bool the carrier of (TOP-REAL 2)
p1 /^ 1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*(p1 /. 1)*> ^ (p1 /^ 1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))) ) } is set
union { (LSeg (((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (<*> the carrier of (TOP-REAL 2))) ) } is set
<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))) ) } is set
union { (LSeg ((<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2))) ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ (<*(p1 /. 1)*> ^ (<*> the carrier of (TOP-REAL 2)))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (P ^ <*(p1 /. 1)*>) is closed Element of bool the carrier of (TOP-REAL 2)
len (P ^ <*(p1 /. 1)*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P ^ <*(p1 /. 1)*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*(p1 /. 1)*>) ) } is set
union { (LSeg ((P ^ <*(p1 /. 1)*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P ^ <*(p1 /. 1)*>) ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ {} is non empty set
L~ <*(p1 /. 1)*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*(p1 /. 1)*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*(p1 /. 1)*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(p1 /. 1)*> ) } is set
union { (LSeg (<*(p1 /. 1)*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*(p1 /. 1)*> ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ <*(p1 /. 1)*>) is non empty Element of bool the carrier of (TOP-REAL 2)
(P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)) ) } is set
union { (LSeg (((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P ^ <*(p1 /. 1)*>) ^ (p1 /^ 1)) ) } is set
L~ (<*(p1 /. 1)*> ^ (p1 /^ 1)) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*(p1 /. 1)*> ^ (p1 /^ 1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*(p1 /. 1)*> ^ (p1 /^ 1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (p1 /^ 1)) ) } is set
union { (LSeg ((<*(p1 /. 1)*> ^ (p1 /^ 1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*(p1 /. 1)*> ^ (p1 /^ 1)) ) } is set
((L~ P) \/ (LSeg ((P /. (len P)),(p1 /. 1)))) \/ (L~ (<*(p1 /. 1)*> ^ (p1 /^ 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P | p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P | p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | p1) ) } is set
union { (LSeg ((P | p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | p1) ) } is set
P | 0 is ext-real non positive non negative empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V14() V15() non-empty empty-yielding V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like functional V32() V37() V39( {} ) FinSequence-like FinSubsequence-like FinSequence-membered real V44() V172() V173() V174() V175() V176() V177() V178() FinSequence of the carrier of (TOP-REAL 2)
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p1 is ext-real V14() real V44() set
(P | p1) ^ (P /^ p1) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P | p1) /. (len (P | p1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /^ p1) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p1) /. (len (P | p1))),((P /^ p1) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ (P | p1)) \/ (LSeg (((P | p1) /. (len (P | p1))),((P /^ p1) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (P /^ p1) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P /^ p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ p1) ) } is set
union { (LSeg ((P /^ p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ p1) ) } is set
((L~ (P | p1)) \/ (LSeg (((P | p1) /. (len (P | p1))),((P /^ p1) /. 1)))) \/ (L~ (P /^ p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p1) /. (len (P | p1))),((P /^ p1) /. 1))) \/ (L~ (P /^ p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ (P | p1)) \/ ((LSeg (((P | p1) /. (len (P | p1))),((P /^ p1) /. 1))) \/ (L~ (P /^ p1))) is non empty Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P -: p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P -: p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
union { (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P :- p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P :- p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
union { (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
(L~ (P -: p1)) \/ (L~ (P :- p1)) is Element of bool the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P /^ (p1 .. P)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 .. P) is ext-real V14() real V44() set
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P | (p1 .. P)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P | (p1 .. P)) /. (len (P | (p1 .. P))) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P | (p1 .. P)) ^ (P /^ (p1 .. P)) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P | (p1 .. P)) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P | (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | (p1 .. P)) ) } is set
union { (LSeg ((P | (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | (p1 .. P)) ) } is set
(P /^ (p1 .. P)) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | (p1 .. P)) /. (len (P | (p1 .. P)))),((P /^ (p1 .. P)) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ (P | (p1 .. P))) \/ (LSeg (((P | (p1 .. P)) /. (len (P | (p1 .. P)))),((P /^ (p1 .. P)) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (P /^ (p1 .. P)) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P /^ (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ (p1 .. P)) ) } is set
union { (LSeg ((P /^ (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ (p1 .. P)) ) } is set
((L~ (P | (p1 .. P))) \/ (LSeg (((P | (p1 .. P)) /. (len (P | (p1 .. P)))),((P /^ (p1 .. P)) /. 1)))) \/ (L~ (P /^ (p1 .. P))) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | (p1 .. P)) /. (len (P | (p1 .. P)))),((P /^ (p1 .. P)) /. 1))) \/ (L~ (P /^ (p1 .. P))) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ (P | (p1 .. P))) \/ ((LSeg (((P | (p1 .. P)) /. (len (P | (p1 .. P)))),((P /^ (p1 .. P)) /. 1))) \/ (L~ (P /^ (p1 .. P)))) is non empty Element of bool the carrier of (TOP-REAL 2)
<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))) is closed Element of bool the carrier of (TOP-REAL 2)
len (<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))) ) } is set
union { (LSeg ((<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P))) ) } is set
(L~ (P | (p1 .. P))) \/ (L~ (<*((P | (p1 .. P)) /. (len (P | (p1 .. P))))*> ^ (P /^ (p1 .. P)))) is Element of bool the carrier of (TOP-REAL 2)
(L~ (P | (p1 .. P))) \/ (L~ (P :- p1)) is Element of bool the carrier of (TOP-REAL 2)
P /^ (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P /^ (p1 .. P)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 .. P) is ext-real V14() real V44() set
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> ^ (P /^ (p1 .. P)) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P | (p1 .. P)) is closed Element of bool the carrier of (TOP-REAL 2)
len (P | (p1 .. P)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P | (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | (p1 .. P)) ) } is set
union { (LSeg ((P | (p1 .. P)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | (p1 .. P)) ) } is set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (P,p2,p1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (Ins (P,p2,p1)) is closed Element of bool the carrier of (TOP-REAL 2)
len (Ins (P,p2,p1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((Ins (P,p2,p1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Ins (P,p2,p1)) ) } is set
union { (LSeg ((Ins (P,p2,p1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Ins (P,p2,p1)) ) } is set
P | p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P | p2) ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len ((P | p2) ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len (P | p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len (P | p2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. ((len (P | p2)) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
dom (P | p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P /^ p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P | p2) /. (len (P | p2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(P /^ p2) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (((P | p2) ^ <*p1*>) ^ (P /^ p2)) is closed Element of bool the carrier of (TOP-REAL 2)
len (((P | p2) ^ <*p1*>) ^ (P /^ p2)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((((P | p2) ^ <*p1*>) ^ (P /^ p2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (((P | p2) ^ <*p1*>) ^ (P /^ p2)) ) } is set
union { (LSeg ((((P | p2) ^ <*p1*>) ^ (P /^ p2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (((P | p2) ^ <*p1*>) ^ (P /^ p2)) ) } is set
L~ ((P | p2) ^ <*p1*>) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (((P | p2) ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P | p2) ^ <*p1*>) ) } is set
union { (LSeg (((P | p2) ^ <*p1*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P | p2) ^ <*p1*>) ) } is set
LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ ((P | p2) ^ <*p1*>)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (P /^ p2) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P /^ p2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ p2) ) } is set
union { (LSeg ((P /^ p2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P /^ p2) ) } is set
((L~ ((P | p2) ^ <*p1*>)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)))) \/ (L~ (P /^ p2)) is non empty Element of bool the carrier of (TOP-REAL 2)
L~ (P | p2) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P | p2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | p2) ) } is set
union { (LSeg ((P | p2),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P | p2) ) } is set
LSeg (((P | p2) /. (len (P | p2))),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(L~ (P | p2)) \/ (LSeg (((P | p2) /. (len (P | p2))),p1)) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ (P | p2)) \/ (LSeg (((P | p2) /. (len (P | p2))),p1))) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
