REAL is non empty non trivial non finite complex-membered ext-real-membered real-membered V171() non bounded_below non bounded_above interval set
NAT is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below Element of bool REAL
bool REAL is set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 real-membered pathwise_connected compact SubSpace of R^1
R^1 is non empty strict TopSpace-like T_0 T_1 T_2 real-membered TopStruct
the carrier of I[01] is non empty complex-membered ext-real-membered real-membered set
[:I[01],I[01]:] is non empty strict TopSpace-like T_0 T_1 T_2 compact TopStruct
the carrier of [:I[01],I[01]:] is non empty set
omega is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below set
bool omega is set
{} is empty trivial Relation-like non-empty empty-yielding NAT -defined {} -valued Function-like one-to-one constant functional finite finite-yielding V29() onto FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
RAT is non empty non trivial non finite complex-membered ext-real-membered real-membered rational-membered V171() set
the empty trivial Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set is empty trivial Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() FinSequence-like FinSubsequence-like FinSequence-membered complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
{{},1} is non empty finite set
I[01] is non empty strict TopSpace-like T_0 T_1 T_2 real-membered pathwise_connected compact TopStruct
the carrier of I[01] is non empty complex-membered ext-real-membered real-membered set
INT is non empty non trivial non finite complex-membered ext-real-membered real-membered rational-membered integer-membered V171() set
[:1,1:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:1,1:] is set
[:[:1,1:],1:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:1,1:],1:] is set
[:[:1,1:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:1,1:],REAL:] is set
[:REAL,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
[:[:REAL,REAL:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:REAL,REAL:],REAL:] is set
2 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
[:2,2:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:2,2:],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:2,2:],REAL:] is set
RealSpace is strict real-membered MetrStruct
[: the carrier of I[01], the carrier of I[01]:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of I[01], the carrier of I[01]:] is set
bool the carrier of [:I[01],I[01]:] is set
bool NAT is set
COMPLEX is non empty non trivial non finite complex-membered V171() set
bool [:REAL,REAL:] is set
TOP-REAL 2 is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() 2 -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
[:I[01],I[01]:] is non empty strict TopSpace-like T_0 T_1 T_2 compact TopStruct
the carrier of [:I[01],I[01]:] is non empty set
[:COMPLEX,COMPLEX:] is Relation-like complex-yielding set
bool [:COMPLEX,COMPLEX:] is set
[:COMPLEX,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:COMPLEX,REAL:] is set
R^1 is non empty strict TopSpace-like T_0 T_1 T_2 real-membered pathwise_connected interval SubSpace of R^1
the carrier of R^1 is non empty complex-membered ext-real-membered real-membered set
bool the carrier of R^1 is set
bool (bool the carrier of R^1) is set
Tunit_circle 2 is non empty TopSpace-like pathwise_connected V202() compact SubSpace of TOP-REAL 2
the carrier of (Tunit_circle 2) is non empty set
[: the carrier of R^1, the carrier of (Tunit_circle 2):] is Relation-like set
bool [: the carrier of R^1, the carrier of (Tunit_circle 2):] is set
CircleMap is non empty Relation-like the carrier of R^1 -defined the carrier of R^1 -defined the carrier of (Tunit_circle 2) -valued the carrier of (Tunit_circle 2) -valued Function-like total total quasi_total quasi_total onto continuous Element of bool [: the carrier of R^1, the carrier of (Tunit_circle 2):]
c[10] is Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[10] is non empty strict TopSpace-like SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[10]) is non empty set
0 is empty trivial ordinal natural real Relation-like non-empty empty-yielding NAT -defined {} -valued Function-like one-to-one constant functional finite finite-yielding V29() onto V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative V153() V154() complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() Element of NAT
].0,1.[ is non empty complex-membered ext-real-membered real-membered non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
R^1 ].0,1.[ is non empty complex-membered ext-real-membered real-membered interval Element of bool the carrier of R^1
R^1 | (R^1 ].0,1.[) is non empty strict TopSpace-like real-membered pathwise_connected interval SubSpace of R^1
the carrier of (R^1 | (R^1 ].0,1.[)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Topen_unit_circle c[10]), the carrier of (R^1 | (R^1 ].0,1.[)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Topen_unit_circle c[10]), the carrier of (R^1 | (R^1 ].0,1.[)):] is set
c[-10] is Element of the carrier of (Tunit_circle 2)
Topen_unit_circle c[-10] is non empty strict TopSpace-like SubSpace of Tunit_circle 2
the carrier of (Topen_unit_circle c[-10]) is non empty set
1 / 2 is real V101() ext-real non negative Element of REAL
3 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
3 / 2 is real V101() ext-real non negative Element of REAL
].(1 / 2),(3 / 2).[ is non empty complex-membered ext-real-membered real-membered non left_end non right_end bounded_below bounded_above real-bounded interval Element of bool REAL
R^1 ].(1 / 2),(3 / 2).[ is non empty complex-membered ext-real-membered real-membered interval Element of bool the carrier of R^1
R^1 | (R^1 ].(1 / 2),(3 / 2).[) is non empty strict TopSpace-like real-membered pathwise_connected interval SubSpace of R^1
the carrier of (R^1 | (R^1 ].(1 / 2),(3 / 2).[)) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Topen_unit_circle c[-10]), the carrier of (R^1 | (R^1 ].(1 / 2),(3 / 2).[)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Topen_unit_circle c[-10]), the carrier of (R^1 | (R^1 ].(1 / 2),(3 / 2).[)):] is set
the carrier of R^1 is non empty complex-membered ext-real-membered real-membered set
[:[:COMPLEX,COMPLEX:],COMPLEX:] is Relation-like complex-yielding set
bool [:[:COMPLEX,COMPLEX:],COMPLEX:] is set
[:RAT,RAT:] is Relation-like RAT -valued complex-yielding ext-real-valued real-valued set
bool [:RAT,RAT:] is set
[:[:RAT,RAT:],RAT:] is Relation-like RAT -valued complex-yielding ext-real-valued real-valued set
bool [:[:RAT,RAT:],RAT:] is set
[:INT,INT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued set
bool [:INT,INT:] is set
[:[:INT,INT:],INT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued set
bool [:[:INT,INT:],INT:] is set
[:NAT,NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
[:[:NAT,NAT:],NAT:] is Relation-like RAT -valued INT -valued complex-yielding ext-real-valued real-valued natural-valued set
bool [:[:NAT,NAT:],NAT:] is set
K687() is non empty V116() L10()
the carrier of K687() is non empty set
K692() is non empty V116() V223() V224() V225() V227() V253() V254() V255() V256() V257() V258() L10()
K693() is non empty V116() V225() V227() V256() V257() V258() M30(K692())
K694() is non empty V116() V223() V225() V227() V256() V257() V258() V259() M33(K692(),K693())
K696() is non empty V116() V223() V225() V227() L10()
K697() is non empty V116() V223() V225() V227() V259() M30(K696())
Closed-Interval-TSpace (0,1) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (0,1)) is non empty complex-membered ext-real-membered real-membered set
bool the carrier of (TOP-REAL 2) is set
K743(0,1) is real V101() ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
K744(0,1) is real V101() ext-real Element of the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of R^1 is set
[.0,1.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
0[01] is real V101() ext-real Element of the carrier of I[01]
1[01] is real V101() ext-real Element of the carrier of I[01]
- 1 is real V101() ext-real non positive Element of REAL
5 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
bool the carrier of I[01] is set
Seg 1 is non empty finite V32(1) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
K745(0,1,K743(0,1),K744(0,1)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):] is set
id (Closed-Interval-TSpace (0,1)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like one-to-one total quasi_total onto bijective continuous V100( Closed-Interval-TSpace (0,1), Closed-Interval-TSpace (0,1)) complex-yielding ext-real-valued real-valued being_homeomorphism Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
id the carrier of (Closed-Interval-TSpace (0,1)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like one-to-one total quasi_total onto bijective V70() V72() V73() V77() complex-yielding ext-real-valued real-valued increasing non-decreasing Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
K746(0,1,K743(0,1),K744(0,1)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
n is TopSpace-like TopStruct
the carrier of n is set
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
[: the carrier of n, the carrier of r:] is Relation-like set
bool [: the carrier of n, the carrier of r:] is set
x is Relation-like the carrier of n -defined the carrier of r -valued Function-like total quasi_total Element of bool [: the carrier of n, the carrier of r:]
bool the carrier of r is set
f is Element of bool the carrier of r
x " f is Element of bool the carrier of n
bool the carrier of n is set
rng x is Element of bool the carrier of r
bool the carrier of r is set
f is Element of the carrier of r
{f} is non empty trivial finite set
dom x is Element of bool the carrier of n
bool the carrier of n is set
the_value_of x is set
g is set
x . g is set
{(the_value_of x)} is non empty trivial finite set
(dom x) --> (the_value_of x) is Relation-like dom x -defined {(the_value_of x)} -valued Function-like constant total quasi_total Element of bool [:(dom x),{(the_value_of x)}:]
[:(dom x),{(the_value_of x)}:] is Relation-like set
bool [:(dom x),{(the_value_of x)}:] is set
n --> f is Relation-like the carrier of n -defined the carrier of r -valued Function-like total quasi_total continuous Element of bool [: the carrier of n, the carrier of r:]
the carrier of n --> f is Relation-like the carrier of n -defined the carrier of r -valued Function-like constant total quasi_total Element of bool [: the carrier of n, the carrier of r:]
L[01] (0,1,0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
(id (Closed-Interval-TSpace (0,1))) * (id (Closed-Interval-TSpace (0,1))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like one-to-one total total quasi_total quasi_total onto bijective continuous complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
r is real V101() ext-real set
n is real V101() ext-real set
x is real V101() ext-real set
f is real V101() ext-real set
C is real V101() ext-real set
g is real V101() ext-real set
Closed-Interval-TSpace (g,C) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (g,C)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (x,f) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (x,f)) is non empty complex-membered ext-real-membered real-membered set
Closed-Interval-TSpace (n,r) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (n,r)) is non empty complex-membered ext-real-membered real-membered set
L[01] (g,C,n,r) is non empty Relation-like the carrier of (Closed-Interval-TSpace (g,C)) -defined the carrier of (Closed-Interval-TSpace (n,r)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (n,r)):]
[: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (n,r)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (n,r)):] is set
L[01] (n,r,x,f) is non empty Relation-like the carrier of (Closed-Interval-TSpace (n,r)) -defined the carrier of (Closed-Interval-TSpace (x,f)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (n,r)), the carrier of (Closed-Interval-TSpace (x,f)):]
[: the carrier of (Closed-Interval-TSpace (n,r)), the carrier of (Closed-Interval-TSpace (x,f)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (n,r)), the carrier of (Closed-Interval-TSpace (x,f)):] is set
(L[01] (n,r,x,f)) * (L[01] (g,C,n,r)) is non empty Relation-like the carrier of (Closed-Interval-TSpace (g,C)) -defined the carrier of (Closed-Interval-TSpace (x,f)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (x,f)):]
[: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (x,f)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (x,f)):] is set
L[01] (g,C,x,f) is non empty Relation-like the carrier of (Closed-Interval-TSpace (g,C)) -defined the carrier of (Closed-Interval-TSpace (x,f)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (g,C)), the carrier of (Closed-Interval-TSpace (x,f)):]
dom ((L[01] (n,r,x,f)) * (L[01] (g,C,n,r))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (g,C))
bool the carrier of (Closed-Interval-TSpace (g,C)) is set
[#] (Closed-Interval-TSpace (g,C)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (g,C))
dom (L[01] (g,C,x,f)) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (g,C))
U is set
((L[01] (n,r,x,f)) * (L[01] (g,C,n,r))) . U is real V101() ext-real set
(L[01] (g,C,x,f)) . U is real V101() ext-real set
[.g,C.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
V is real V101() ext-real set
rng (L[01] (g,C,n,r)) is non empty complex-membered ext-real-membered real-membered Element of bool REAL
[#] (Closed-Interval-TSpace (n,r)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (n,r))
bool the carrier of (Closed-Interval-TSpace (n,r)) is set
(L[01] (g,C,n,r)) . U is real V101() ext-real set
dom (L[01] (g,C,n,r)) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (g,C))
c is real V101() ext-real set
[.n,r.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(L[01] (n,r,x,f)) . c is real V101() ext-real set
f - x is real V101() ext-real set
r - n is real V101() ext-real set
(f - x) / (r - n) is real V101() ext-real set
c - n is real V101() ext-real set
((f - x) / (r - n)) * (c - n) is real V101() ext-real set
(((f - x) / (r - n)) * (c - n)) + x is real V101() ext-real set
((f - x) / (r - n)) * c is real V101() ext-real set
C - g is real V101() ext-real set
(r - n) / (C - g) is real V101() ext-real set
V - g is real V101() ext-real set
((r - n) / (C - g)) * (V - g) is real V101() ext-real set
(((r - n) / (C - g)) * (V - g)) + n is real V101() ext-real set
((f - x) / (r - n)) * ((((r - n) / (C - g)) * (V - g)) + n) is real V101() ext-real set
((f - x) / (r - n)) * ((r - n) / (C - g)) is real V101() ext-real set
(((f - x) / (r - n)) * ((r - n) / (C - g))) * (V - g) is real V101() ext-real set
((f - x) / (r - n)) * n is real V101() ext-real set
((((f - x) / (r - n)) * ((r - n) / (C - g))) * (V - g)) + (((f - x) / (r - n)) * n) is real V101() ext-real set
(f - x) / (C - g) is real V101() ext-real set
(r - n) / (r - n) is real V101() ext-real set
((f - x) / (C - g)) * ((r - n) / (r - n)) is real V101() ext-real set
(((f - x) / (C - g)) * ((r - n) / (r - n))) * (V - g) is real V101() ext-real set
((((f - x) / (C - g)) * ((r - n) / (r - n))) * (V - g)) + (((f - x) / (r - n)) * n) is real V101() ext-real set
((f - x) / (C - g)) * 1 is real V101() ext-real set
(((f - x) / (C - g)) * 1) * (V - g) is real V101() ext-real set
((((f - x) / (C - g)) * 1) * (V - g)) + (((f - x) / (r - n)) * n) is real V101() ext-real set
((f - x) / (C - g)) * (V - g) is real V101() ext-real set
(((f - x) / (C - g)) * (V - g)) + (((f - x) / (r - n)) * n) is real V101() ext-real set
(L[01] (n,r,x,f)) . ((L[01] (g,C,n,r)) . U) is real V101() ext-real set
n is non empty ordinal natural real V101() ext-real positive non negative set
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL n) is non empty set
REAL n is non empty functional FinSequence-membered FinSequenceSet of REAL
n -tuples_on REAL is non empty functional FinSequence-membered FinSequenceSet of REAL
r is Relation-like Function-like set
dom r is set
r .: (n -tuples_on REAL) is set
x is set
n + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg n is non empty finite V32(n) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
f is set
r . f is set
g is Relation-like NAT -defined REAL -valued Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
g . 1 is real V101() ext-real set
Funcs ((Seg n),REAL) is non empty functional FUNCTION_DOMAIN of Seg n, REAL
rng g is finite complex-membered ext-real-membered real-membered bounded_below bounded_above real-bounded Element of bool REAL
C is Relation-like Function-like set
dom C is set
rng C is set
{x} is non empty trivial finite set
(Seg n) --> x is non empty Relation-like Seg n -defined Seg n -defined {x} -valued Function-like constant finite total total quasi_total FinSequence-like FinSubsequence-like Element of bool [:(Seg n),{x}:]
[:(Seg n),{x}:] is Relation-like finite set
bool [:(Seg n),{x}:] is finite V29() set
dom ((Seg n) --> x) is non empty finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
rng ((Seg n) --> x) is non empty trivial finite Element of bool {x}
bool {x} is finite V29() set
g is Relation-like NAT -defined REAL -valued Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of n -tuples_on REAL
r . g is set
g . 1 is real V101() ext-real set
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
x is set
f is Element of the carrier of r
[#] (TOP-REAL n) is non empty non proper closed Element of bool the carrier of (TOP-REAL n)
the carrier of (TOP-REAL n) is non empty non trivial non finite set
bool the carrier of (TOP-REAL n) is set
g is non empty a_neighborhood of f
r | g is non empty strict TopSpace-like SubSpace of r
(TOP-REAL n) | ([#] (TOP-REAL n)) is non empty strict TopSpace-like SubSpace of TOP-REAL n
the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))) is non empty set
the carrier of (r | g) is non empty set
[: the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))), the carrier of (r | g):] is Relation-like set
bool [: the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))), the carrier of (r | g):] is set
C is non empty Relation-like the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))) -defined the carrier of (r | g) -valued Function-like total quasi_total Element of bool [: the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))), the carrier of (r | g):]
dom C is non empty Element of bool the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n)))
bool the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n))) is set
[#] ((TOP-REAL n) | ([#] (TOP-REAL n))) is non empty non proper closed Element of bool the carrier of ((TOP-REAL n) | ([#] (TOP-REAL n)))
rng C is non empty Element of bool the carrier of (r | g)
bool the carrier of (r | g) is set
[#] (r | g) is non empty non proper closed Element of bool the carrier of (r | g)
n is ordinal natural real V101() ext-real non negative set
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL n) is non empty set
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Sphere ((0. (TOP-REAL n)),1) is closed Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
{r} is non empty trivial functional finite V29() set
(Sphere ((0. (TOP-REAL n)),1)) \ {r} is Element of bool the carrier of (TOP-REAL n)
x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
TOP-REAL x is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() x -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL x) is non empty set