(((L~ (P | p2)) \/ (LSeg (((P | p2) /. (len (P | p2))),p1))) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)))) \/ (L~ (P /^ p2)) is non empty Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p2) /. (len (P | p2))),p1)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ (P | p2)) \/ ((LSeg (((P | p2) /. (len (P | p2))),p1)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)))) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ (P | p2)) \/ ((LSeg (((P | p2) /. (len (P | p2))),p1)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))))) \/ (L~ (P /^ p2)) is non empty Element of bool the carrier of (TOP-REAL 2)
(L~ (P | p2)) \/ (LSeg (((P | p2) /. (len (P | p2))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ (P | p2)) \/ (LSeg (((P | p2) /. (len (P | p2))),((P /^ p2) /. 1)))) \/ (L~ (P /^ p2)) is non empty Element of bool the carrier of (TOP-REAL 2)
(P | p2) ^ (P /^ p2) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P | p2) ^ (P /^ p2)) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P | p2) ^ (P /^ p2)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P | p2) ^ (P /^ p2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P | p2) ^ (P /^ p2)) ) } is set
union { (LSeg (((P | p2) ^ (P /^ p2)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P | p2) ^ (P /^ p2)) ) } is set
|[0,0]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[1,1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[0,0]| `2 is ext-real V14() real Element of REAL
|[1,1]| `1 is ext-real V14() real Element of REAL
|[1,1]| `2 is ext-real V14() real Element of REAL
|[0,0]| `1 is ext-real V14() real Element of REAL
|[(|[0,0]| `1),(|[1,1]| `2)]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
<*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
the non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2) is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p1) is Element of bool the carrier of (TOP-REAL 2)
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p1)) /\ (LSeg (P,(p1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
P /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (p1 + 1))} is non empty trivial V39(1) set
2 - 2 is ext-real V14() real V44() set
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*P,p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P | p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P | p1),(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P | p1),f1)) /\ (LSeg ((P | p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(P | p1) /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((P | p1) /. (f1 + 1))} is non empty trivial V39(1) set
dom (P | p1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f1) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f1)) /\ (LSeg ((P | p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f1)) /\ (LSeg (P,(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
P /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (f1 + 1))} is non empty trivial V39(1) set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p1),(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P /^ p1),f1)) /\ (LSeg ((P /^ p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(P /^ p1) /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((P /^ p1) /. (f1 + 1))} is non empty trivial V39(1) set
dom (P /^ p1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
(len P) - p1 is ext-real V14() real V44() set
p1 + (f1 + 2) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p1 + f1) + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p1 + f1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,(p1 + f1))) /\ (LSeg ((P /^ p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
p1 + (f1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p1 + (f1 + 1))) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,(p1 + f1))) /\ (LSeg (P,(p1 + (f1 + 1)))) is Element of bool the carrier of (TOP-REAL 2)
(p1 + f1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. ((p1 + f1) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. ((p1 + f1) + 1))} is non empty trivial V39(1) set
P /. (p1 + (f1 + 1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (p1 + (f1 + 1)))} is non empty trivial V39(1) set
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like unfolded FinSequence of the carrier of (TOP-REAL 2)
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like unfolded FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
Seg (len P) is V32() V39( len P) V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((Rev P),p1) is Element of bool the carrier of (TOP-REAL 2)
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((Rev P),(p1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((Rev P),p1)) /\ (LSeg ((Rev P),(p1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(Rev P) /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((Rev P) /. (p1 + 1))} is non empty trivial V39(1) set
(p1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 + 1) is ext-real V14() real V44() set
(len P) - p1 is ext-real V14() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + (p1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (p1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f1) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f1)) /\ (LSeg ((Rev P),(p1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,(p2 + 1))) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (p2 + 1))} is non empty trivial V39(1) set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (P,1) is closed Element of bool the carrier of (TOP-REAL 2)
{(P /. 1)} is non empty trivial V39(1) set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (p1,(P /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,(P /. 1))) /\ (LSeg (P,1)) is Element of bool the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> ^ P is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*p1*> /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len (<*p1*> ^ P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len <*p1*>) + (len P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((<*p1*> ^ P),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((<*p1*> ^ P),(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((<*p1*> ^ P),f1)) /\ (LSeg ((<*p1*> ^ P),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(<*p1*> ^ P) /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((<*p1*> ^ P) /. (f1 + 1))} is non empty trivial V39(1) set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
<*p1*> /. (len <*p1*>) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((<*p1*> /. (len <*p1*>)),(P /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
f1 - (len <*p1*>) is ext-real V14() real V44() set
(len <*p1*>) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 2) - (len <*p1*>) is ext-real V14() real V44() set
f2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(len <*p1*>) + (f2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len <*p1*>) + f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg ((<*p1*> ^ P),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,(f2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,(f2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
P /. (f2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (f2 + 1))} is non empty trivial V39(1) set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (len P))} is non empty trivial V39(1) set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg ((P /. (len P)),p1)) is Element of bool the carrier of (TOP-REAL 2)
len <*p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*p1*> /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len (P ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ <*p1*>),f2) is Element of bool the carrier of (TOP-REAL 2)
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ <*p1*>),(f2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P ^ <*p1*>),f2)) /\ (LSeg ((P ^ <*p1*>),(f2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(P ^ <*p1*>) /. (f2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((P ^ <*p1*>) /. (f2 + 1))} is non empty trivial V39(1) set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
LSeg (P,f2) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg ((P ^ <*p1*>),(f2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,(f2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,(f2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
P /. (f2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (f2 + 1))} is non empty trivial V39(1) set
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
LSeg ((P /. (len P)),(<*p1*> /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (len P))} is non empty trivial V39(1) set
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),(p1 /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,1) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P /. (len P)),(p1 /. 1))) /\ (LSeg (p1,1)) is Element of bool the carrier of (TOP-REAL 2)
{(p1 /. 1)} is non empty trivial V39(1) set
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg ((P /. (len P)),(p1 /. 1))) is Element of bool the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P ^ p1),f1)) /\ (LSeg ((P ^ p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(P ^ p1) /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{((P ^ p1) /. (f1 + 1))} is non empty trivial V39(1) set
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f1) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f1)) /\ (LSeg ((P ^ p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,(f1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f1)) /\ (LSeg (P,(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
P /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (f1 + 1))} is non empty trivial V39(1) set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
f1 - (len P) is ext-real V14() real V44() set
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f1 + 2) - (len P) is ext-real V14() real V44() set
f2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
(len P) + (f2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (p1,f2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,f2)) /\ (LSeg ((P ^ p1),(f1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,(f2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (p1,f2)) /\ (LSeg (p1,(f2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
p1 /. (f2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(p1 /. (f2 + 1))} is non empty trivial V39(1) set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (P,p2,p1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P | p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P | p2) ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len ((P | p2) ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P /^ p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /^ p2) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
dom (P | p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
(P | p2) /. (len (P | p2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(len (P | p2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. ((len (P | p2)) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p2) /. (len (P | p2))),p1)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
P2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P | p2),p4) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p4) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P | p2),p4)) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
{(P /. p2)} is non empty trivial V39(1) set
f1 is set
(LSeg ((P | p2),p4)) /\ (LSeg (((P | p2) /. (len (P | p2))),p1)) is Element of bool the carrier of (TOP-REAL 2)
{((P | p2) /. (len (P | p2)))} is non empty trivial V39(1) set
((P | p2) ^ <*p1*>) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P | p2) ^ <*p1*>),p2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),(((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p2) ^ <*p1*>),p2)) /\ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is Element of bool the carrier of (TOP-REAL 2)
{(((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)))} is non empty trivial V39(1) set
<*((P /^ p2) /. 1)*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
LSeg ((P /^ p2),1) is closed Element of bool the carrier of (TOP-REAL 2)
(P /^ p2) /. (1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P /^ p2) /. 1),((P /^ p2) /. (1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{(P /. (p2 + 1))} is non empty trivial V39(1) set
LSeg (P,(p2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg (P,(p2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg ((P /^ p2),1)) is Element of bool the carrier of (TOP-REAL 2)
P2 is set
(LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) /\ (LSeg ((P /^ p2),1)) is Element of bool the carrier of (TOP-REAL 2)
{((P /^ p2) /. 1)} is non empty trivial V39(1) set
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p1) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg (P,p1)) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*P,p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P | p1),p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P | p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P | p1),p2)) /\ (LSeg ((P | p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f1) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P | p1),p2)) /\ (LSeg ((P | p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg ((P | p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg (P,f1)) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p1),p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P /^ p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P /^ p1),p2)) /\ (LSeg ((P /^ p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p1 + p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p1 + p2)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,(p1 + f1)) is closed Element of bool the carrier of (TOP-REAL 2)
(len P) - p1 is ext-real V14() real V44() set
(LSeg ((P /^ p1),p2)) /\ (LSeg ((P /^ p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,(p1 + p2))) /\ (LSeg ((P /^ p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,(p1 + p2))) /\ (LSeg (P,(p1 + f1))) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like s.n.c. FinSequence of the carrier of (TOP-REAL 2)
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like s.n.c. FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((Rev P),p1) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((Rev P),p2) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((Rev P),p1)) /\ (LSeg ((Rev P),p2)) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
(len P) - p1 is ext-real V14() real V44() set
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 + 1) is ext-real V14() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 - 1 is ext-real V14() real V44() set
(f2 - 1) + 1 is ext-real V14() real V44() set
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f1) is closed Element of bool the carrier of (TOP-REAL 2)
f2 + p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((Rev P),p1)) /\ (LSeg ((Rev P),p2)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg ((Rev P),p2)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,f1)) is Element of bool the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ p1 is closed Element of bool the carrier of (TOP-REAL 2)
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
union { (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
p1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. (len P)),(p1 /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(L~ P) /\ (L~ p1) is Element of bool the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P ^ p1),f1) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P ^ p1),p2)) /\ (LSeg ((P ^ p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f1) is Element of bool the carrier of (TOP-REAL 2)
f1 - (len P) is ext-real V14() real V44() set
(f1 + 1) - (len P) is ext-real V14() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((len P) + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (p1,f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,p2) is Element of bool the carrier of (TOP-REAL 2)
(p2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),((len P) + f2)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,f2) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P ^ p1),p2)) /\ (LSeg ((P ^ p1),f1)) is Element of bool the carrier of (TOP-REAL 2)
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),((len P) + f2)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,f2) is closed Element of bool the carrier of (TOP-REAL 2)
p2 - (len P) is ext-real V14() real V44() set
P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P ^ p1),((len P) + P1)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,P1) is closed Element of bool the carrier of (TOP-REAL 2)
(p2 + 1) - (len P) is ext-real V14() real V44() set
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (P,p2,p1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((Ins (P,p2,p1)),f2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((Ins (P,p2,p1)),P1) is Element of bool the carrier of (TOP-REAL 2)
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Ins (P,p2,p1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Ins (P,p2,p1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(P | p2) ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len ((P | p2) ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len (P | p2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((f2 + 1) + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (((P | p2) ^ <*p1*>),P1) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P | p2),P1) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,P1) is Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) ^ <*p1*>),f2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P | p2),f2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f2) is Element of bool the carrier of (TOP-REAL 2)
(len P) - p2 is ext-real V14() real V44() set
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P /^ p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /^ p2) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
dom ((P | p2) ^ <*p1*>) is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
(Ins (P,p2,p1)) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(p2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(Ins (P,p2,p1)) /. ((p2 + 1) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
dom (P | p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P | p2) /. (len (P | p2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((Ins (P,p2,p1)),(p2 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (p1,((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
((P | p2) ^ <*p1*>) /. (len (P | p2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((Ins (P,p2,p1)),p2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) ^ <*p1*>),p2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p2) /. (len (P | p2))),p1)) \/ (LSeg ((((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))),((P /^ p2) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (((P | p2) /. (len (P | p2))),((P /^ p2) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P | p2) /. (len (P | p2))),p1)) /\ (LSeg (p1,((P /^ p2) /. 1))) is Element of bool the carrier of (TOP-REAL 2)
{p1} is non empty trivial V39(1) set
LSeg (((P | p2) ^ <*p1*>),f2) is Element of bool the carrier of (TOP-REAL 2)
LSeg ((P | p2),f2) is Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f2) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
{(P /. p2)} is non empty trivial V39(1) set
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
f2 is set
(LSeg ((Ins (P,p2,p1)),p2)) /\ (LSeg ((Ins (P,p2,p1)),(p2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,p2)) is Element of bool the carrier of (TOP-REAL 2)
P1 - (p2 + 1) is ext-real V14() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 - 1 is ext-real V14() real V44() set
p2 + f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p2),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f1) is closed Element of bool the carrier of (TOP-REAL 2)
P1 - (p2 + 1) is ext-real V14() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 - 1 is ext-real V14() real V44() set
p2 + f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p2),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f1) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f2) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,f2)) /\ (LSeg (P,f1)) is Element of bool the carrier of (TOP-REAL 2)