f is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
0. (TOP-REAL x) is Relation-like NAT -defined Function-like finite V32(x) V45( TOP-REAL x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
the ZeroF of (TOP-REAL x) is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
f - (0. (TOP-REAL x)) is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
f - (0. (TOP-REAL x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(f - (0. (TOP-REAL x))).| is real V101() ext-real non negative Element of REAL
- (0. (TOP-REAL x)) is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
- (0. (TOP-REAL x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
f + (- (0. (TOP-REAL x))) is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
f + (- (0. (TOP-REAL x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(f + (- (0. (TOP-REAL x)))).| is real V101() ext-real non negative Element of REAL
- 1 is real V101() ext-real non positive set
(- 1) * (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + ((- 1) * (0. (TOP-REAL n))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
r + ((- 1) * (0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(r + ((- 1) * (0. (TOP-REAL n)))).| is real V101() ext-real non negative Element of REAL
r + (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
r + (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(r + (0. (TOP-REAL n))).| is real V101() ext-real non negative Element of REAL
|.r.| is real V101() ext-real non negative Element of REAL
|.(0. (TOP-REAL n)).| is real V101() ext-real non negative Element of REAL
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(1 + 1) * r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + 1) * r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
g is real V101() ext-real set
g * r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
g * r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(g * r) + (g * r) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(g * r) + (g * r) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(g * r) + r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(g * r) + r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
r + r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
r + (- r) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
r + (- r) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(- r).| is real V101() ext-real non negative Element of REAL
(- r) + (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- r) + (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((- r) + (0. (TOP-REAL n))).| is real V101() ext-real non negative Element of REAL
(- r) + ((- 1) * (0. (TOP-REAL n))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- r) + ((- 1) * (0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((- r) + ((- 1) * (0. (TOP-REAL n)))).| is real V101() ext-real non negative Element of REAL
- (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- r) + (- (0. (TOP-REAL n))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- r) + (- (0. (TOP-REAL n))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((- r) + (- (0. (TOP-REAL n)))).| is real V101() ext-real non negative Element of REAL
- f is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
- f is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- f) - (0. (TOP-REAL x)) is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
(- f) - (0. (TOP-REAL x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((- f) - (0. (TOP-REAL x))).| is real V101() ext-real non negative Element of REAL
Sphere ((0. (TOP-REAL x)),1) is closed bounded Element of bool the carrier of (TOP-REAL x)
bool the carrier of (TOP-REAL x) is set
n is non empty TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is Element of the carrier of n
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
dom f is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
inf (dom f) is ext-real set
sup (dom f) is ext-real set
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is non empty TopSpace-like SubSpace of n
the carrier of r is non empty set
x is Element of the carrier of n
f is Element of the carrier of n
g is Element of the carrier of r
C is Element of the carrier of r
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,f
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,f
p is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total Path of g,C
U is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total Path of g,C
[: the carrier of [:I[01],I[01]:], the carrier of r:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of r:] is set
V is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of r -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of r:]
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
c is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
p . 0 is set
p . 1 is set
f2 . 0 is set
f2 . 1 is set
fc1 is real V101() ext-real Element of the carrier of I[01]
c . (fc1,0) is set
f2 . fc1 is Element of the carrier of n
fc2 is real V101() ext-real Element of the carrier of I[01]
c . (fc2,1) is set
x . fc2 is Element of the carrier of n
c0 is real V101() ext-real Element of the carrier of I[01]
c . (0,c0) is set
f0 is real V101() ext-real Element of the carrier of I[01]
c . (1,f0) is set
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is non empty TopSpace-like SubSpace of n
the carrier of r is non empty set
x is Element of the carrier of n
f is Element of the carrier of n
Paths (x,f) is non empty set
EqRel (n,x,f) is Relation-like Paths (x,f) -defined Paths (x,f) -valued Element of bool [:(Paths (x,f)),(Paths (x,f)):]
[:(Paths (x,f)),(Paths (x,f)):] is Relation-like set
bool [:(Paths (x,f)),(Paths (x,f)):] is set
g is Element of the carrier of r
C is Element of the carrier of r
Paths (g,C) is non empty set
EqRel (r,g,C) is Relation-like Paths (g,C) -defined Paths (g,C) -valued Element of bool [:(Paths (g,C)),(Paths (g,C)):]
[:(Paths (g,C)),(Paths (g,C)):] is Relation-like set
bool [:(Paths (g,C)),(Paths (g,C)):] is set
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,f
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,f
Class ((EqRel (n,x,f)),f2) is Element of bool (Paths (x,f))
bool (Paths (x,f)) is set
Class ((EqRel (n,x,f)),x) is Element of bool (Paths (x,f))
p is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total Path of g,C
U is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total Path of g,C
Class ((EqRel (r,g,C)),p) is Element of bool (Paths (g,C))
bool (Paths (g,C)) is set
Class ((EqRel (r,g,C)),U) is Element of bool (Paths (g,C))
n is non empty trivial finite 1 -element TopSpace-like pathwise_connected TopStruct
the carrier of n is non empty trivial finite set
r is Element of the carrier of n
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
the carrier of (FundamentalGroup (n,r)) is non empty set
Loops r is non empty set
Paths (r,r) is non empty set
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),f) is Element of bool (Loops r)
bool (Loops r) is set
{(Class ((EqRel (n,r)),f))} is non empty trivial finite set
g is set
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),C) is Element of bool (Loops r)
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
g is set
Class (EqRel (n,r)) is a_partition of Loops r
n is ordinal natural real V101() ext-real non negative set
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL n) is non empty set
bool the carrier of (TOP-REAL n) is set
[#] (TOP-REAL n) is non empty non proper closed Element of bool the carrier of (TOP-REAL n)
r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
{r} is non empty trivial functional finite V29() set
([#] (TOP-REAL n)) \ {r} is Element of bool the carrier of (TOP-REAL n)
x is Element of bool the carrier of (TOP-REAL n)
(TOP-REAL n) | x is strict TopSpace-like SubSpace of TOP-REAL n
f is non empty TopSpace-like SubSpace of TOP-REAL n
[#] f is non empty non proper closed Element of bool the carrier of f
the carrier of f is non empty set
bool the carrier of f is set
g is Element of the carrier of f
C is Element of the carrier of f
f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
LSeg (f2,x) is Element of bool the carrier of (TOP-REAL n)
(TOP-REAL n) | (LSeg (f2,x)) is strict TopSpace-like SubSpace of TOP-REAL n
[#] ((TOP-REAL n) | (LSeg (f2,x))) is non proper closed Element of bool the carrier of ((TOP-REAL n) | (LSeg (f2,x)))
the carrier of ((TOP-REAL n) | (LSeg (f2,x))) is set
bool the carrier of ((TOP-REAL n) | (LSeg (f2,x))) is set
p is non empty TopSpace-like SubSpace of f
the carrier of p is non empty set
[: the carrier of I[01], the carrier of p:] is Relation-like set
bool [: the carrier of I[01], the carrier of p:] is set
U is non empty Relation-like the carrier of I[01] -defined the carrier of p -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of p:]
U . 0 is set
U . 1 is set
[: the carrier of I[01], the carrier of f:] is Relation-like set
bool [: the carrier of I[01], the carrier of f:] is set
V is non empty Relation-like the carrier of I[01] -defined the carrier of f -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of f:]
V . 0 is set
V . 1 is set
g is Element of the carrier of f
C is Element of the carrier of f
f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
LSeg (f2,x) is Element of bool the carrier of (TOP-REAL n)
p is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
TOP-REAL p is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() p -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL p) is non empty set
U is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
V is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
c is real V101() ext-real Element of REAL
1 - c is real V101() ext-real set
(1 - c) * U is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
(1 - c) * U is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * V is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
c * V is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * U) + (c * V) is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
((1 - c) * U) + (c * V) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x - f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x - f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
n - 1 is real V101() ext-real set
fc2 is ordinal natural real V101() ext-real non negative set
fc2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
TOP-REAL (fc2 + 1) is non empty non trivial non finite TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() fc2 + 1 -locally_euclidean V359() RLTopStruct
0. (TOP-REAL (fc2 + 1)) is Relation-like NAT -defined Function-like finite V32(fc2 + 1) V45( TOP-REAL (fc2 + 1)) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL (fc2 + 1))
the carrier of (TOP-REAL (fc2 + 1)) is non empty non trivial non finite set
the ZeroF of (TOP-REAL (fc2 + 1)) is Relation-like NAT -defined Function-like finite V32(fc2 + 1) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL (fc2 + 1))
TPlane ((x - f2),r) is non empty TopSpace-like SubSpace of TOP-REAL n
[#] (TPlane ((x - f2),r)) is non empty non proper closed Element of bool the carrier of (TPlane ((x - f2),r))
the carrier of (TPlane ((x - f2),r)) is non empty set
bool the carrier of (TPlane ((x - f2),r)) is set
Plane ((x - f2),r) is Element of bool the carrier of (TOP-REAL n)
(TOP-REAL n) | (Plane ((x - f2),r)) is strict TopSpace-like SubSpace of TOP-REAL n
[#] ((TOP-REAL n) | (Plane ((x - f2),r))) is non proper closed Element of bool the carrier of ((TOP-REAL n) | (Plane ((x - f2),r)))
the carrier of ((TOP-REAL n) | (Plane ((x - f2),r))) is set
bool the carrier of ((TOP-REAL n) | (Plane ((x - f2),r))) is set
c0 is set
c0 \ {r} is Element of bool c0
bool c0 is set
f0 is set
{ b1 where b1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n) : |((x - f2),(b1 - r))| = 0 } is set
c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - r is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|((x - f2),(c1 - r))| is real V101() ext-real Element of REAL
|((x - f2),(x - f2))| is real V101() ext-real Element of REAL
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
LSeg (f2,c1) is Element of bool the carrier of (TOP-REAL n)
c2 is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
ci1 is real V101() ext-real Element of REAL
1 - ci1 is real V101() ext-real set
(1 - ci1) * U is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
(1 - ci1) * U is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * c2 is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
ci1 * c2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * U) + (ci1 * c2) is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
((1 - ci1) * U) + (ci1 * c2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL n)) + (1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) + (1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL n)) + c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) + c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 - f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ci1) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - ci1) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 - ((1 - ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - ((1 - ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - ((1 - ci1) * f2)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - ((1 - ci1) * f2)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 - ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- ((1 - ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (- ((1 - ci1) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (- ((1 - ci1) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (- ((1 - ci1) * f2))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (- ((1 - ci1) * f2))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 - ci1) is real V101() ext-real set
(- (1 - ci1)) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (1 - ci1)) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + ((- (1 - ci1)) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + ((- (1 - ci1)) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + ((- (1 - ci1)) * f2)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + ((- (1 - ci1)) * f2)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is real V101() ext-real non positive set
(- 1) + ci1 is real V101() ext-real set
((- 1) + ci1) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) + ci1) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (((- 1) + ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (((- 1) + ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (((- 1) + ci1) * f2)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (((- 1) + ci1) * f2)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- 1) * f2) + (ci1 * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) * f2) + (ci1 * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (((- 1) * f2) + (ci1 * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (((- 1) * f2) + (ci1 * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (((- 1) * f2) + (ci1 * f2))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (((- 1) * f2) + (ci1 * f2))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- f2) + (ci1 * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- f2) + (ci1 * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + ((- f2) + (ci1 * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + ((- f2) + (ci1 * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + ((- f2) + (ci1 * f2))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + ((- f2) + (ci1 * f2))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (- f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (- f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (- f2)) + (ci1 * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (- f2)) + (ci1 * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 + (- f2)) + (ci1 * f2)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 + (- f2)) + (ci1 * f2)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + (ci1 * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + (ci1 * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - f2) + (ci1 * f2)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - f2) + (ci1 * f2)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - f2) + (ci1 * f2)) + (- (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - f2) + (ci1 * f2)) + (- (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - f2) + (ci1 * f2)) + (ci1 * (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - f2) + (ci1 * f2)) + (ci1 * (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(ci1 * f2) + (ci1 * (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(ci1 * f2) + (ci1 * (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + ((ci1 * f2) + (ci1 * (- c1))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + ((ci1 * f2) + (ci1 * (- c1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
f2 + (- c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
f2 + (- c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (f2 + (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (f2 + (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + (ci1 * (f2 + (- c1))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + (ci1 * (f2 + (- c1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- (c1 - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- (c1 - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + (ci1 * (- (c1 - f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + (ci1 * (- (c1 - f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * (c1 - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * (c1 - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + (- (ci1 * (c1 - f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + (- (ci1 * (c1 - f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ci1 is real V101() ext-real set
(- ci1) * (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ci1) * (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - f2) + ((- ci1) * (c1 - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - f2) + ((- ci1) * (c1 - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * (c1 - f2)) + ((- ci1) * (c1 - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 * (c1 - f2)) + ((- ci1) * (c1 - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 + (- ci1) is real V101() ext-real set
(1 + (- ci1)) * (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + (- ci1)) * (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ci1) * (c1 - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - ci1) * (c1 - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|((x - f2),(c1 - f2))| is real V101() ext-real Element of REAL
(1 - ci1) * |((x - f2),(c1 - f2))| is real V101() ext-real set
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * f2) + (c * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c) * f2) + (c * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (((1 - c) * f2) + (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (((1 - c) * f2) + (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * f2) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + (- (((1 - c) * f2) + (c * x)))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + (- (((1 - c) * f2) + (c * x)))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 - c) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- ((1 - c) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- ((1 - c) * f2)) - (c * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ((1 - c) * f2)) - (c * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * f2) + ((- ((1 - c) * f2)) - (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + ((- ((1 - c) * f2)) - (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + ((- ((1 - c) * f2)) - (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + ((- ((1 - c) * f2)) - (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (c * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (c * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- ((1 - c) * f2)) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ((1 - c) * f2)) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * f2) + ((- ((1 - c) * f2)) + (- (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + ((- ((1 - c) * f2)) + (- (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + ((- ((1 - c) * f2)) + (- (c * x)))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + ((- ((1 - c) * f2)) + (- (c * x)))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * f2) + (- ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + (- ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + (- ((1 - c) * f2))) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + (- ((1 - c) * f2))) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - ci1) * f2) + (- ((1 - c) * f2))) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((((1 - ci1) * f2) + (- ((1 - c) * f2))) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 - c) is real V101() ext-real set
(- (1 - c)) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (1 - c)) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * f2) + ((- (1 - c)) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) * f2) + ((- (1 - c)) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) * f2) + ((- (1 - c)) * f2)) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) * f2) + ((- (1 - c)) * f2)) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - ci1) * f2) + ((- (1 - c)) * f2)) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((((1 - ci1) * f2) + ((- (1 - c)) * f2)) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ci1) + (- (1 - c)) is real V101() ext-real set
((1 - ci1) + (- (1 - c))) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - ci1) + (- (1 - c))) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - ci1) + (- (1 - c))) * f2) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - ci1) + (- (1 - c))) * f2) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((((1 - ci1) + (- (1 - c))) * f2) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((((1 - ci1) + (- (1 - c))) * f2) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c + (- ci1) is real V101() ext-real set
(c + (- ci1)) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c + (- ci1)) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c + (- ci1)) * f2) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c + (- ci1)) * f2) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((c + (- ci1)) * f2) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((c + (- ci1)) * f2) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- ci1) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ci1) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * f2) + ((- ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * f2) + ((- ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c * f2) + ((- ci1) * f2)) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c * f2) + ((- ci1) * f2)) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((c * f2) + ((- ci1) * f2)) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((c * f2) + ((- ci1) * f2)) + (- (c * x))) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * f2) + (- (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * f2) + (- (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c * f2) + (- (c * x))) + ((- ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c * f2) + (- (c * x))) + ((- ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((c * f2) + (- (c * x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((c * f2) + (- (c * x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * (- x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * (- x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * f2) + (c * (- x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * f2) + (c * (- x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c * f2) + (c * (- x))) + ((- ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c * f2) + (c * (- x))) + ((- ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((c * f2) + (c * (- x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((c * f2) + (c * (- x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
f2 + (- x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
f2 + (- x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * (f2 + (- x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * (f2 + (- x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (f2 + (- x))) + ((- ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (f2 + (- x))) + ((- ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c * (f2 + (- x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c * (f2 + (- x))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (x - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (x - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * (- (x - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * (- (x - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + ((- ci1) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + ((- ci1) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c * (- (x - f2))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c * (- (x - f2))) + ((- ci1) * f2)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- ci1) * f2) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- ci1) * f2) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + (((- ci1) * f2) + (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + (((- ci1) * f2) + (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(ci1 * c1) + (- (ci1 * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(ci1 * c1) + (- (ci1 * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + ((ci1 * c1) + (- (ci1 * f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + ((ci1 * c1) + (- (ci1 * f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(ci1 * c1) + (ci1 * (- f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(ci1 * c1) + (ci1 * (- f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + ((ci1 * c1) + (ci1 * (- f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + ((ci1 * c1) + (ci1 * (- f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (c1 + (- f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (c1 + (- f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + (ci1 * (c1 + (- f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + (ci1 * (c1 + (- f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * (- (x - f2))) + (ci1 * (c1 - f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * (- (x - f2))) + (ci1 * (c1 - f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(((c * (- (x - f2))) + (ci1 * (c1 - f2))),((c * (- (x - f2))) + (ci1 * (c1 - f2))))| is real V101() ext-real Element of REAL
|((c * (- (x - f2))),(c * (- (x - f2))))| is real V101() ext-real Element of REAL
|((c * (- (x - f2))),(ci1 * (c1 - f2)))| is real V101() ext-real Element of REAL
2 * |((c * (- (x - f2))),(ci1 * (c1 - f2)))| is real V101() ext-real set
|((c * (- (x - f2))),(c * (- (x - f2))))| + (2 * |((c * (- (x - f2))),(ci1 * (c1 - f2)))|) is real V101() ext-real set
|((ci1 * (c1 - f2)),(ci1 * (c1 - f2)))| is real V101() ext-real Element of REAL
(|((c * (- (x - f2))),(c * (- (x - f2))))| + (2 * |((c * (- (x - f2))),(ci1 * (c1 - f2)))|)) + |((ci1 * (c1 - f2)),(ci1 * (c1 - f2)))| is real V101() ext-real set
|((- (x - f2)),(c * (- (x - f2))))| is real V101() ext-real Element of REAL
c * |((- (x - f2)),(c * (- (x - f2))))| is real V101() ext-real set
|((- (x - f2)),(- (x - f2)))| is real V101() ext-real Element of REAL
c * |((- (x - f2)),(- (x - f2)))| is real V101() ext-real set
c * (c * |((- (x - f2)),(- (x - f2)))|) is real V101() ext-real set
c * |((x - f2),(x - f2))| is real V101() ext-real set
c * (c * |((x - f2),(x - f2))|) is real V101() ext-real set
c * c is real V101() ext-real set
(c * c) * |((x - f2),(x - f2))| is real V101() ext-real set
|((c1 - f2),(ci1 * (c1 - f2)))| is real V101() ext-real Element of REAL
ci1 * |((c1 - f2),(ci1 * (c1 - f2)))| is real V101() ext-real set
|((c1 - f2),(c1 - f2))| is real V101() ext-real Element of REAL
ci1 * |((c1 - f2),(c1 - f2))| is real V101() ext-real set
ci1 * (ci1 * |((c1 - f2),(c1 - f2))|) is real V101() ext-real set
ci1 * ci1 is real V101() ext-real set
(ci1 * ci1) * |((c1 - f2),(c1 - f2))| is real V101() ext-real set
|((- (x - f2)),(ci1 * (c1 - f2)))| is real V101() ext-real Element of REAL
c * |((- (x - f2)),(ci1 * (c1 - f2)))| is real V101() ext-real set
|((- (x - f2)),(c1 - f2))| is real V101() ext-real Element of REAL
ci1 * |((- (x - f2)),(c1 - f2))| is real V101() ext-real set
c * (ci1 * |((- (x - f2)),(c1 - f2))|) is real V101() ext-real set
- |((x - f2),(c1 - f2))| is real V101() ext-real set
ci1 * (- |((x - f2),(c1 - f2))|) is real V101() ext-real set
c * (ci1 * (- |((x - f2),(c1 - f2))|)) is real V101() ext-real set
1 * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * f2) + (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 * f2) + (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
LSeg (c1,x) is Element of bool the carrier of (TOP-REAL n)
c2 is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
ci1 is real V101() ext-real Element of REAL
1 - ci1 is real V101() ext-real set
(1 - ci1) * V is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
(1 - ci1) * V is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * c2 is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
ci1 * c2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - ci1) * V) + (ci1 * c2) is Relation-like NAT -defined Function-like finite V32(p) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL p)
((1 - ci1) * V) + (ci1 * c2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL n)) + (1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) + (1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(0. (TOP-REAL n)) + c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) + c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 - x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ci1) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - ci1) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 - ((1 - ci1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 - ((1 - ci1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - ((1 - ci1) * x)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - ((1 - ci1) * x)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 - ci1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- ((1 - ci1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (- ((1 - ci1) * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (- ((1 - ci1) * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (- ((1 - ci1) * x))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (- ((1 - ci1) * x))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 - ci1) is real V101() ext-real set
(- (1 - ci1)) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (1 - ci1)) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + ((- (1 - ci1)) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + ((- (1 - ci1)) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + ((- (1 - ci1)) * x)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + ((- (1 - ci1)) * x)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- 1 is real V101() ext-real non positive set
(- 1) + ci1 is real V101() ext-real set
((- 1) + ci1) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) + ci1) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (((- 1) + ci1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (((- 1) + ci1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (((- 1) + ci1) * x)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (((- 1) + ci1) * x)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- 1) * x) + (ci1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) * x) + (ci1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (((- 1) * x) + (ci1 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (((- 1) * x) + (ci1 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (((- 1) * x) + (ci1 * x))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (((- 1) * x) + (ci1 * x))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- x) + (ci1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- x) + (ci1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + ((- x) + (ci1 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + ((- x) + (ci1 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + ((- x) + (ci1 * x))) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + ((- x) + (ci1 * x))) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c1 + (- x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c1 + (- x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 + (- x)) + (ci1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 + (- x)) + (ci1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 + (- x)) + (ci1 * x)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 + (- x)) + (ci1 * x)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + (ci1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + (ci1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - x) + (ci1 * x)) - (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - x) + (ci1 * x)) - (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - x) + (ci1 * x)) + (- (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - x) + (ci1 * x)) + (- (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c1 - x) + (ci1 * x)) + (ci1 * (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c1 - x) + (ci1 * x)) + (ci1 * (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(ci1 * x) + (ci1 * (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(ci1 * x) + (ci1 * (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + ((ci1 * x) + (ci1 * (- c1))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + ((ci1 * x) + (ci1 * (- c1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (- c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (- c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (x + (- c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (x + (- c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + (ci1 * (x + (- c1))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + (ci1 * (x + (- c1))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + (ci1 * (- (c1 - x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + (ci1 * (- (c1 - x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + (- (ci1 * (c1 - x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + (- (ci1 * (c1 - x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ci1 is real V101() ext-real set
(- ci1) * (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ci1) * (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c1 - x) + ((- ci1) * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c1 - x) + ((- ci1) * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * (c1 - x)) + ((- ci1) * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 * (c1 - x)) + ((- ci1) * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 + (- ci1) is real V101() ext-real set
(1 + (- ci1)) * (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + (- ci1)) * (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - ci1) * (c1 - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - ci1) * (c1 - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|((x - f2),(c1 - x))| is real V101() ext-real Element of REAL
(1 - ci1) * |((x - f2),(c1 - x))| is real V101() ext-real set
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + (- ci1)) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + (- ci1)) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 + (- ci1)) * x) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 + (- ci1)) * x) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * f2) + (c * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c) * f2) + (c * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (((1 - c) * f2) + (c * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (((1 - c) * f2) + (c * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 + (- ci1)) * x) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 + (- ci1)) * x) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
1 * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- ci1) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- ci1) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * x) + ((- ci1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 * x) + ((- ci1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 * x) + ((- ci1) * x)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 * x) + ((- ci1) * x)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * x) + ((- ci1) * x)) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 * x) + ((- ci1) * x)) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((- ci1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((- ci1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((- ci1) * x)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((- ci1) * x)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((x + ((- ci1) * x)) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((x + ((- ci1) * x)) + (ci1 * c1)) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- ci1) * x) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- ci1) * x) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (((- ci1) * x) + (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (((- ci1) * x) + (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (((- ci1) * x) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (((- ci1) * x) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (ci1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (ci1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- (ci1 * x)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (ci1 * x)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((- (ci1 * x)) + (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((- (ci1 * x)) + (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((- (ci1 * x)) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((- (ci1 * x)) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * (- x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * (- x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(ci1 * (- x)) + (ci1 * c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(ci1 * (- x)) + (ci1 * c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((ci1 * (- x)) + (ci1 * c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((ci1 * (- x)) + (ci1 * c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((ci1 * (- x)) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((ci1 * (- x)) + (ci1 * c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- x) + c1 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- x) + c1 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
ci1 * ((- x) + c1) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