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg (P,p2)) /\ (LSeg (P,f1)) is Element of bool the carrier of (TOP-REAL 2)
P /. f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. f1)} is non empty trivial V39(1) set
(LSeg ((Ins (P,p2,p1)),f2)) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
f2 is set
{(P /. (p2 + 1))} is non empty trivial V39(1) set
(LSeg ((Ins (P,p2,p1)),p2)) /\ (LSeg ((Ins (P,p2,p1)),(p2 + 1))) is Element of bool the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P1 - 1 is ext-real V14() real V44() set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
P1 - (p2 + 1) is ext-real V14() real V44() set
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p2),f1) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((Ins (P,p2,p1)),(p2 + 1))) /\ (LSeg ((Ins (P,p2,p1)),P1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (P,p2)) /\ (LSeg (P,f2)) is Element of bool the carrier of (TOP-REAL 2)
P1 - (p2 + 1) is ext-real V14() real V44() set
(p2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 - (p2 + 1) is ext-real V14() real V44() set
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) - (p2 + 1) is ext-real V14() real V44() set
((len P) + 1) - (p2 + 1) is ext-real V14() real V44() set
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
f2 - 1 is ext-real V14() real V44() set
P1 - 1 is ext-real V14() real V44() set
p2 + f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) - 1 is ext-real V14() real V44() set
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p2),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
f1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P /^ p2),f1) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Ins (P,p2,p1)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(<*> the carrier of (TOP-REAL 2)) /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((<*> the carrier of (TOP-REAL 2)) /. p1) `1 is ext-real V14() real Element of REAL
(<*> the carrier of (TOP-REAL 2)) /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((<*> the carrier of (TOP-REAL 2)) /. (p1 + 1)) `1 is ext-real V14() real Element of REAL
((<*> the carrier of (TOP-REAL 2)) /. p1) `2 is ext-real V14() real Element of REAL
((<*> the carrier of (TOP-REAL 2)) /. (p1 + 1)) `2 is ext-real V14() real Element of REAL
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
<*P*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len <*P*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*P*> /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*P*> /. p2) `1 is ext-real V14() real Element of REAL
<*P*> /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*P*> /. (p2 + 1)) `1 is ext-real V14() real Element of REAL
(<*P*> /. p2) `2 is ext-real V14() real Element of REAL
(<*P*> /. (p2 + 1)) `2 is ext-real V14() real Element of REAL
0 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P `1 is ext-real V14() real Element of REAL
P `2 is ext-real V14() real Element of REAL
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 `1 is ext-real V14() real Element of REAL
p1 `2 is ext-real V14() real Element of REAL
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len <*P,p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
<*P,p1*> /. f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*P,p1*> /. f1) `1 is ext-real V14() real Element of REAL
<*P,p1*> /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*P,p1*> /. (f1 + 1)) `1 is ext-real V14() real Element of REAL
(<*P,p1*> /. f1) `2 is ext-real V14() real Element of REAL
(<*P,p1*> /. (f1 + 1)) `2 is ext-real V14() real Element of REAL
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P | p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P | p1) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P | p1) /. p2) `1 is ext-real V14() real Element of REAL
(P | p1) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P | p1) /. (p2 + 1)) `1 is ext-real V14() real Element of REAL
((P | p1) /. p2) `2 is ext-real V14() real Element of REAL
((P | p1) /. (p2 + 1)) `2 is ext-real V14() real Element of REAL
dom (P | p1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P /^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P /^ p1) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P /^ p1) /. p2) `1 is ext-real V14() real Element of REAL
(P /^ p1) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P /^ p1) /. (p2 + 1)) `1 is ext-real V14() real Element of REAL
((P /^ p1) /. p2) `2 is ext-real V14() real Element of REAL
((P /^ p1) /. (p2 + 1)) `2 is ext-real V14() real Element of REAL
dom (P /^ p1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 + p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (p1 + p2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (p1 + (p2 + 1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(p1 + p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. ((p1 + p2) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(len P) - p1 is ext-real V14() real V44() set
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
P | p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P | (p1 .. P) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(Rev P) /. p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((Rev P) /. p1) `1 is ext-real V14() real Element of REAL
(Rev P) /. (p1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((Rev P) /. (p1 + 1)) `1 is ext-real V14() real Element of REAL
((Rev P) /. p1) `2 is ext-real V14() real Element of REAL
((Rev P) /. (p1 + 1)) `2 is ext-real V14() real Element of REAL
(len P) - p1 is ext-real V14() real V44() set
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - 1 is ext-real V14() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((len P) - 1) + 1 is ext-real V14() real V44() set
1 + p1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(1 + p1) + p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p1 + 1) - p1 is ext-real V14() real V44() set
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 + (p2 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P /. (len P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /. (len P)) `1 is ext-real V14() real Element of REAL
(P /. (len P)) `2 is ext-real V14() real Element of REAL
p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(p1 /. 1) `1 is ext-real V14() real Element of REAL
(p1 /. 1) `2 is ext-real V14() real Element of REAL
P ^ p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (P ^ p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P ^ p1) /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P ^ p1) /. p2) `1 is ext-real V14() real Element of REAL
(P ^ p1) /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P ^ p1) /. (p2 + 1)) `1 is ext-real V14() real Element of REAL
((P ^ p1) /. p2) `2 is ext-real V14() real Element of REAL
((P ^ p1) /. (p2 + 1)) `2 is ext-real V14() real Element of REAL
len p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (len p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
dom P is V172() V173() V174() V175() V176() V177() Element of bool NAT
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
p2 - (len P) is ext-real V14() real V44() set
(len P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) + (f1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(p2 + 1) - (len P) is ext-real V14() real V44() set
dom p1 is V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 /. (f1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(len P) + f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 /. f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,p2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (P,p2,p1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - p2 is ext-real V14() real V44() set
P /. p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P /. (p2 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P /. p2),(P /. (p2 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
P | p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*p1*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(P | p2) ^ <*p1*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P /^ p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (P | p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(P | p2) /. (len (P | p2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(P /^ p2) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
((P | p2) /. (len (P | p2))) `1 is ext-real V14() real Element of REAL
((P | p2) /. (len (P | p2))) `2 is ext-real V14() real Element of REAL
|[(((P | p2) /. (len (P | p2))) `1),(((P | p2) /. (len (P | p2))) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
len (P /^ p2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (P /^ p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
dom (P | p2) is V172() V173() V174() V175() V176() V177() Element of bool NAT
((P /^ p2) /. 1) `1 is ext-real V14() real Element of REAL
((P /^ p2) /. 1) `2 is ext-real V14() real Element of REAL
len ((P | p2) ^ <*p1*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
|[(((P /^ p2) /. 1) `1),(((P /^ p2) /. 1) `2)]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
<*p1*> /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(<*p1*> /. 1) `1 is ext-real V14() real Element of REAL
(<*p1*> /. 1) `2 is ext-real V14() real Element of REAL
(len (P | p2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((P | p2) ^ <*p1*>) /. ((len (P | p2)) + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))) `1 is ext-real V14() real Element of REAL
(((P | p2) ^ <*p1*>) /. (len ((P | p2) ^ <*p1*>))) `2 is ext-real V14() real Element of REAL
((P | p2) ^ <*p1*>) ^ (P /^ p2) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 .. P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P -: p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P -: p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
union { (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P :- p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P :- p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