ci1 * ((- x) + c1) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (ci1 * ((- x) + c1)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (ci1 * ((- x) + c1)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (ci1 * ((- x) + c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (ci1 * ((- x) + c1))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (ci1 * (c1 - x))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (ci1 * (c1 - x))) + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (- (((1 - c) * f2) + (c * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (- (((1 - c) * f2) + (c * x)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (- (((1 - c) * f2) + (c * x)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c * x) + ((1 - c) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c * x) + ((1 - c) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((c * x) + ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * ((c * x) + ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((- 1) * ((c * x) + ((1 - c) * f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((- 1) * ((c * x) + ((1 - c) * f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((- 1) * ((c * x) + ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((- 1) * ((c * x) + ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * (c * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * (c * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * ((1 - c) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- 1) * ((1 - c) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (((- 1) * (c * x)) + ((- 1) * ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- 1) * c is real V101() ext-real set
((- 1) * c) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- 1) * c) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- 1) * c) * x) + ((- 1) * ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((- 1) * c) * x) + ((- 1) * ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((((- 1) * c) * x) + ((- 1) * ((1 - c) * f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((((- 1) * c) * x) + ((- 1) * ((1 - c) * f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((((- 1) * c) * x) + ((- 1) * ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((((- 1) * c) * x) + ((- 1) * ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- c is real V101() ext-real set
(- c) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- c) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 - c) * f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- ((1 - c) * f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- c) * x) + (- ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- c) * x) + (- ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (((- c) * x) + (- ((1 - c) * f2))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (((- c) * x) + (- ((1 - c) * f2))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + (((- c) * x) + (- ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + (((- c) * x) + (- ((1 - c) * f2)))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + ((- c) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + ((- c) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(x + ((- c) * x)) + (- ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(x + ((- c) * x)) + (- ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((x + ((- c) * x)) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((x + ((- c) * x)) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 * x) + ((- c) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 * x) + ((- c) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 * x) + ((- c) * x)) + (- ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 * x) + ((- c) * x)) + (- ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 * x) + ((- c) * x)) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 * x) + ((- c) * x)) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
1 + (- c) is real V101() ext-real set
(1 + (- c)) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 + (- c)) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 + (- c)) * x) + (- ((1 - c) * f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 + (- c)) * x) + (- ((1 - c) * f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 + (- c)) * x) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 + (- c)) * x) + (- ((1 - c) * f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- f2 is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * (- f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * (- f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * x) + ((1 - c) * (- f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c) * x) + ((1 - c) * (- f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c) * x) + ((1 - c) * (- f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c) * x) + ((1 - c) * (- f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
x + (- f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x + (- f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * (x + (- f2)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * (x + (- f2)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * (x + (- f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c) * (x + (- f2))) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c) * (x - f2) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c) * (x - f2) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c) * (x - f2)) + (ci1 * (c1 - x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c) * (x - f2)) + (ci1 * (c1 - x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|((((1 - c) * (x - f2)) + (ci1 * (c1 - x))),(((1 - c) * (x - f2)) + (ci1 * (c1 - x))))| is real V101() ext-real Element of REAL
|(((1 - c) * (x - f2)),((1 - c) * (x - f2)))| is real V101() ext-real Element of REAL
|(((1 - c) * (x - f2)),(ci1 * (c1 - x)))| is real V101() ext-real Element of REAL
2 * |(((1 - c) * (x - f2)),(ci1 * (c1 - x)))| is real V101() ext-real set
|(((1 - c) * (x - f2)),((1 - c) * (x - f2)))| + (2 * |(((1 - c) * (x - f2)),(ci1 * (c1 - x)))|) is real V101() ext-real set
|((ci1 * (c1 - x)),(ci1 * (c1 - x)))| is real V101() ext-real Element of REAL
(|(((1 - c) * (x - f2)),((1 - c) * (x - f2)))| + (2 * |(((1 - c) * (x - f2)),(ci1 * (c1 - x)))|)) + |((ci1 * (c1 - x)),(ci1 * (c1 - x)))| is real V101() ext-real set
|((x - f2),((1 - c) * (x - f2)))| is real V101() ext-real Element of REAL
(1 - c) * |((x - f2),((1 - c) * (x - f2)))| is real V101() ext-real set
(1 - c) * |((x - f2),(x - f2))| is real V101() ext-real set
(1 - c) * ((1 - c) * |((x - f2),(x - f2))|) is real V101() ext-real set
(1 - c) * (1 - c) is real V101() ext-real set
((1 - c) * (1 - c)) * |((x - f2),(x - f2))| is real V101() ext-real set
|((c1 - x),(ci1 * (c1 - x)))| is real V101() ext-real Element of REAL
ci1 * |((c1 - x),(ci1 * (c1 - x)))| is real V101() ext-real set
|((c1 - x),(c1 - x))| is real V101() ext-real Element of REAL
ci1 * |((c1 - x),(c1 - x))| is real V101() ext-real set
ci1 * (ci1 * |((c1 - x),(c1 - x))|) is real V101() ext-real set
ci1 * ci1 is real V101() ext-real set
(ci1 * ci1) * |((c1 - x),(c1 - x))| is real V101() ext-real set
|((x - f2),(ci1 * (c1 - x)))| is real V101() ext-real Element of REAL
(1 - c) * |((x - f2),(ci1 * (c1 - x)))| is real V101() ext-real set
ci1 * |((x - f2),(c1 - x))| is real V101() ext-real set
(1 - c) * (ci1 * |((x - f2),(c1 - x))|) is real V101() ext-real set
(0. (TOP-REAL n)) + (1 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(0. (TOP-REAL n)) + (1 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c2 is Element of the carrier of f
LSeg (f2,x) is Element of bool the carrier of (TOP-REAL n)
LSeg (f2,x) is Element of bool the carrier of (TOP-REAL n)
f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
f2 is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
bool the carrier of n is set
[#] n is non empty non proper closed Element of bool the carrier of n
r is Element of the carrier of n
{r} is non empty trivial finite set
([#] n) \ {r} is Element of bool the carrier of n
x is ordinal natural real V101() ext-real non negative set
TOP-REAL x is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() x -locally_euclidean V359() RLTopStruct
f is non empty Element of bool the carrier of n
n | f is non empty strict TopSpace-like SubSpace of n
the carrier of (TOP-REAL x) is non empty set
[: the carrier of n, the carrier of (TOP-REAL x):] is Relation-like set
bool [: the carrier of n, the carrier of (TOP-REAL x):] is set
g is non empty Relation-like the carrier of n -defined the carrier of (TOP-REAL x) -valued Function-like total quasi_total Element of bool [: the carrier of n, the carrier of (TOP-REAL x):]
g . r is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
bool the carrier of (TOP-REAL x) is set
[#] (TOP-REAL x) is non empty non proper closed Element of bool the carrier of (TOP-REAL x)
C is Relation-like NAT -defined Function-like finite V32(x) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL x)
{C} is non empty trivial functional finite V29() set
([#] (TOP-REAL x)) \ {C} is Element of bool the carrier of (TOP-REAL x)
f2 is non empty Element of bool the carrier of (TOP-REAL x)
(TOP-REAL x) | f2 is non empty strict TopSpace-like SubSpace of TOP-REAL x
dom g is non empty Element of bool the carrier of n
rng g is non empty Element of bool the carrier of (TOP-REAL x)
g " ([#] (TOP-REAL x)) is Element of bool the carrier of n
g " {C} is Element of bool the carrier of n
x is set
{x} is non empty trivial finite set
g . x is set
g " f2 is Element of bool the carrier of n
f2 |` g is Relation-like the carrier of n -defined the carrier of (TOP-REAL x) -valued f2 -valued the carrier of (TOP-REAL x) -valued Function-like Element of bool [: the carrier of n, the carrier of (TOP-REAL x):]
dom (f2 |` g) is Element of bool the carrier of n
n | (g " f2) is strict TopSpace-like SubSpace of n
[#] (n | (g " f2)) is non proper closed Element of bool the carrier of (n | (g " f2))
the carrier of (n | (g " f2)) is set
bool the carrier of (n | (g " f2)) is set
rng (f2 |` g) is Element of bool f2
bool f2 is set
[#] ((TOP-REAL x) | f2) is non empty non proper closed Element of bool the carrier of ((TOP-REAL x) | f2)
the carrier of ((TOP-REAL x) | f2) is non empty set
bool the carrier of ((TOP-REAL x) | f2) is set
[: the carrier of (n | (g " f2)), the carrier of ((TOP-REAL x) | f2):] is Relation-like set
bool [: the carrier of (n | (g " f2)), the carrier of ((TOP-REAL x) | f2):] is set
p is Relation-like the carrier of (n | (g " f2)) -defined the carrier of ((TOP-REAL x) | f2) -valued Function-like total quasi_total Element of bool [: the carrier of (n | (g " f2)), the carrier of ((TOP-REAL x) | f2):]
n is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL n) is non empty set
r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
TPlane (r,x) is non empty TopSpace-like SubSpace of TOP-REAL n
Plane (r,x) is Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
g is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
C is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
LSeg (g,C) is Element of bool the carrier of (TOP-REAL n)
f2 is ordinal natural real V101() ext-real non negative set
TOP-REAL f2 is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() f2 -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL f2) is non empty set
x is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
p is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
{ b1 where b1 is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2) : |(x,(b1 - p))| = 0 } is set
U is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
U - p is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
U - p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(x,(U - p))| is real V101() ext-real Element of REAL
V is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
V - p is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
V - p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(x,(V - p))| is real V101() ext-real Element of REAL
c is set
fc1 is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
c0 is real V101() ext-real Element of REAL
1 - c0 is real V101() ext-real set
(1 - c0) * g is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c0) * g is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c0 * C is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c0 * C is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c0) * (U - p) is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
(1 - c0) * (U - p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(x,((1 - c0) * (U - p)))| is real V101() ext-real Element of REAL
(1 - c0) * 0 is real V101() ext-real set
c0 * (V - p) is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
c0 * (V - p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(x,(c0 * (V - p)))| is real V101() ext-real Element of REAL
c0 * 0 is real V101() ext-real set
((1 - c0) * (U - p)) + (c0 * (V - p)) is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
((1 - c0) * (U - p)) + (c0 * (V - p)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
g - x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
g - x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c0) * (g - x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c0) * (g - x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c0 * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
c0 * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * C) - (c0 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * C) - (c0 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * (g - x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * (g - x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(1 - c0) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(1 - c0) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) - ((1 - c0) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) - ((1 - c0) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) - ((1 - c0) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) - ((1 - c0) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- ((1 - c0) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- ((1 - c0) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (- ((1 - c0) * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (- ((1 - c0) * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) + (- ((1 - c0) * x))) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) + (- ((1 - c0) * x))) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (1 - c0) is real V101() ext-real set
(- (1 - c0)) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (1 - c0)) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + ((- (1 - c0)) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + ((- (1 - c0)) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) + ((- (1 - c0)) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) + ((- (1 - c0)) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
c0 - 1 is real V101() ext-real set
(c0 - 1) * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 - 1) * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + ((c0 - 1) * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + ((c0 - 1) * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) + ((c0 - 1) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) + ((c0 - 1) * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
fc2 is real V101() ext-real set
fc2 * x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
fc2 * x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * x) - (fc2 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * x) - (fc2 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + ((c0 * x) - (fc2 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + ((c0 * x) - (fc2 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) + ((c0 * x) - (fc2 * x))) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) + ((c0 * x) - (fc2 * x))) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c0 * x) - (fc2 * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c0 * x) - (fc2 * x)) + ((c0 * C) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((c0 * x) - (fc2 * x)) + ((c0 * C) - (c0 * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((c0 * x) - (fc2 * x)) + ((c0 * C) - (c0 * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (c0 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (c0 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * C) + (- (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * C) + (- (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c0 * x) - (fc2 * x)) + ((c0 * C) + (- (c0 * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c0 * x) - (fc2 * x)) + ((c0 * C) + (- (c0 * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((c0 * x) - (fc2 * x)) + ((c0 * C) + (- (c0 * x)))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((c0 * x) - (fc2 * x)) + ((c0 * C) + (- (c0 * x)))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- (fc2 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
- (fc2 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * x) + (- (fc2 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * x) + (- (fc2 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((c0 * x) + (- (fc2 * x))) + ((c0 * C) + (- (c0 * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((c0 * x) + (- (fc2 * x))) + ((c0 * C) + (- (c0 * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((c0 * x) + (- (fc2 * x))) + ((c0 * C) + (- (c0 * x)))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((c0 * x) + (- (fc2 * x))) + ((c0 * C) + (- (c0 * x)))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- (fc2 * x)) + (c0 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + (c0 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- (fc2 * x)) + (c0 * x)) + (- (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- (fc2 * x)) + (c0 * x)) + (- (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((- (fc2 * x)) + (c0 * x)) + (- (c0 * x))) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((- (fc2 * x)) + (c0 * x)) + (- (c0 * x))) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + ((((- (fc2 * x)) + (c0 * x)) + (- (c0 * x))) + (c0 * C)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + ((((- (fc2 * x)) + (c0 * x)) + (- (c0 * x))) + (c0 * C)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * x) + (- (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * x) + (- (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- (fc2 * x)) + ((c0 * x) + (- (c0 * x))) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + ((c0 * x) + (- (c0 * x))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- (fc2 * x)) + ((c0 * x) + (- (c0 * x)))) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- (fc2 * x)) + ((c0 * x) + (- (c0 * x)))) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((- (fc2 * x)) + ((c0 * x) + (- (c0 * x)))) + (c0 * C)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((- (fc2 * x)) + ((c0 * x) + (- (c0 * x)))) + (c0 * C)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(c0 * x) - (c0 * x) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(c0 * x) - (c0 * x) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- (fc2 * x)) + ((c0 * x) - (c0 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + ((c0 * x) - (c0 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- (fc2 * x)) + ((c0 * x) - (c0 * x))) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- (fc2 * x)) + ((c0 * x) - (c0 * x))) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((- (fc2 * x)) + ((c0 * x) - (c0 * x))) + (c0 * C)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((- (fc2 * x)) + ((c0 * x) - (c0 * x))) + (c0 * C)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + (0. (TOP-REAL n)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + (0. (TOP-REAL n)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((- (fc2 * x)) + (0. (TOP-REAL n))) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((- (fc2 * x)) + (0. (TOP-REAL n))) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + (((- (fc2 * x)) + (0. (TOP-REAL n))) + (c0 * C)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + (((- (fc2 * x)) + (0. (TOP-REAL n))) + (c0 * C)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(- (fc2 * x)) + (c0 * C) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(- (fc2 * x)) + (c0 * C) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
((1 - c0) * g) + ((- (fc2 * x)) + (c0 * C)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
((1 - c0) * g) + ((- (fc2 * x)) + (c0 * C)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(((1 - c0) * g) + (c0 * C)) + (- (fc2 * x)) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
(((1 - c0) * g) + (c0 * C)) + (- (fc2 * x)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
- p is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
- p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
fc1 + (- p) is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
fc1 + (- p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
fc1 - p is Relation-like NAT -defined Function-like finite V32(f2) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f2)
fc1 - p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|(x,((1 - c0) * (U - p)))| + |(x,(c0 * (V - p)))| is real V101() ext-real set
|(x,(fc1 - p))| is real V101() ext-real Element of REAL
(TOP-REAL n) | (Plane (r,x)) is strict TopSpace-like SubSpace of TOP-REAL n
[#] ((TOP-REAL n) | (Plane (r,x))) is non proper closed Element of bool the carrier of ((TOP-REAL n) | (Plane (r,x)))
the carrier of ((TOP-REAL n) | (Plane (r,x))) is set
bool the carrier of ((TOP-REAL n) | (Plane (r,x))) is set
[#] (TPlane (r,x)) is non empty non proper closed Element of bool the carrier of (TPlane (r,x))
the carrier of (TPlane (r,x)) is non empty set
bool the carrier of (TPlane (r,x)) is set
n is non empty TopSpace-like TopStruct
n is non empty TopSpace-like TopStruct
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
Loops r is non empty set
Paths (r,r) is non empty set
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
Class ((EqRel (n,r)),x) is Element of bool (Loops r)
bool (Loops r) is set
the carrier of (FundamentalGroup (n,r)) is non empty set
Class ((EqRel (n,r)),f) is Element of bool (Loops r)
n is ordinal natural real V101() ext-real non negative set
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() RLTopStruct
the carrier of (TOP-REAL n) is non empty set
r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
FundamentalGroup ((TOP-REAL n),r) is non empty trivial finite 1 -element V116() V223() V224() V225() V227() V253() V254() V255() V256() V257() V258() L10()
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
the carrier of (FundamentalGroup (n,r)) is non empty set
Loops r is non empty set
Paths (r,r) is non empty set
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),x) is Element of bool (Loops r)
bool (Loops r) is set
{(Class ((EqRel (n,r)),x))} is non empty trivial finite set
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is Element of the carrier of n
EqRel (n,r,x) is Relation-like Paths (r,x) -defined Paths (r,x) -valued Element of bool [:(Paths (r,x)),(Paths (r,x)):]
Paths (r,x) is non empty set
[:(Paths (r,x)),(Paths (r,x)):] is Relation-like set
bool [:(Paths (r,x)),(Paths (r,x)):] is set
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
- g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,r
f + (- g) is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
(f + (- g)) + g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r
the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r + g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
Class ((EqRel (n,r,x)),f) is Element of bool (Paths (r,x))
bool (Paths (r,x)) is set
Class ((EqRel (n,r,x)),g) is Element of bool (Paths (r,x))
r is Element of the carrier of n
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
the carrier of (FundamentalGroup (n,r)) is non empty set
x is Element of the carrier of (FundamentalGroup (n,r))
f is Element of the carrier of (FundamentalGroup (n,r))
Loops r is non empty set
Paths (r,r) is non empty set
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),g) is Element of bool (Loops r)
bool (Loops r) is set
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),C) is Element of bool (Loops r)
n is non empty TopSpace-like () TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
n is non empty TopSpace-like TopStruct
r is non empty TopSpace-like TopStruct
the carrier of n is non empty set
the carrier of r is non empty set
[: the carrier of n, the carrier of r:] is Relation-like set
bool [: the carrier of n, the carrier of r:] is set
x is non empty Relation-like the carrier of n -defined the carrier of r -valued Function-like total quasi_total Element of bool [: the carrier of n, the carrier of r:]
f is Element of the carrier of r
FundamentalGroup (r,f) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
rng x is non empty Element of bool the carrier of r
bool the carrier of r is set
[#] r is non empty non proper closed Element of bool the carrier of r
g is Element of the carrier of n
x . g is Element of the carrier of r
FundamentalGroup (n,g) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
the carrier of (FundamentalGroup (n,g)) is non empty set
FundamentalGroup (r,(x . g)) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
the carrier of (FundamentalGroup (r,(x . g))) is non empty set
FundGrIso (x,g) is non empty Relation-like the carrier of (FundamentalGroup (n,g)) -defined the carrier of (FundamentalGroup (r,(x . g))) -valued Function-like total quasi_total Element of bool [: the carrier of (FundamentalGroup (n,g)), the carrier of (FundamentalGroup (r,(x . g))):]
[: the carrier of (FundamentalGroup (n,g)), the carrier of (FundamentalGroup (r,(x . g))):] is Relation-like set
bool [: the carrier of (FundamentalGroup (n,g)), the carrier of (FundamentalGroup (r,(x . g))):] is set
n is non empty TopSpace-like TopStruct
r is non empty TopSpace-like TopStruct
n is non empty TopSpace-like () TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Loops r is non empty set
Paths (r,r) is non empty set
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
Class ((EqRel (n,r)),x) is Element of bool (Loops r)
bool (Loops r) is set
FundamentalGroup (n,r) is non empty trivial finite 1 -element V116() V223() V224() V225() V227() V253() V254() V255() V256() V257() V258() L10()
the carrier of (FundamentalGroup (n,r)) is non empty trivial finite set
Class ((EqRel (n,r)),f) is Element of bool (Loops r)
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous Path of r,r
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
[: the carrier of n, the carrier of r:] is Relation-like set
bool [: the carrier of n, the carrier of r:] is set
x is Element of the carrier of n
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of x,x
g is non empty Relation-like the carrier of n -defined the carrier of r -valued Function-like total quasi_total continuous Element of bool [: the carrier of n, the carrier of r:]
g . x is Element of the carrier of r
g * f is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -defined the carrier of r -valued the carrier of r -valued Function-like total total quasi_total quasi_total quasi_total continuous Path of g . x,g . x
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,x) Path of x,x
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
f2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
I[01] --> (g . x) is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of r:]
[: the carrier of I[01], the carrier of r:] is Relation-like set
bool [: the carrier of I[01], the carrier of r:] is set
the carrier of I[01] --> (g . x) is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of r:]
[: the carrier of [:I[01],I[01]:], the carrier of r:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of r:] is set
g * f2 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of r -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of r:]
x is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like constant total quasi_total continuous (r,g . x) Path of g . x,g . x
p is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of r -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of r:]
U is real V101() ext-real Element of the carrier of I[01]
p . (U,0) is set
(g * f) . U is Element of the carrier of r
p . (U,1) is set
x . U is Element of the carrier of r
p . (0,U) is set
p . (1,U) is set
V is real V101() ext-real Element of the carrier of I[01]
f2 . (U,V) is set
g . (f2 . (U,V)) is set
f . U is Element of the carrier of n
g . (f . U) is Element of the carrier of r
c is real V101() ext-real Element of the carrier of I[01]
f2 . (U,c) is set
g . (f2 . (U,c)) is set
C . U is Element of the carrier of n
g . (C . U) is Element of the carrier of r
f2 . (V,U) is set
g . (f2 . (V,U)) is set
f2 . (c,U) is set
g . (f2 . (c,U)) is set
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
x is Element of the carrier of n
r is non empty TopSpace-like TopStruct
the carrier of r is non empty set
[: the carrier of n, the carrier of r:] is Relation-like set
bool [: the carrier of n, the carrier of r:] is set
g is non empty Relation-like the carrier of n -defined the carrier of r -valued Function-like total quasi_total continuous Element of bool [: the carrier of n, the carrier of r:]
g . x is Element of the carrier of r
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous (n,x) Path of x,x
g * f is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -defined the carrier of r -valued the carrier of r -valued Function-like total total quasi_total quasi_total quasi_total continuous Path of g . x,g . x
C is non empty Relation-like the carrier of I[01] -defined the carrier of r -valued Function-like total quasi_total continuous Path of g . x,g . x
n is non empty TopSpace-like () TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
FundamentalGroup (n,r) is non empty V116() V223() V224() V225() V253() V254() V255() V256() V257() V258() L10()
the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r
the carrier of (FundamentalGroup (n,r)) is non empty set
Loops r is non empty set
Paths (r,r) is non empty set
EqRel (n,r) is non empty Relation-like Loops r -defined Loops r -valued total quasi_total V70() V72() V77() Element of bool [:(Loops r),(Loops r):]
[:(Loops r),(Loops r):] is Relation-like set
bool [:(Loops r),(Loops r):] is set
EqRel (n,r,r) is Relation-like Paths (r,r) -defined Paths (r,r) -valued Element of bool [:(Paths (r,r)),(Paths (r,r)):]
[:(Paths (r,r)),(Paths (r,r)):] is Relation-like set
bool [:(Paths (r,r)),(Paths (r,r)):] is set
Class ((EqRel (n,r)), the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r) is Element of bool (Loops r)
bool (Loops r) is set
{(Class ((EqRel (n,r)), the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r))} is non empty trivial finite set
g is set
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
Class ((EqRel (n,r)),C) is Element of bool (Loops r)
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r
g is set
Class (EqRel (n,r)) is a_partition of Loops r
n is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() () RLTopStruct
the carrier of (TOP-REAL n) is non empty set
r is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
TPlane (r,x) is non empty TopSpace-like pathwise_connected convex SubSpace of TOP-REAL n
the carrier of (TPlane (r,x)) is non empty set
f is Element of the carrier of (TPlane (r,x))
FundamentalGroup ((TPlane (r,x)),f) is non empty trivial finite 1 -element V116() V223() V224() V225() V227() V253() V254() V255() V256() V257() V258() L10()
n is non empty TopSpace-like TopStruct
the carrier of n is non empty set
r is Element of the carrier of n
x is non empty TopSpace-like SubSpace of n
the carrier of x is non empty set
f is Element of the carrier of x
g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Path of r,r
C is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like total quasi_total continuous Path of f,f
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like constant total quasi_total continuous (x,f) Path of f,f
I[01] --> f is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of x:]
[: the carrier of I[01], the carrier of x:] is Relation-like set
bool [: the carrier of I[01], the carrier of x:] is set
the carrier of I[01] --> f is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of x:]
I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> r is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total continuous (n,r) Path of r,r
n is TopStruct
the carrier of n is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
n is TopStruct
the carrier of n is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
r is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
x is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
dom x is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
f is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | f is strict TopSpace-like real-membered SubSpace of R^1
g is TopSpace-like real-membered SubSpace of R^1
[#] g is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of g
the carrier of g is complex-membered ext-real-membered real-membered set
bool the carrier of g is set
[#] n is non proper Element of bool the carrier of n
bool the carrier of n is set
[:([#] g),([#] n):] is Relation-like set
bool [:([#] g),([#] n):] is set
C is Relation-like [#] g -defined [#] n -valued Element of bool [:([#] g),([#] n):]
dom C is complex-membered ext-real-membered real-membered Element of bool ([#] g)
bool ([#] g) is set
[: the carrier of g, the carrier of n:] is Relation-like set
bool [: the carrier of g, the carrier of n:] is set
f2 is Relation-like the carrier of g -defined the carrier of n -valued Function-like quasi_total Element of bool [: the carrier of g, the carrier of n:]
x is Element of bool the carrier of n
f2 " x is complex-membered ext-real-membered real-membered Element of bool the carrier of g
n is TopStruct
the carrier of n is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
r is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
n is TopStruct
the carrier of n is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
bool (PFuncs (REAL,([#] n))) is set
x is set
f is Relation-like Function-like Element of PFuncs (REAL,([#] n))
n is TopStruct
(n) is functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
x is Relation-like Function-like Element of PFuncs (REAL,([#] n))
n is TopStruct
the carrier of n is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
[#] n is non proper Element of bool the carrier of n
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
x is Relation-like Function-like Element of PFuncs (REAL,([#] n))
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
n is TopStruct
the carrier of n is set
[#] n is non proper Element of bool the carrier of n
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Element of the carrier of n
x is Element of the carrier of n
f is Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like quasi_total Path of r,x
f . 0 is set
f . 1 is set
[#] I[01] is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
dom f is complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] R^1 is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | g is strict TopSpace-like real-membered SubSpace of R^1
rng f is Element of bool the carrier of n
C is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
f2 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
C is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
x is Relation-like Function-like Element of PFuncs (REAL,([#] n))
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
dom r is set
rng r is set
x is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom x is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
[#] R^1 is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
rng x is Element of bool the carrier of n
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
dom r is set
x is set
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
r is Relation-like Function-like Element of (n)
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
the Element of the carrier of n is Element of the carrier of n
I[01] --> the Element of the carrier of n is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
the carrier of I[01] --> the Element of the carrier of n is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like constant total quasi_total Element of bool [: the carrier of I[01], the carrier of n:]
(I[01] --> the Element of the carrier of n) . 0 is set
(I[01] --> the Element of the carrier of n) . 1 is set
the non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of the Element of the carrier of n, the Element of the carrier of n is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of the Element of the carrier of n, the Element of the carrier of n
g is Relation-like Function-like Element of (n)
dom g is complex-membered ext-real-membered real-membered set
inf [.0,1.] is ext-real set
sup [.0,1.] is ext-real set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like (n) Element of (n)
dom r is complex-membered ext-real-membered real-membered set
inf (dom r) is ext-real set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like (n) Element of (n)
dom r is complex-membered ext-real-membered real-membered set
sup (dom r) is ext-real set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
x is Relation-like Function-like (n) Element of (n)
dom x is non empty complex-membered ext-real-membered real-membered set
r is Relation-like Function-like Element of (n)
x is Relation-like Function-like (n) Element of (n)
dom x is non empty complex-membered ext-real-membered real-membered set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
r . (inf (dom r)) is set
rng r is non empty set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
rng r is non empty set
n is non empty TopStruct
the carrier of n is non empty set
[#] n is non empty non proper Element of bool the carrier of n
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Element of the carrier of n
x is Element of the carrier of n
f is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of r,x
g is Relation-like Function-like Element of (n)
dom g is complex-membered ext-real-membered real-membered set
inf (dom g) is ext-real set
sup (dom g) is ext-real set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
x is real V101() ext-real set
f is real V101() ext-real set
[.x,f.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
r | [.x,f.] is Relation-like Function-like set
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
g | [.x,f.] is Relation-like the carrier of R^1 -defined [.x,f.] -defined the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
dom g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
f2 is complex-membered ext-real-membered real-membered interval Element of bool REAL
x is complex-membered ext-real-membered real-membered interval Element of bool REAL
f2 /\ x is complex-membered ext-real-membered real-membered interval Element of bool REAL
dom (g | [.x,f.]) is complex-membered ext-real-membered real-membered Element of bool [.x,f.]