union { (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
(L~ (P -: p1)) /\ (L~ (P :- p1)) is Element of bool the carrier of (TOP-REAL 2)
{p1} is non empty trivial V39(1) set
(P :- p1) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(p1 .. P) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len P) - (p1 .. P) is ext-real V14() real V44() set
((len P) - (p1 .. P)) + 1 is ext-real V14() real V44() set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
rng (P :- p1) is non empty set
dom (P :- p1) is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
dom (P -: p1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
p2 is set
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P -: p1),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P,f2) is closed Element of bool the carrier of (TOP-REAL 2)
P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P :- p1),P1) is closed Element of bool the carrier of (TOP-REAL 2)
P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
P2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 + (p1 .. P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P,(p4 + (p1 .. P))) is closed Element of bool the carrier of (TOP-REAL 2)
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P -: p1),f2)) /\ (LSeg ((P :- p1),P1)) is Element of bool the carrier of (TOP-REAL 2)
P /. (p1 .. P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(P /. (p1 .. P))} is non empty trivial V39(1) set
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P -: p1),f2)) /\ (LSeg ((P :- p1),P1)) is Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P -: p1),f2)) /\ (LSeg ((P :- p1),P1)) is Element of bool the carrier of (TOP-REAL 2)
rng (P -: p1) is set
(P -: p1) /. (p1 .. P) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P `1 is ext-real V14() real Element of REAL
P `2 is ext-real V14() real Element of REAL
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 `1 is ext-real V14() real Element of REAL
p1 `2 is ext-real V14() real Element of REAL
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len <*P,p1*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
Rev P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Rev P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len P is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
dom p1 is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 /. P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ p1 is closed Element of bool the carrier of (TOP-REAL 2)
len p1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
union { (LSeg (p1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p1 ) } is set
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P `1 is ext-real V14() real Element of REAL
P `2 is ext-real V14() real Element of REAL
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 `1 is ext-real V14() real Element of REAL
p1 `2 is ext-real V14() real Element of REAL
LSeg (P,p1) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
<*P,p1*> is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ p2 is closed Element of bool the carrier of (TOP-REAL 2)
len p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p2 ) } is set
union { (LSeg (p2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p2 ) } is set
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P -: p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P -: p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
union { (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P :- p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P :- p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
union { (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
(L~ (P -: p1)) \/ (L~ (P :- p1)) is Element of bool the carrier of (TOP-REAL 2)
P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
rng P is set
L~ P is closed Element of bool the carrier of (TOP-REAL 2)
len P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
union { (LSeg (P,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P ) } is set
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P :- p1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P :- p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P :- p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
union { (LSeg ((P :- p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P :- p1) ) } is set
P -: p1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ (P -: p1) is closed Element of bool the carrier of (TOP-REAL 2)
len (P -: p1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
union { (LSeg ((P -: p1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P -: p1) ) } is set
(L~ (P -: p1)) \/ (L~ (P :- p1)) is Element of bool the carrier of (TOP-REAL 2)
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
rng p1 is non empty set
P .. p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 -: P is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
len (p1 -: P) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
rng p1 is non empty set
P .. p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p1 :- P is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (p1 :- P) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + (P .. p1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len p1) - (P .. p1) is ext-real V14() real V44() set
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((len p1) - (P .. p1)) + 1 is ext-real V14() real V44() set
P is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
LSeg (p2,p1) is closed Element of bool the carrier of (TOP-REAL 2)
rng p2 is non empty set
Ins (p2,p1,P) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
len (Ins (p2,p1,P)) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len p2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len p2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
|[0,0]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[1,1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[0,0]| `1 is ext-real V14() real Element of REAL
|[1,1]| `2 is ext-real V14() real Element of REAL
|[(|[0,0]| `1),(|[1,1]| `2)]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
<*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
|[0,0]| `2 is ext-real V14() real Element of REAL
|[1,1]| `1 is ext-real V14() real Element of REAL
L~ <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is closed Element of bool the carrier of (TOP-REAL 2)
len <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (<*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> ) } is set
union { (LSeg (<*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*>,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len <*|[0,0]|,|[(|[0,0]| `1),(|[1,1]| `2)]|,|[1,1]|*> ) } is set
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
len f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
Rev f1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
len f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
(L~ f1) /\ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
(L~ f1) \/ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
{p2,p1} is non empty set
Rev f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
Rev f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 /. (len P1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ P1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
union { (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
P2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P2 /. (len P2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ P2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
union { (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
(L~ P1) /\ (L~ P2) is Element of bool the carrier of (TOP-REAL 2)
(L~ P1) \/ (L~ P2) is Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,f1} is non empty set
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 /. (len P1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
L~ P1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
union { (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
(L~ f2) /\ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
(L~ f2) \/ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
rng f2 is non empty set
f2 :- f1 is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev (f2 :- f1) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
f1 .. f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom f2 is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
f2 . 1 is set
f2 -: f1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
dom p4 is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
dom P1 is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
(len P1) - 1 is ext-real V14() real V44() set
f1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 | f1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. FinSequence of the carrier of (TOP-REAL 2)
f1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
rng (Rev (f2 :- f1)) is set
rng (f2 :- f1) is non empty set
rng P1 is non empty set
(rng P1) /\ (rng f2) is set
(P1 | f1) ^ (Rev (f2 :- f1)) is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
dom (P1 | f1) is V172() V173() V174() V175() V176() V177() Element of bool NAT
len (P1 | f1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
Seg (len (P1 | f1)) is V32() V39( len (P1 | f1)) V172() V173() V174() V175() V176() V177() Element of bool NAT
len (f2 :- f1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len (Rev (f2 :- f1)) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
dom (Rev (f2 :- f1)) is V172() V173() V174() V175() V176() V177() Element of bool NAT
1 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(1 + 1) - 1 is ext-real V14() real V44() set
(P1 | f1) /. (len (P1 | f1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 /. f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(Rev (f2 :- f1)) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(f2 :- f1) /. (len (f2 :- f1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1)) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,f1) is closed Element of bool the carrier of (TOP-REAL 2)
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P1 | f1),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,f2) is closed Element of bool the carrier of (TOP-REAL 2)