bool [.x,f.] is set
R^1 | (dom g) is strict TopSpace-like real-membered SubSpace of R^1
p is TopSpace-like real-membered SubSpace of R^1
the carrier of p is complex-membered ext-real-membered real-membered set
[: the carrier of p, the carrier of n:] is Relation-like set
bool [: the carrier of p, the carrier of n:] is set
U is Relation-like the carrier of p -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of p, the carrier of n:]
[#] p is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of p
bool the carrier of p is set
V is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
(dom g) /\ [.x,f.] is complex-membered ext-real-membered real-membered Element of bool REAL
c is complex-membered ext-real-membered real-membered Element of bool the carrier of p
p | c is strict TopSpace-like real-membered SubSpace of p
the carrier of (p | c) is complex-membered ext-real-membered real-membered set
[: the carrier of (p | c), the carrier of n:] is Relation-like set
bool [: the carrier of (p | c), the carrier of n:] is set
U | c is Relation-like the carrier of p -defined c -defined the carrier of p -defined the carrier of n -valued Function-like Element of bool [: the carrier of p, the carrier of n:]
fc1 is Relation-like the carrier of (p | c) -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of (p | c), the carrier of n:]
g | (dom g) is Relation-like the carrier of R^1 -defined dom g -defined the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
(g | (dom g)) | [.x,f.] is Relation-like the carrier of R^1 -defined [.x,f.] -defined the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
R^1 | V is strict TopSpace-like real-membered SubSpace of R^1
the carrier of (R^1 | V) is complex-membered ext-real-membered real-membered set
bool the carrier of (R^1 | V) is set
c0 is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | c0 is strict TopSpace-like real-membered SubSpace of R^1
f0 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom x is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
f is non empty ext-real-membered left_end right_end interval set
inf f is ext-real set
sup f is ext-real set
[.(inf f),(sup f).] is interval set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
(n,r) is Element of the carrier of n
inf (dom r) is real V101() ext-real set
r . (inf (dom r)) is set
(n,r) is Element of the carrier of n
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | (dom g) is strict TopSpace-like real-membered SubSpace of R^1
C is TopSpace-like real-membered SubSpace of R^1
the carrier of C is complex-membered ext-real-membered real-membered set
[: the carrier of C, the carrier of n:] is Relation-like set
bool [: the carrier of C, the carrier of n:] is set
f2 is Relation-like the carrier of C -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of C, the carrier of n:]
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of n:]
x . 0 is set
x . 1 is set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
(n,r) is Element of the carrier of n
r . (inf (dom r)) is set
(n,r) is Element of the carrier of n
r . (sup (dom r)) is set
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | (dom g) is strict TopSpace-like real-membered SubSpace of R^1
C is TopSpace-like real-membered SubSpace of R^1
the carrier of C is complex-membered ext-real-membered real-membered set
[: the carrier of C, the carrier of n:] is Relation-like set
bool [: the carrier of C, the carrier of n:] is set
f2 is Relation-like the carrier of C -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of C, the carrier of n:]
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x is non empty TopStruct
the carrier of x is non empty set
[: the carrier of I[01], the carrier of x:] is Relation-like set
bool [: the carrier of I[01], the carrier of x:] is set
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
p is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of x:]
f2 * p is Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like Element of bool [: the carrier of I[01], the carrier of n:]
dom (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 0 is real V101() ext-real set
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
((sup (dom r)) - (inf (dom r))) / (1 - 0) is real V101() ext-real set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0)) + (inf (dom r)) is real V101() ext-real set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 1 is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0)) + (inf (dom r)) is real V101() ext-real set
U is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of n:]
U . 0 is set
U . 1 is set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
(n,r) is Element of the carrier of n
r . (inf (dom r)) is set
(n,r) is Element of the carrier of n
r . (sup (dom r)) is set
x is Element of the carrier of n
f is Element of the carrier of n
dom (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 0 is real V101() ext-real set
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
((sup (dom r)) - (inf (dom r))) / (1 - 0) is real V101() ext-real set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0)) + (inf (dom r)) is real V101() ext-real set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 1 is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0)) + (inf (dom r)) is real V101() ext-real set
g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,f
g . 0 is set
g . 1 is set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,r) is Element of the carrier of n
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
r . (inf (dom r)) is set
rng r is non empty set
(n,r) is Element of the carrier of n
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
n is non empty TopStruct
the carrier of n is non empty set
[#] n is non empty non proper Element of bool the carrier of n
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
x is real V101() ext-real set
r is real V101() ext-real set
Closed-Interval-TSpace (r,x) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace (r,x)) is non empty complex-membered ext-real-membered real-membered set
L[01] (r,x,0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace (r,x)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of (Closed-Interval-TSpace (0,1)):] is set
f is Element of the carrier of n
g is Element of the carrier of n
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of f,g
C * (L[01] (r,x,0,1)) is Relation-like the carrier of (Closed-Interval-TSpace (r,x)) -defined the carrier of n -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of n:]
[: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of n:] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (r,x)), the carrier of n:] is set
C . 0 is set
C . 1 is set
rng (L[01] (r,x,0,1)) is non empty complex-membered ext-real-membered real-membered Element of bool REAL
[#] (Closed-Interval-TSpace (0,1)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
dom C is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
dom (C * (L[01] (r,x,0,1))) is complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (r,x))
bool the carrier of (Closed-Interval-TSpace (r,x)) is set
dom (L[01] (r,x,0,1)) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (r,x))
[#] (Closed-Interval-TSpace (r,x)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (r,x))
[.r,x.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
rng (C * (L[01] (r,x,0,1))) is Element of bool the carrier of n
x is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
dom x is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | (dom x) is strict TopSpace-like real-membered SubSpace of R^1
[#] (R^1 | (dom x)) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | (dom x))
the carrier of (R^1 | (dom x)) is complex-membered ext-real-membered real-membered set
bool the carrier of (R^1 | (dom x)) is set
[: the carrier of (R^1 | (dom x)), the carrier of n:] is Relation-like set
bool [: the carrier of (R^1 | (dom x)), the carrier of n:] is set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is set
U is Relation-like the carrier of (R^1 | (dom x)) -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of (R^1 | (dom x)), the carrier of n:]
c is Relation-like Function-like Element of (n)
dom c is complex-membered ext-real-membered real-membered set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,r) is Element of the carrier of n
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
r . (inf (dom r)) is set
(n,r) is Element of the carrier of n
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | (dom g) is strict TopSpace-like real-membered SubSpace of R^1
C is TopSpace-like real-membered SubSpace of R^1
the carrier of C is complex-membered ext-real-membered real-membered set
[: the carrier of C, the carrier of n:] is Relation-like set
bool [: the carrier of C, the carrier of n:] is set
f2 is Relation-like the carrier of C -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of C, the carrier of n:]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
f2 * (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of n -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is set
rng (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool REAL
[#] (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))))
bool the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
dom (f2 * (L[01] (0,1,(inf (dom r)),(sup (dom r))))) is complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
dom (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
[#] (Closed-Interval-TSpace (0,1)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
rng (f2 * (L[01] (0,1,(inf (dom r)),(sup (dom r))))) is Element of bool the carrier of n
[: the carrier of I[01], the carrier of n:] is Relation-like set
bool [: the carrier of I[01], the carrier of n:] is set
V is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of n:]
dom V is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 0 is real V101() ext-real set
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
((sup (dom r)) - (inf (dom r))) / (1 - 0) is real V101() ext-real set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0)) + (inf (dom r)) is real V101() ext-real set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 1 is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0)) + (inf (dom r)) is real V101() ext-real set
V . 0 is set
V . 1 is set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
C is Element of the carrier of n
f2 is Element of the carrier of n
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of C,f2
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom f is non empty complex-membered ext-real-membered real-membered set
inf (dom f) is real V101() ext-real set
sup (dom f) is real V101() ext-real set
L[01] (0,1,(inf (dom f)),(sup (dom f))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):]
Closed-Interval-TSpace ((inf (dom f)),(sup (dom f))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):] is set
(L[01] (0,1,(inf (dom f)),(sup (dom f)))) * f is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
p is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of C,f2
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom g is non empty complex-membered ext-real-membered real-membered set
inf (dom g) is real V101() ext-real set
sup (dom g) is real V101() ext-real set
L[01] (0,1,(inf (dom g)),(sup (dom g))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom g)),(sup (dom g)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom g)),(sup (dom g)))):]
Closed-Interval-TSpace ((inf (dom g)),(sup (dom g))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom g)),(sup (dom g)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom g)),(sup (dom g)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom g)),(sup (dom g)))):] is set
(L[01] (0,1,(inf (dom g)),(sup (dom g)))) * g is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
n is non empty TopSpace-like TopStruct
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,f) is Element of the carrier of n
dom f is non empty complex-membered ext-real-membered real-membered set
inf (dom f) is real V101() ext-real set
f . (inf (dom f)) is set
(n,f) is Element of the carrier of n
sup (dom f) is real V101() ext-real set
f . (sup (dom f)) is set
L[01] (0,1,(inf (dom f)),(sup (dom f))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):]
Closed-Interval-TSpace ((inf (dom f)),(sup (dom f))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom f)),(sup (dom f)))):] is set
(L[01] (0,1,(inf (dom f)),(sup (dom f)))) * f is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
g is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of (n,f),(n,f)
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
f is Element of the carrier of n
g is Element of the carrier of n
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of f,g
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of f,g
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
dom x is non empty complex-membered ext-real-membered real-membered set
inf (dom x) is real V101() ext-real set
sup (dom x) is real V101() ext-real set
dom C is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
dom f2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
L[01] (0,1,(inf (dom x)),(sup (dom x))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):]
Closed-Interval-TSpace ((inf (dom x)),(sup (dom x))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is set
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) * x is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
x is Element of the carrier of n
p is Element of the carrier of n
U is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,p
V is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of x,p
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
c is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
c . (0,0) is set
U . 0 is set
c . (0,1) is set
V . 0 is set
c . (1,0) is set
U . 1 is set
c . (1,1) is set
V . 1 is set
C * (L[01] (0,1,0,1)) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of n -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:] is set
f2 * (L[01] (0,1,0,1)) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of n -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of n:]
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,r) is Element of the carrier of n
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
r . (inf (dom r)) is set
(n,x) is Element of the carrier of n
dom x is non empty complex-membered ext-real-membered real-membered set
inf (dom x) is real V101() ext-real set
x . (inf (dom x)) is set
(n,r) is Element of the carrier of n
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
(n,x) is Element of the carrier of n
sup (dom x) is real V101() ext-real set
x . (sup (dom x)) is set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
L[01] (0,1,(inf (dom x)),(sup (dom x))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):]
Closed-Interval-TSpace ((inf (dom x)),(sup (dom x))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is set
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) * x is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
f is Element of the carrier of n
g is Element of the carrier of n
C is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of f,g
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of f,g
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
x is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
x . (0,0) is set
C . 0 is set
x . (0,1) is set
f2 . 0 is set
x . (1,0) is set
C . 1 is set
x . (1,1) is set
f2 . 1 is set
dom (L[01] (0,1,(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
dom (L[01] (0,1,(inf (dom x)),(sup (dom x)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) . 0 is real V101() ext-real set