f2 /. (1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((f2 /. 1),(f2 /. (1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (f2,1) is closed Element of bool the carrier of (TOP-REAL 2)
L~ (Rev (f2 :- f1)) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((Rev (f2 :- f1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (f2 :- f1)) ) } is set
union { (LSeg ((Rev (f2 :- f1)),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (Rev (f2 :- f1)) ) } is set
L~ (f2 :- f1) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((f2 :- f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f2 :- f1) ) } is set
union { (LSeg ((f2 :- f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f2 :- f1) ) } is set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((f2 :- f1),f2) is closed Element of bool the carrier of (TOP-REAL 2)
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
c₁₃ + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
x is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
x + (f1 .. f2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,(x + (f1 .. f2))) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (f2,1)) /\ (LSeg (f2,(x + (f1 .. f2)))) is Element of bool the carrier of (TOP-REAL 2)
(len f2) - (len f2) is ext-real V14() real V44() set
((len f2) - (len f2)) + 1 is ext-real V14() real V44() set
1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,(1 + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (f2,1)) /\ (LSeg (f2,(1 + 1))) is Element of bool the carrier of (TOP-REAL 2)
{(f2 /. (1 + 1))} is non empty trivial V39(1) set
f2 /. 2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(f2 /. 2)} is non empty trivial V39(1) set
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len (Rev (f2 :- f1))) - (f2 + 1) is ext-real V14() real V44() set
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(c₁₃ + 1) + f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((Rev (f2 :- f1)),f2) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg ((f2 :- f1),(c₁₃ + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
c₁₃ + (f1 .. f2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,(c₁₃ + (f1 .. f2))) is closed Element of bool the carrier of (TOP-REAL 2)
(len f2) - 1 is ext-real V14() real V44() set
x is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. x is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((f2 /. x),(f2 /. (len f2))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
x + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,x) is closed Element of bool the carrier of (TOP-REAL 2)
(len f2) - f2 is ext-real V14() real V44() set
(len f2) - (f1 .. f2) is ext-real V14() real V44() set
((len f2) - (f1 .. f2)) + 1 is ext-real V14() real V44() set
(((len f2) - (f1 .. f2)) + 1) - 1 is ext-real V14() real V44() set
((((len f2) - (f1 .. f2)) + 1) - 1) + (f1 .. f2) is ext-real V14() real V44() set
(((((len f2) - (f1 .. f2)) + 1) - 1) + (f1 .. f2)) - f2 is ext-real V14() real V44() set
(len (Rev (f2 :- f1))) - 1 is ext-real V14() real V44() set
((len (Rev (f2 :- f1))) - 1) + (f1 .. f2) is ext-real V14() real V44() set
(((len (Rev (f2 :- f1))) - 1) + (f1 .. f2)) - f2 is ext-real V14() real V44() set
(c₁₃ + (f1 .. f2)) + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (x + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((f2 /. x),(f2 /. (x + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(c₁₃ + (f1 .. f2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg (f2,(c₁₃ + (f1 .. f2)))) /\ (LSeg (f2,x)) is Element of bool the carrier of (TOP-REAL 2)
{(f2 /. x)} is non empty trivial V39(1) set
(len f2) - x is ext-real V14() real V44() set
(len f2) - (len f2) is ext-real V14() real V44() set
2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
1 + 2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len f2) - (1 + 2) is ext-real V14() real V44() set
((len f2) - 1) - 2 is ext-real V14() real V44() set
((len f2) - f2) + (1 + 1) is ext-real V14() real V44() set
(c₁₃ + (f1 .. f2)) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
((c₁₃ + (f1 .. f2)) + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg (f2,x)) /\ (LSeg (f2,(c₁₃ + (f1 .. f2)))) is Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) /\ (LSeg ((Rev (f2 :- f1)),f2)) is Element of bool the carrier of (TOP-REAL 2)
x is set
(LSeg ((Rev (f2 :- f1)),f2)) /\ (LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) is Element of bool the carrier of (TOP-REAL 2)
(len (Rev (f2 :- f1))) - 2 is ext-real V14() real V44() set
LSeg ((Rev (f2 :- f1)),1) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) /\ (LSeg ((Rev (f2 :- f1)),1)) is Element of bool the carrier of (TOP-REAL 2)
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(c₁₃ + 1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((f2 :- f1),(c₁₃ + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
c₁₃ + (f1 .. f2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,(c₁₃ + (f1 .. f2))) is closed Element of bool the carrier of (TOP-REAL 2)
f2 is set
(Rev (f2 :- f1)) /. (1 + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (((Rev (f2 :- f1)) /. 1),((Rev (f2 :- f1)) /. (1 + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
{((Rev (f2 :- f1)) /. 1)} is non empty trivial V39(1) set
len ((P1 | f1) ^ (Rev (f2 :- f1))) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P1 | f1),c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
<*((Rev (f2 :- f1)) /. 1)*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
c₁₃ + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(LSeg ((P1 | f1),c₁₃)) /\ (LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) is Element of bool the carrier of (TOP-REAL 2)
{((P1 | f1) /. (len (P1 | f1)))} is non empty trivial V39(1) set
<*((P1 | f1) /. (len (P1 | f1)))*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
f2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P1 | f1),c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg ((P1 | f1),c₁₃)) /\ (LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) is Element of bool the carrier of (TOP-REAL 2)
{((P1 | f1) /. (len (P1 | f1)))} is non empty trivial V39(1) set
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
rng p4 is non empty set
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
rng (P1 | f1) is set
(rng (P1 | f1)) /\ (rng (Rev (f2 :- f1))) is set
p2 .. P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p2 .. (P1 | f1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
Seg (len P1) is non empty V32() V39( len P1) V172() V173() V174() V175() V176() V177() Element of bool NAT
P1 /. (len (P1 | f1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((P1 /. (len (P1 | f1))),p2) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,(len (P1 | f1))) is closed Element of bool the carrier of (TOP-REAL 2)
L~ (P1 | f1) is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg ((P1 | f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P1 | f1) ) } is set
union { (LSeg ((P1 | f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (P1 | f1) ) } is set
c₁₃ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
c₁₃ + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg ((P1 | f1),c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (P1,c₁₃) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (P1,c₁₃)) /\ (LSeg (P1,(len (P1 | f1)))) is Element of bool the carrier of (TOP-REAL 2)
c₁₃ + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{(P1 /. (len (P1 | f1)))} is non empty trivial V39(1) set
(L~ (P1 | f1)) /\ (L~ (Rev (f2 :- f1))) is Element of bool the carrier of (TOP-REAL 2)
{p1} is non empty trivial V39(1) set
{p2} is non empty trivial V39(1) set
dom (f2 :- f1) is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
p1 .. (f2 :- f1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 :- f1) . (p1 .. (f2 :- f1)) is set
x is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() set
x + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
j is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
j + (f1 .. f2) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(f2 :- f1) /. (p1 .. (f2 :- f1)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 /. (j + (f1 .. f2)) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
c₁₃ is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
Rev c₁₃ is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
((P1 | f1) /. (len (P1 | f1))) `1 is ext-real V14() real Element of REAL
((Rev (f2 :- f1)) /. 1) `1 is ext-real V14() real Element of REAL
((P1 | f1) /. (len (P1 | f1))) `2 is ext-real V14() real Element of REAL
((Rev (f2 :- f1)) /. 1) `2 is ext-real V14() real Element of REAL
(len (P1 | f1)) + (len (Rev (f2 :- f1))) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len ((P1 | f1) ^ (Rev (f2 :- f1))) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(L~ P1) \/ (L~ (Rev (f2 :- f1))) is Element of bool the carrier of (TOP-REAL 2)
<*p2*> is non empty trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(1) FinSequence-like FinSubsequence-like special FinSequence of the carrier of (TOP-REAL 2)
(P1 | f1) ^ <*p2*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ ((P1 | f1) ^ <*p2*>) is closed Element of bool the carrier of (TOP-REAL 2)
len ((P1 | f1) ^ <*p2*>) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (((P1 | f1) ^ <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P1 | f1) ^ <*p2*>) ) } is set
union { (LSeg (((P1 | f1) ^ <*p2*>),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len ((P1 | f1) ^ <*p2*>) ) } is set
(L~ ((P1 | f1) ^ <*p2*>)) \/ (L~ (Rev (f2 :- f1))) is Element of bool the carrier of (TOP-REAL 2)
(L~ (P1 | f1)) \/ (LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1))) is non empty Element of bool the carrier of (TOP-REAL 2)
((L~ (P1 | f1)) \/ (LSeg (((P1 | f1) /. (len (P1 | f1))),((Rev (f2 :- f1)) /. 1)))) \/ (L~ (Rev (f2 :- f1))) is non empty Element of bool the carrier of (TOP-REAL 2)
x is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ x is closed Element of bool the carrier of (TOP-REAL 2)
len x is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (x,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len x ) } is set
union { (LSeg (x,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len x ) } is set
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
x /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
x /. (len x) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
(L~ p4) /\ (L~ x) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) \/ (L~ x) is Element of bool the carrier of (TOP-REAL 2)
dom x is non empty V172() V173() V174() V175() V176() V177() Element of bool NAT
x . 1 is set
(P1 | f1) . 1 is set
(P1 | f1) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p4 /. (f1 .. f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
x . (len x) is set
x . ((len (P1 | f1)) + (len (Rev (f2 :- f1)))) is set
(Rev (f2 :- f1)) . (len (Rev (f2 :- f1))) is set
(Rev (f2 :- f1)) . (len (f2 :- f1)) is set
(f2 :- f1) . 1 is set
(f2 :- f1) /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
rng x is non empty set
j is set
(L~ p4) /\ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) /\ (L~ (Rev (f2 :- f1))) is Element of bool the carrier of (TOP-REAL 2)
((L~ p4) /\ (L~ P1)) \/ ((L~ p4) /\ (L~ (Rev (f2 :- f1)))) is Element of bool the carrier of (TOP-REAL 2)
f2 . (f1 .. f2) is set
f2 /. (f1 .. f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
j + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 /. (j + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg ((f2 /. j),(f2 /. (j + 1))) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (f2,j) is closed Element of bool the carrier of (TOP-REAL 2)
i is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
i + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (p4,i) is closed Element of bool the carrier of (TOP-REAL 2)
LSeg (f2,i) is closed Element of bool the carrier of (TOP-REAL 2)
i + (1 + 1) is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,(i + 1)) is closed Element of bool the carrier of (TOP-REAL 2)
(LSeg (f2,i)) /\ (LSeg (f2,(i + 1))) is Element of bool the carrier of (TOP-REAL 2)
f2 /. (i + 1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{(f2 /. (i + 1))} is non empty trivial V39(1) set
(LSeg (f2,i)) /\ (LSeg (f2,j)) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) /\ (L~ (f2 :- f1)) is Element of bool the carrier of (TOP-REAL 2)
{f1} is non empty trivial V39(1) set
{p1} \/ {f1} is non empty set
p2 .. f2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(len f2) - (len f2) is ext-real V14() real V44() set
((len f2) - (len f2)) + 1 is ext-real V14() real V44() set
0 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
(L~ p4) /\ (L~ (f2 :- f1)) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) /\ {} is V15() V172() V173() V174() V175() V176() V177() Element of bool the carrier of (TOP-REAL 2)
L~ (f2 -: f1) is closed Element of bool the carrier of (TOP-REAL 2)
len (f2 -: f1) is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg ((f2 -: f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f2 -: f1) ) } is set
union { (LSeg ((f2 -: f1),b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len (f2 -: f1) ) } is set
(L~ (f2 -: f1)) \/ (L~ (f2 :- f1)) is Element of bool the carrier of (TOP-REAL 2)
((L~ (f2 -: f1)) \/ (L~ (f2 :- f1))) \/ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
(L~ P1) \/ (L~ (f2 :- f1)) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) \/ ((L~ P1) \/ (L~ (f2 :- f1))) is Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P1 /. (len P1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
L~ P1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
union { (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
(L~ f2) /\ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
(L~ f2) \/ (L~ P1) is Element of bool the carrier of (TOP-REAL 2)
{p1,f1} is non empty set
rng f2 is non empty set
rng f2 is non empty set
P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (f2,P2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (f2,P2,f1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
(len f2) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
rng p4 is non empty set
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
rng f2 is non empty set
P2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P2 /. (len P2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ P2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
union { (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
(L~ P2) /\ (L~ p4) is Element of bool the carrier of (TOP-REAL 2)
(L~ P2) \/ (L~ p4) is Element of bool the carrier of (TOP-REAL 2)
rng P1 is non empty set
rng P1 is non empty set
P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P2 + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
LSeg (P1,P2) is closed Element of bool the carrier of (TOP-REAL 2)
Ins (P1,P2,f1) is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
(len P1) + 1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
rng p4 is non empty set
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
rng P1 is non empty set
P2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
P2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len P2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
P2 /. (len P2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ P2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
union { (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
(L~ P2) /\ (L~ p4) is Element of bool the carrier of (TOP-REAL 2)
(L~ P2) \/ (L~ p4) is Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is Element of bool the carrier of (TOP-REAL 2)
f2 is Element of bool the carrier of (TOP-REAL 2)
f1 /\ f2 is Element of bool the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 \/ f2 is Element of bool the carrier of (TOP-REAL 2)
P1 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P1 is closed Element of bool the carrier of (TOP-REAL 2)
len P1 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
union { (LSeg (P1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P1 ) } is set
P1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P1 /. (len P1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P2 is V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
L~ P2 is closed Element of bool the carrier of (TOP-REAL 2)
len P2 is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
{ (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
union { (LSeg (P2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len P2 ) } is set
P2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P2 /. (len P2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p4 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
p4 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len p4 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
p4 /. (len p4) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ p4 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
union { (LSeg (p4,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len p4 ) } is set
f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
(L~ p4) /\ (L~ f1) is Element of bool the carrier of (TOP-REAL 2)
(L~ p4) \/ (L~ f1) is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
(L~ f1) /\ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
(L~ f1) \/ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
P1 is closed Element of bool the carrier of (TOP-REAL 2)
P2 is closed Element of bool the carrier of (TOP-REAL 2)
P1 /\ P2 is Element of bool the carrier of (TOP-REAL 2)
P1 \/ P2 is Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is Element of bool the carrier of (TOP-REAL 2)
f2 is Element of bool the carrier of (TOP-REAL 2)
f1 /\ f2 is Element of bool the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 \/ f2 is Element of bool the carrier of (TOP-REAL 2)
P is ext-real V14() real set
p2 is ext-real V14() real set
|[P,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is ext-real V14() real set
|[P,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,p2]|,|[P,f1]|) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
p1 is ext-real V14() real set
|[p1,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,f1]|,|[p1,f1]|) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[p1,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[p1,f1]|,|[p1,p2]|) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,p2]|,|[P,p2]|) is non empty closed compact V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
P is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
TOP-REAL P is non empty TopSpace-like T_0 T_1 T_2 V138() V184() V185() V186() V187() V188() V189() V190() strict RLTopStruct
the carrier of (TOP-REAL P) is non empty functional set
p1 is V39(P) FinSequence-like V164() Element of the carrier of (TOP-REAL P)
p2 is V39(P) FinSequence-like V164() Element of the carrier of (TOP-REAL P)
LSeg (p1,p2) is non empty closed compact V217( TOP-REAL P) Element of bool the carrier of (TOP-REAL P)
bool the carrier of (TOP-REAL P) is set
P is ext-real V14() real set
p1 is ext-real V14() real set
p2 is ext-real V14() real set
f1 is ext-real V14() real set
(P,p1,p2,f1) is Element of bool the carrier of (TOP-REAL 2)
|[P,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[P,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,p2]|,|[P,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
|[p1,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,f1]|,|[p1,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[p1,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[p1,f1]|,|[p1,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,p2]|,|[P,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
P is ext-real V14() real set
p1 is ext-real V14() real set
p2 is ext-real V14() real set
f1 is ext-real V14() real set
(P,p1,p2,f1) is non empty compact Element of bool the carrier of (TOP-REAL 2)
|[P,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[P,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,p2]|,|[P,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
|[p1,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,f1]|,|[p1,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[p1,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[p1,f1]|,|[p1,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,p2]|,|[P,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( ( b₁ `1 = P & b<sub>1</sub> `2 <= f1 & p2 <= b₁ `2 ) or ( b<sub>1</sub> `1 <= p1 & P <= b₁ `1 & b<sub>1</sub> `2 = f1 ) or ( b₁ `1 <= p1 & P <= b<sub>1</sub> `1 & b₁ `2 = p2 ) or ( b<sub>1</sub> `1 = p1 & b₁ `2 <= f1 & p2 <= b<sub>1</sub> `2 ) ) } is set