(sup (dom x)) - (inf (dom x)) is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
((sup (dom x)) - (inf (dom x))) / (1 - 0) is real V101() ext-real set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((sup (dom x)) - (inf (dom x))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom x)) - (inf (dom x))) / (1 - 0)) * (0 - 0)) + (inf (dom x)) is real V101() ext-real set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 0 is real V101() ext-real set
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
((sup (dom r)) - (inf (dom r))) / (1 - 0) is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0)) + (inf (dom r)) is real V101() ext-real set
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) . 1 is real V101() ext-real set
(((sup (dom x)) - (inf (dom x))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom x)) - (inf (dom x))) / (1 - 0)) * (1 - 0)) + (inf (dom x)) is real V101() ext-real set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) . 1 is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0)) + (inf (dom r)) is real V101() ext-real set
n is non empty TopSpace-like TopStruct
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom x is non empty complex-membered ext-real-membered real-membered set
f is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | f is strict TopSpace-like real-membered SubSpace of R^1
[:(R^1 | f),I[01]:] is strict TopSpace-like TopStruct
the carrier of [:(R^1 | f),I[01]:] is set
[: the carrier of [:(R^1 | f),I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:(R^1 | f),I[01]:], the carrier of n:] is set
the carrier of (R^1 | f) is complex-membered ext-real-membered real-membered set
inf f is ext-real set
sup f is ext-real set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
[#] I[01] is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
inf (dom x) is real V101() ext-real set
sup (dom x) is real V101() ext-real set
L[01] (0,1,(inf (dom x)),(sup (dom x))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):]
Closed-Interval-TSpace ((inf (dom x)),(sup (dom x))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is set
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) * x is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
g is Element of the carrier of n
C is Element of the carrier of n
f2 is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of g,C
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of g,C
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
p is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
L[01] ((inf (dom r)),(sup (dom r)),0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace (0,1)):] is set
c is non empty TopSpace-like TopStruct
the carrier of c is non empty set
[: the carrier of c, the carrier of I[01]:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of c, the carrier of I[01]:] is set
[:c,I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:c,I[01]:] is non empty set
fc1 is non empty Relation-like the carrier of c -defined the carrier of I[01] -valued Function-like total quasi_total continuous complex-yielding ext-real-valued real-valued Element of bool [: the carrier of c, the carrier of I[01]:]
fc2 is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like total quasi_total continuous complex-yielding ext-real-valued real-valued Element of bool [: the carrier of I[01], the carrier of I[01]:]
[:fc1,fc2:] is non empty Relation-like the carrier of [:c,I[01]:] -defined the carrier of [:I[01],I[01]:] -valued Function-like total quasi_total continuous Element of bool [: the carrier of [:c,I[01]:], the carrier of [:I[01],I[01]:]:]
[: the carrier of [:c,I[01]:], the carrier of [:I[01],I[01]:]:] is Relation-like set
bool [: the carrier of [:c,I[01]:], the carrier of [:I[01],I[01]:]:] is set
p * [:fc1,fc2:] is non empty Relation-like the carrier of [:c,I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:c,I[01]:], the carrier of n:]
[: the carrier of [:c,I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:c,I[01]:], the carrier of n:] is set
f0 is Relation-like the carrier of [:(R^1 | f),I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:(R^1 | f),I[01]:], the carrier of n:]
dom fc1 is non empty Element of bool the carrier of c
bool the carrier of c is set
[#] (R^1 | f) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f)
bool the carrier of (R^1 | f) is set
dom fc2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
fc2 . 0 is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
(1 - 0) / (1 - 0) is real V101() ext-real non negative set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
((1 - 0) / (1 - 0)) * (0 - 0) is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((1 - 0) / (1 - 0)) * (0 - 0)) + 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
fc2 . 1 is real V101() ext-real set
((1 - 0) / (1 - 0)) * (1 - 0) is real V101() ext-real non negative set
(((1 - 0) / (1 - 0)) * (1 - 0)) + 0 is real V101() ext-real non negative set
rng fc1 is non empty complex-membered ext-real-membered real-membered Element of bool REAL
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
c1 is real V101() ext-real Element of the carrier of (R^1 | f)
f0 . (c1,0) is set
r . c1 is set
f0 . (c1,1) is set
x . c1 is set
[c1,0] is non empty set
{c1,0} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{c1} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{c1,0},{c1}} is non empty finite V29() set
[:(dom fc1),(dom fc2):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:c,I[01]:]
bool the carrier of [:c,I[01]:] is set
dom [:fc1,fc2:] is non empty Element of bool the carrier of [:c,I[01]:]
[c1,1] is non empty set
{c1,1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{c1,1},{c1}} is non empty finite V29() set
fc1 . c1 is real V101() ext-real set
[#] (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))))
bool the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is set
L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
[: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
dom (L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))))
(L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) . c1 is real V101() ext-real set
((sup (dom r)) - (inf (dom r))) / ((sup (dom r)) - (inf (dom r))) is real V101() ext-real set
c1 - (inf (dom r)) is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / ((sup (dom r)) - (inf (dom r)))) * (c1 - (inf (dom r))) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / ((sup (dom r)) - (inf (dom r)))) * (c1 - (inf (dom r)))) + (inf (dom r)) is real V101() ext-real set
1 * (c1 - (inf (dom r))) is real V101() ext-real set
(1 * (c1 - (inf (dom r)))) + (inf (dom r)) is real V101() ext-real set
f0 . [c1,0] is set
[:fc1,fc2:] . [c1,0] is set
p . ([:fc1,fc2:] . [c1,0]) is set
[:fc1,fc2:] . (c1,0) is set
p . ([:fc1,fc2:] . (c1,0)) is set
[(fc1 . c1),(fc2 . 0)] is non empty set
{(fc1 . c1),(fc2 . 0)} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{(fc1 . c1)} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(fc1 . c1),(fc2 . 0)},{(fc1 . c1)}} is non empty finite V29() set
p . [(fc1 . c1),(fc2 . 0)] is set
p . ((fc1 . c1),0) is set
f2 . (fc1 . c1) is set
fc1 * ((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r) is Relation-like the carrier of c -defined Function-like set
(fc1 * ((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r)) . c1 is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * fc1 is Relation-like the carrier of c -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [: the carrier of c, the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
[: the carrier of c, the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of c, the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * fc1) * r is Relation-like the carrier of c -defined Function-like set
(((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * fc1) * r) . c1 is set
(L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -defined Function-like set
((L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) * r) . c1 is set
f0 . [c1,1] is set
[:fc1,fc2:] . [c1,1] is set
p . ([:fc1,fc2:] . [c1,1]) is set
[:fc1,fc2:] . (c1,1) is set
p . ([:fc1,fc2:] . (c1,1)) is set
[(fc1 . c1),(fc2 . 1)] is non empty set
{(fc1 . c1),(fc2 . 1)} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(fc1 . c1),(fc2 . 1)},{(fc1 . c1)}} is non empty finite V29() set
p . [(fc1 . c1),(fc2 . 1)] is set
p . ((fc1 . c1),1) is set
x . (fc1 . c1) is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * x is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
fc1 * ((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * x) is Relation-like the carrier of c -defined Function-like set
(fc1 * ((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * x)) . c1 is set
((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * fc1) * x is Relation-like the carrier of c -defined Function-like set
(((L[01] (0,1,(inf (dom r)),(sup (dom r)))) * fc1) * x) . c1 is set
(L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) * x is Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -defined Function-like set
((L[01] ((inf (dom r)),(sup (dom r)),(inf (dom r)),(sup (dom r)))) * x) . c1 is set
c1 is real V101() ext-real Element of the carrier of I[01]
f0 . ((inf f),c1) is set
f0 . ((sup f),c1) is set
[(inf f),c1] is non empty set
{(inf f),c1} is non empty finite ext-real-membered left_end right_end set
{(inf f)} is non empty trivial finite ext-real-membered left_end right_end set
{{(inf f),c1},{(inf f)}} is non empty finite V29() set
[:(dom fc1),(dom fc2):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:c,I[01]:]
bool the carrier of [:c,I[01]:] is set
dom [:fc1,fc2:] is non empty Element of bool the carrier of [:c,I[01]:]
[(sup f),c1] is non empty set
{(sup f),c1} is non empty finite ext-real-membered left_end right_end set
{(sup f)} is non empty trivial finite ext-real-membered left_end right_end set
{{(sup f),c1},{(sup f)}} is non empty finite V29() set
fc2 . c1 is real V101() ext-real Element of the carrier of I[01]
c1 - 0 is real V101() ext-real set
((1 - 0) / (1 - 0)) * (c1 - 0) is real V101() ext-real set
(((1 - 0) / (1 - 0)) * (c1 - 0)) + 0 is real V101() ext-real set
fc1 . (inf f) is real V101() ext-real set
(1 - 0) / ((sup (dom r)) - (inf (dom r))) is real V101() ext-real set
(inf (dom r)) - (inf (dom r)) is real V101() ext-real set
((1 - 0) / ((sup (dom r)) - (inf (dom r)))) * ((inf (dom r)) - (inf (dom r))) is real V101() ext-real set
(((1 - 0) / ((sup (dom r)) - (inf (dom r)))) * ((inf (dom r)) - (inf (dom r)))) + 0 is real V101() ext-real set
fc1 . (sup f) is real V101() ext-real set
((1 - 0) / ((sup (dom r)) - (inf (dom r)))) * ((sup (dom r)) - (inf (dom r))) is real V101() ext-real set
(((1 - 0) / ((sup (dom r)) - (inf (dom r)))) * ((sup (dom r)) - (inf (dom r)))) + 0 is real V101() ext-real set
((sup (dom r)) - (inf (dom r))) / ((sup (dom r)) - (inf (dom r))) is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / ((sup (dom r)) - (inf (dom r)))) * 1 is real V101() ext-real set
f0 . [(inf f),c1] is set
[:fc1,fc2:] . [(inf f),c1] is set
p . ([:fc1,fc2:] . [(inf f),c1]) is set
[:fc1,fc2:] . ((inf f),c1) is set
p . ([:fc1,fc2:] . ((inf f),c1)) is set
[(fc1 . (inf f)),(fc2 . c1)] is non empty set
{(fc1 . (inf f)),(fc2 . c1)} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{(fc1 . (inf f))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(fc1 . (inf f)),(fc2 . c1)},{(fc1 . (inf f))}} is non empty finite V29() set
p . [(fc1 . (inf f)),(fc2 . c1)] is set
p . ((fc1 . (inf f)),c1) is set
f0 . [(sup f),c1] is set
[:fc1,fc2:] . [(sup f),c1] is set
p . ([:fc1,fc2:] . [(sup f),c1]) is set
[:fc1,fc2:] . ((sup f),c1) is set
p . ([:fc1,fc2:] . ((sup f),c1)) is set
[(fc1 . (sup f)),(fc2 . c1)] is non empty set
{(fc1 . (sup f)),(fc2 . c1)} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{(fc1 . (sup f))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(fc1 . (sup f)),(fc2 . c1)},{(fc1 . (sup f))}} is non empty finite V29() set
p . [(fc1 . (sup f)),(fc2 . c1)] is set
p . ((fc1 . (sup f)),c1) is set
[.(inf (dom r)),(inf (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
{(inf (dom r))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
(n,r) is Element of the carrier of n
r . (inf (dom r)) is set
[:(R^1 | f),I[01]:] --> (n,r) is Relation-like the carrier of [:(R^1 | f),I[01]:] -defined the carrier of n -valued Function-like total quasi_total continuous Element of bool [: the carrier of [:(R^1 | f),I[01]:], the carrier of n:]
the carrier of [:(R^1 | f),I[01]:] --> (n,r) is Relation-like the carrier of [:(R^1 | f),I[01]:] -defined the carrier of n -valued Function-like constant total quasi_total quasi_total continuous Element of bool [: the carrier of [:(R^1 | f),I[01]:], the carrier of n:]
f2 is real V101() ext-real Element of the carrier of (R^1 | f)
([:(R^1 | f),I[01]:] --> (n,r)) . (f2,0) is set
r . f2 is set
([:(R^1 | f),I[01]:] --> (n,r)) . (f2,1) is set
x . f2 is set
[#] (R^1 | f) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f)
bool the carrier of (R^1 | f) is set
[f2,0] is non empty set
{f2,0} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{f2} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{f2,0},{f2}} is non empty finite V29() set
[:([#] (R^1 | f)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | f),I[01]:]
bool the carrier of [:(R^1 | f),I[01]:] is set
[f2,1] is non empty set
{f2,1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{f2,1},{f2}} is non empty finite V29() set
([:(R^1 | f),I[01]:] --> (n,r)) . [f2,0] is set
([:(R^1 | f),I[01]:] --> (n,r)) . [f2,1] is set
(n,x) is Element of the carrier of n
inf (dom x) is real V101() ext-real set
x . (inf (dom x)) is set
f2 is real V101() ext-real Element of the carrier of I[01]
([:(R^1 | f),I[01]:] --> (n,r)) . ((inf f),f2) is set
([:(R^1 | f),I[01]:] --> (n,r)) . ((sup f),f2) is set
[#] (R^1 | f) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f)
bool the carrier of (R^1 | f) is set
[(inf f),f2] is non empty set
{(inf f),f2} is non empty finite ext-real-membered left_end right_end set
{(inf f)} is non empty trivial finite ext-real-membered left_end right_end set
{{(inf f),f2},{(inf f)}} is non empty finite V29() set
[:([#] (R^1 | f)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | f),I[01]:]
bool the carrier of [:(R^1 | f),I[01]:] is set
[(sup f),f2] is non empty set
{(sup f),f2} is non empty finite ext-real-membered left_end right_end set
{(sup f)} is non empty trivial finite ext-real-membered left_end right_end set
{{(sup f),f2},{(sup f)}} is non empty finite V29() set
([:(R^1 | f),I[01]:] --> (n,r)) . [(inf f),f2] is set
([:(R^1 | f),I[01]:] --> (n,r)) . [(sup f),f2] is set
g is Relation-like the carrier of [:(R^1 | f),I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:(R^1 | f),I[01]:], the carrier of n:]
C is Element of the carrier of n
f2 is Element of the carrier of n
[#] (R^1 | f) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f)
bool the carrier of (R^1 | f) is set
g . ((inf f),0) is set
(n,r) is Element of the carrier of n
r . (inf (dom r)) is set
g . ((sup f),0) is set
(n,r) is Element of the carrier of n
r . (sup (dom r)) is set
L[01] (0,1,(inf (dom r)),(sup (dom r))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom r)),(sup (dom r)))):] is set
(L[01] (0,1,(inf (dom r)),(sup (dom r)))) * r is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
g . ((inf f),1) is set
(n,x) is Element of the carrier of n
inf (dom x) is real V101() ext-real set
x . (inf (dom x)) is set
g . ((sup f),1) is set
(n,x) is Element of the carrier of n
sup (dom x) is real V101() ext-real set
x . (sup (dom x)) is set
L[01] (0,1,(inf (dom x)),(sup (dom x))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):]
Closed-Interval-TSpace ((inf (dom x)),(sup (dom x))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom x)),(sup (dom x)))):] is set