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 = p2 & P <= b<sub>1</sub> `1 & b₁ `1 <= p1 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = p1 & p2 <= b₁ `2 & b<sub>1</sub> `2 <= f1 ) } is set
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 = f1 & P <= b<sub>1</sub> `1 & b₁ `1 <= p1 ) } is set
{ b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = P & p2 <= b₁ `2 & b<sub>1</sub> `2 <= f1 ) } is set
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = P & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 = f1 & P <= b₁ `1 & b<sub>1</sub> `1 <= p1 ) } is set
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = p1 & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 = p2 & P <= b₁ `1 & b<sub>1</sub> `1 <= p1 ) } is set
( { b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = P & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 = f1 & P <= b₁ `1 & b<sub>1</sub> `1 <= p1 ) } ) \/ ( { b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = p1 & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 = p2 & P <= b₁ `1 & b<sub>1</sub> `1 <= p1 ) } ) is set
x is set
j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j `1 is ext-real V14() real Element of REAL
j `2 is ext-real V14() real Element of REAL
x is set
j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j `1 is ext-real V14() real Element of REAL
j `2 is ext-real V14() real Element of REAL
j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j `2 is ext-real V14() real Element of REAL
j `1 is ext-real V14() real Element of REAL
j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j `1 is ext-real V14() real Element of REAL
j `2 is ext-real V14() real Element of REAL
j is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
j `2 is ext-real V14() real Element of REAL
j `1 is ext-real V14() real Element of REAL
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = P & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ (LSeg (|[P,f1]|,|[p1,f1]|)) is non empty set
( { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = P & p2 <= b₁ `2 & b<sub>1</sub> `2 <= f1 ) } \/ (LSeg (|[P,f1]|,|[p1,f1]|))) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty set
( { b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = P & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `2 = f1 & P <= b₁ `1 & b<sub>1</sub> `1 <= p1 ) } ) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty set
{ b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `1 = p1 & p2 <= b<sub>1</sub> `2 & b₁ `2 <= f1 ) } \/ (LSeg (|[p1,p2]|,|[P,p2]|)) is non empty set
( { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = P & p2 <= b₁ `2 & b<sub>1</sub> `2 <= f1 ) } \/ { b₁ where b₁ is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b₁ `2 = f1 & P <= b<sub>1</sub> `1 & b₁ `1 <= p1 ) } ) \/ ( { b<sub>1</sub> where b<sub>1</sub> is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2) : ( b<sub>1</sub> `1 = p1 & p2 <= b₁ `2 & b<sub>1</sub> `2 <= f1 ) } \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty set
P is ext-real V14() real set
p1 is ext-real V14() real set
p2 is ext-real V14() real set
f1 is ext-real V14() real set
(P,p1,p2,f1) is non empty compact Element of bool the carrier of (TOP-REAL 2)
|[P,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[P,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,p2]|,|[P,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
|[p1,f1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[P,f1]|,|[p1,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[p1,p2]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[p1,f1]|,|[p1,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,p2]|,|[P,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) \/ ((LSeg (|[p1,f1]|,|[p1,p2]|)) \/ (LSeg (|[p1,p2]|,|[P,p2]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
|[p1,f1]| `1 is ext-real V14() real Element of REAL
{|[P,p2]|,|[p1,f1]|} is non empty set
|[p1,p2]| `1 is ext-real V14() real Element of REAL
|[p1,f1]| `2 is ext-real V14() real Element of REAL
|[p1,p2]| `2 is ext-real V14() real Element of REAL
<*|[P,p2]|,|[P,f1]|,|[p1,f1]|*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
<*|[P,p2]|,|[p1,p2]|,|[p1,f1]|*> is non empty V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like V32() V39(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of (TOP-REAL 2)
|[P,p2]| `1 is ext-real V14() real Element of REAL
len <*|[P,p2]|,|[p1,p2]|,|[p1,f1]|*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
len <*|[P,p2]|,|[P,f1]|,|[p1,f1]|*> is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
|[P,p2]| `2 is ext-real V14() real Element of REAL
f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
(L~ f1) /\ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
(L~ f1) \/ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) /\ (LSeg (|[p1,f1]|,|[p1,p2]|)) is Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) /\ (LSeg (|[p1,p2]|,|[P,p2]|)) is Element of bool the carrier of (TOP-REAL 2)
(((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) /\ (LSeg (|[p1,f1]|,|[p1,p2]|))) \/ (((LSeg (|[P,p2]|,|[P,f1]|)) \/ (LSeg (|[P,f1]|,|[p1,f1]|))) /\ (LSeg (|[p1,p2]|,|[P,p2]|))) is Element of bool the carrier of (TOP-REAL 2)
LSeg (|[P,f1]|,|[P,p2]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,f1]|,|[P,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[P,f1]|,|[P,p2]|)) \/ (LSeg (|[p1,f1]|,|[P,f1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
LSeg (|[p1,p2]|,|[p1,f1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[P,f1]|,|[P,p2]|)) \/ (LSeg (|[p1,f1]|,|[P,f1]|))) /\ (LSeg (|[p1,p2]|,|[p1,f1]|)) is Element of bool the carrier of (TOP-REAL 2)
{|[P,p2]|} is non empty trivial V39(1) set
(((LSeg (|[P,f1]|,|[P,p2]|)) \/ (LSeg (|[p1,f1]|,|[P,f1]|))) /\ (LSeg (|[p1,p2]|,|[p1,f1]|))) \/ {|[P,p2]|} is non empty set
{|[p1,f1]|} is non empty trivial V39(1) set
{|[p1,f1]|} \/ {|[P,p2]|} is non empty set
R^2-unit_square is non empty Element of bool the carrier of (TOP-REAL 2)
|[0,0]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
|[0,1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,0]|,|[0,1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
|[1,1]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[0,1]|,|[1,1]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
|[1,0]| is non empty non trivial V15() V18( NAT ) Function-like V32() V39(2) FinSequence-like FinSubsequence-like V164() Element of the carrier of (TOP-REAL 2)
LSeg (|[1,1]|,|[1,0]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
LSeg (|[1,0]|,|[0,0]|) is non empty closed compact V217( TOP-REAL 2) V217( TOP-REAL 2) Element of bool the carrier of (TOP-REAL 2)
(LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|)) is non empty Element of bool the carrier of (TOP-REAL 2)
((LSeg (|[0,0]|,|[0,1]|)) \/ (LSeg (|[0,1]|,|[1,1]|))) \/ ((LSeg (|[1,1]|,|[1,0]|)) \/ (LSeg (|[1,0]|,|[0,0]|))) is non empty Element of bool the carrier of (TOP-REAL 2)
(0,1,0,1) is non empty compact Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is non empty being_S-P_arc Element of bool the carrier of (TOP-REAL 2)
(TOP-REAL 2) | p1 is non empty strict TopSpace-like SubSpace of TOP-REAL 2
the carrier of ((TOP-REAL 2) | p1) is non empty set
[: the carrier of I[01], the carrier of ((TOP-REAL 2) | p1):] is V15() set
bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | p1):] is set
p2 is V15() Function-like V29( the carrier of I[01], the carrier of ((TOP-REAL 2) | p1)) Element of bool [: the carrier of I[01], the carrier of ((TOP-REAL 2) | p1):]
rng p2 is set
[#] ((TOP-REAL 2) | p1) is non empty non proper closed Element of bool the carrier of ((TOP-REAL 2) | p1)
bool the carrier of ((TOP-REAL 2) | p1) is set
P is non empty non trivial being_special_polygon Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is Element of bool the carrier of (TOP-REAL 2)
f2 is Element of bool the carrier of (TOP-REAL 2)
f1 /\ f2 is Element of bool the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 \/ f2 is Element of bool the carrier of (TOP-REAL 2)
P2 is Element of bool the carrier of (TOP-REAL 2)
P1 is Element of bool the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
P is Element of bool the carrier of (TOP-REAL 2)
p1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
p2 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
{p1,p2} is non empty set
f1 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f1 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
f2 is non empty non trivial V15() V18( NAT ) V19( the carrier of (TOP-REAL 2)) Function-like one-to-one V32() FinSequence-like FinSubsequence-like special unfolded s.n.c. being_S-Seq FinSequence of the carrier of (TOP-REAL 2)
f2 /. 1 is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f1 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f1 /. (len f1) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
len f2 is ext-real positive non negative non empty epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT
f2 /. (len f2) is V39(2) FinSequence-like V164() Element of the carrier of (TOP-REAL 2)
L~ f1 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
union { (LSeg (f1,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f1 ) } is set
L~ f2 is closed Element of bool the carrier of (TOP-REAL 2)
{ (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
union { (LSeg (f2,b₁)) where b₁ is ext-real non negative epsilon-transitive epsilon-connected ordinal natural V14() V32() V37() real V44() V45() V172() V173() V174() V175() V176() V177() Element of NAT : ( 1 <= b₁ & b₁ + 1 <= len f2 ) } is set
(L~ f1) /\ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
(L~ f1) \/ (L~ f2) is Element of bool the carrier of (TOP-REAL 2)
P1 is closed Element of bool the carrier of (TOP-REAL 2)
P2 is closed Element of bool the carrier of (TOP-REAL 2)
P1 /\ P2 is Element of bool the carrier of (TOP-REAL 2)
P1 \/ P2 is Element of bool the carrier of (TOP-REAL 2)