(L[01] (0,1,(inf (dom x)),(sup (dom x)))) * x is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
c is non empty TopSpace-like TopStruct
the carrier of c is non empty set
[: the carrier of I[01], the carrier of c:] is Relation-like set
bool [: the carrier of I[01], the carrier of c:] is set
[:c,I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:c,I[01]:] is non empty set
fc1 is non empty Relation-like the carrier of I[01] -defined the carrier of c -valued Function-like total quasi_total continuous Element of bool [: the carrier of I[01], the carrier of c:]
fc2 is non empty Relation-like the carrier of I[01] -defined the carrier of I[01] -valued Function-like total quasi_total continuous complex-yielding ext-real-valued real-valued Element of bool [: the carrier of I[01], the carrier of I[01]:]
[:fc1,fc2:] is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of [:c,I[01]:] -valued Function-like total quasi_total continuous Element of bool [: the carrier of [:I[01],I[01]:], the carrier of [:c,I[01]:]:]
[: the carrier of [:I[01],I[01]:], the carrier of [:c,I[01]:]:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of [:c,I[01]:]:] is set
g * [:fc1,fc2:] is Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
[: the carrier of [:I[01],I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:I[01],I[01]:], the carrier of n:] is set
dom fc1 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom fc2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
fc2 . 0 is real V101() ext-real set
1 - 0 is non empty real V101() ext-real positive non negative set
(1 - 0) / (1 - 0) is real V101() ext-real non negative set
0 - 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
((1 - 0) / (1 - 0)) * (0 - 0) is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
(((1 - 0) / (1 - 0)) * (0 - 0)) + 0 is empty trivial real Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional finite finite-yielding V29() V101() FinSequence-like FinSubsequence-like FinSequence-membered ext-real non positive non negative complex-yielding ext-real-valued real-valued natural-valued increasing decreasing non-decreasing non-increasing complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V171() bounded_below bounded_above real-bounded interval Function-yielding V204() set
fc2 . 1 is real V101() ext-real set
((1 - 0) / (1 - 0)) * (1 - 0) is real V101() ext-real non negative set
(((1 - 0) / (1 - 0)) * (1 - 0)) + 0 is real V101() ext-real non negative set
f0 is non empty Relation-like the carrier of [:I[01],I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:I[01],I[01]:], the carrier of n:]
x is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of C,f2
p is non empty Relation-like the carrier of I[01] -defined the carrier of n -valued Function-like total quasi_total Path of C,f2
c1 is real V101() ext-real Element of the carrier of I[01]
f0 . (c1,0) is set
x . c1 is Element of the carrier of n
f0 . (c1,1) is set
p . c1 is Element of the carrier of n
f0 . (0,c1) is set
f0 . (1,c1) is set
[c1,0] is non empty set
{c1,0} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{c1} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{c1,0},{c1}} is non empty finite V29() set
[:(dom fc1),(dom fc2):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:I[01],I[01]:]
dom [:fc1,fc2:] is non empty Element of bool the carrier of [:I[01],I[01]:]
[c1,1] is non empty set
{c1,1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{c1,1},{c1}} is non empty finite V29() set
[0,c1] is non empty set
{0,c1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{0} is non empty trivial functional finite V29() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded set
{{0,c1},{0}} is non empty finite V29() set
[1,c1] is non empty set
{1,c1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{1} is non empty trivial finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded set
{{1,c1},{1}} is non empty finite V29() set
fc1 . 0 is set
(sup (dom r)) - (inf (dom r)) is real V101() ext-real set
((sup (dom r)) - (inf (dom r))) / (1 - 0) is real V101() ext-real set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (0 - 0)) + (inf (dom r)) is real V101() ext-real set
fc1 . 1 is set
(((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0) is real V101() ext-real set
((((sup (dom r)) - (inf (dom r))) / (1 - 0)) * (1 - 0)) + (inf (dom r)) is real V101() ext-real set
fc2 . c1 is real V101() ext-real Element of the carrier of I[01]
c1 - 0 is real V101() ext-real set
((1 - 0) / (1 - 0)) * (c1 - 0) is real V101() ext-real set
(((1 - 0) / (1 - 0)) * (c1 - 0)) + 0 is real V101() ext-real set
f0 . [c1,0] is set
[:fc1,fc2:] . [c1,0] is set
g . ([:fc1,fc2:] . [c1,0]) is set
[:fc1,fc2:] . (c1,0) is set
g . ([:fc1,fc2:] . (c1,0)) is set
fc1 . c1 is Element of the carrier of c
[(fc1 . c1),(fc2 . 0)] is non empty set
{(fc1 . c1),(fc2 . 0)} is non empty finite set
{(fc1 . c1)} is non empty trivial finite set
{{(fc1 . c1),(fc2 . 0)},{(fc1 . c1)}} is non empty finite V29() set
g . [(fc1 . c1),(fc2 . 0)] is set
g . ((fc1 . c1),0) is set
r . (fc1 . c1) is set
f0 . [c1,1] is set
[:fc1,fc2:] . [c1,1] is set
g . ([:fc1,fc2:] . [c1,1]) is set
[:fc1,fc2:] . (c1,1) is set
g . ([:fc1,fc2:] . (c1,1)) is set
[(fc1 . c1),(fc2 . 1)] is non empty set
{(fc1 . c1),(fc2 . 1)} is non empty finite set
{{(fc1 . c1),(fc2 . 1)},{(fc1 . c1)}} is non empty finite V29() set
g . [(fc1 . c1),(fc2 . 1)] is set
g . ((fc1 . c1),1) is set
x . (fc1 . c1) is set
f0 . [0,c1] is set
[:fc1,fc2:] . [0,c1] is set
g . ([:fc1,fc2:] . [0,c1]) is set
[:fc1,fc2:] . (0,c1) is set
g . ([:fc1,fc2:] . (0,c1)) is set
[(fc1 . 0),(fc2 . c1)] is non empty set
{(fc1 . 0),(fc2 . c1)} is non empty finite set
{(fc1 . 0)} is non empty trivial finite set
{{(fc1 . 0),(fc2 . c1)},{(fc1 . 0)}} is non empty finite V29() set
g . [(fc1 . 0),(fc2 . c1)] is set
g . ((inf f),c1) is set
f0 . [1,c1] is set
[:fc1,fc2:] . [1,c1] is set
g . ([:fc1,fc2:] . [1,c1]) is set
[:fc1,fc2:] . (1,c1) is set
g . ([:fc1,fc2:] . (1,c1)) is set
[(fc1 . 1),(fc2 . c1)] is non empty set
{(fc1 . 1),(fc2 . c1)} is non empty finite set
{(fc1 . 1)} is non empty trivial finite set
{{(fc1 . 1),(fc2 . c1)},{(fc1 . 1)}} is non empty finite V29() set
g . [(fc1 . 1),(fc2 . c1)] is set
g . ((sup f),c1) is set
n is TopStruct
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
x is Relation-like Function-like Element of (n)
r \/ x is Relation-like set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
x is real V101() ext-real set
[.(inf (dom r)),x.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
r | [.(inf (dom r)),x.] is Relation-like Function-like set
[.x,(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
r | [.x,(sup (dom r)).] is Relation-like Function-like set
C is Relation-like Function-like Element of (n)
f2 is Relation-like Function-like Element of (n)
(n,C,f2) is Relation-like Function-like Element of (n)
C \/ f2 is Relation-like set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
[.(inf (dom r)),x.] \/ [.x,(sup (dom r)).] is complex-membered ext-real-membered real-membered Element of bool REAL
r | (dom r) is Relation-like Function-like set
n is non empty TopSpace-like TopStruct
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
sup (dom r) is real V101() ext-real set
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom x is non empty complex-membered ext-real-membered real-membered set
inf (dom x) is real V101() ext-real set
(n,r) is Element of the carrier of n
r . (sup (dom r)) is set
(n,x) is Element of the carrier of n
x . (inf (dom x)) is set
(n,r,x) is Relation-like Function-like Element of (n)
dom (n,r,x) is complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
sup (dom x) is real V101() ext-real set
[.(inf (dom r)),(sup (dom x)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(n,r,x) . (inf (dom r)) is set
(n,r) is Element of the carrier of n
r . (inf (dom r)) is set
(n,r,x) . (sup (dom x)) is set
(n,x) is Element of the carrier of n
x . (sup (dom x)) is set
r \/ x is non empty Relation-like set
dom (r \/ x) is non empty set
(dom r) \/ (dom x) is non empty complex-membered ext-real-membered real-membered set
g is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom g is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
C is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:]
dom C is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
rng g is Element of bool the carrier of n
rng C is Element of bool the carrier of n
rng r is non empty set
rng x is non empty set
(rng r) \/ (rng x) is non empty set
rng (r \/ x) is non empty set
[#] R^1 is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
[.(inf (dom x)),(sup (dom x)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(dom g) /\ (dom C) is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
{(sup (dom r))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
f2 is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | f2 is strict TopSpace-like real-membered SubSpace of R^1
R^1 | (dom g) is strict TopSpace-like real-membered SubSpace of R^1
p is TopSpace-like real-membered SubSpace of R^1
the carrier of p is complex-membered ext-real-membered real-membered set
[: the carrier of p, the carrier of n:] is Relation-like set
bool [: the carrier of p, the carrier of n:] is set
U is Relation-like the carrier of p -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of p, the carrier of n:]
R^1 | (dom C) is strict TopSpace-like real-membered SubSpace of R^1
V is TopSpace-like real-membered SubSpace of R^1
the carrier of V is complex-membered ext-real-membered real-membered set
[: the carrier of V, the carrier of n:] is Relation-like set
bool [: the carrier of V, the carrier of n:] is set
c is Relation-like the carrier of V -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of V, the carrier of n:]
[#] (R^1 | f2) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f2)
the carrier of (R^1 | f2) is complex-membered ext-real-membered real-membered set
bool the carrier of (R^1 | f2) is set
fc2 is TopSpace-like real-membered SubSpace of R^1 | f2
[#] fc2 is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of fc2
the carrier of fc2 is complex-membered ext-real-membered real-membered set
bool the carrier of fc2 is set
c0 is TopSpace-like real-membered SubSpace of R^1 | f2
[#] c0 is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of c0
the carrier of c0 is complex-membered ext-real-membered real-membered set
bool the carrier of c0 is set
([#] fc2) \/ ([#] c0) is complex-membered ext-real-membered real-membered set
(dom g) \/ ([#] c0) is complex-membered ext-real-membered real-membered set
(dom g) \/ (dom C) is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
([#] fc2) /\ ([#] c0) is complex-membered ext-real-membered real-membered Element of bool the carrier of c0
(dom g) /\ ([#] c0) is complex-membered ext-real-membered real-membered Element of bool the carrier of c0
fc1 is real V101() ext-real Element of the carrier of (R^1 | f2)
{fc1} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
Closed-Interval-TSpace ((inf (dom x)),(sup (dom x))) is non empty strict TopSpace-like real-membered SubSpace of R^1
U +* c is Relation-like Function-like set
[: the carrier of (R^1 | f2), the carrier of n:] is Relation-like set
bool [: the carrier of (R^1 | f2), the carrier of n:] is set
f0 is set
c1 is set
[f0,c1] is non empty set
{f0,c1} is non empty finite set
{f0} is non empty trivial finite set
{{f0,c1},{f0}} is non empty finite V29() set
c2 is set
[f0,c2] is non empty set
{f0,c2} is non empty finite set
{{f0,c2},{f0}} is non empty finite V29() set
(dom r) /\ (dom x) is complex-membered ext-real-membered real-membered set
r . fc1 is set
x . fc1 is set
(dom x) /\ (dom r) is complex-membered ext-real-membered real-membered set
x . fc1 is set
r . fc1 is set
f0 is Relation-like Function-like set
dom f0 is set
dom U is complex-membered ext-real-membered real-membered Element of bool the carrier of p
bool the carrier of p is set
dom c is complex-membered ext-real-membered real-membered Element of bool the carrier of V
bool the carrier of V is set
(dom U) \/ (dom c) is complex-membered ext-real-membered real-membered set
c1 is set
f0 . c1 is set
c . c1 is set
U . c1 is set
[c1,(c . c1)] is non empty set
{c1,(c . c1)} is non empty finite set
{c1} is non empty trivial finite set
{{c1,(c . c1)},{c1}} is non empty finite V29() set
[c1,(U . c1)] is non empty set
{c1,(U . c1)} is non empty finite set
{c1} is non empty trivial finite set
{{c1,(U . c1)},{c1}} is non empty finite V29() set
c1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like Element of bool [: the carrier of R^1, the carrier of n:]
dom c1 is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
inf (dom c1) is ext-real set
sup [.(inf (dom r)),(sup (dom x)).] is ext-real set
c1 . (inf (dom r)) is set
[(inf (dom r)),(r . (inf (dom r)))] is non empty set
{(inf (dom r)),(r . (inf (dom r)))} is non empty finite set
{(inf (dom r))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(inf (dom r)),(r . (inf (dom r)))},{(inf (dom r))}} is non empty finite V29() set
c1 . (sup (dom x)) is set
[(sup (dom x)),(x . (sup (dom x)))] is non empty set
{(sup (dom x)),(x . (sup (dom x)))} is non empty finite set
{(sup (dom x))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{(sup (dom x)),(x . (sup (dom x)))},{(sup (dom x))}} is non empty finite V29() set
n is non empty TopSpace-like TopStruct
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
dom x is non empty complex-membered ext-real-membered real-membered set
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom f is non empty complex-membered ext-real-membered real-membered set
dom g is non empty complex-membered ext-real-membered real-membered set
C is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,r,f) is Relation-like Function-like Element of (n)
f2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,x,g) is Relation-like Function-like Element of (n)
(n,r) is Element of the carrier of n
sup (dom r) is real V101() ext-real set
r . (sup (dom r)) is set
(n,f) is Element of the carrier of n
inf (dom f) is real V101() ext-real set
f . (inf (dom f)) is set
inf (dom r) is real V101() ext-real set
[.(inf (dom r)),(sup (dom r)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | x is non empty strict TopSpace-like real-membered SubSpace of R^1
[:(R^1 | x),I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:(R^1 | x),I[01]:] is non empty set
[: the carrier of [:(R^1 | x),I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:(R^1 | x),I[01]:], the carrier of n:] is set
the carrier of (R^1 | x) is non empty complex-membered ext-real-membered real-membered set
inf x is ext-real set
sup x is ext-real set
p is non empty Relation-like the carrier of [:(R^1 | x),I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:(R^1 | x),I[01]:], the carrier of n:]
U is Element of the carrier of n
V is Element of the carrier of n
sup (dom f) is real V101() ext-real set
[.(inf (dom f)),(sup (dom f)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | c is non empty strict TopSpace-like real-membered SubSpace of R^1
[:(R^1 | c),I[01]:] is non empty strict TopSpace-like TopStruct
the carrier of [:(R^1 | c),I[01]:] is non empty set
[: the carrier of [:(R^1 | c),I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:(R^1 | c),I[01]:], the carrier of n:] is set
the carrier of (R^1 | c) is non empty complex-membered ext-real-membered real-membered set
inf c is ext-real set
sup c is ext-real set
fc1 is non empty Relation-like the carrier of [:(R^1 | c),I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:(R^1 | c),I[01]:], the carrier of n:]
fc2 is Element of the carrier of n
c0 is Element of the carrier of n
r \/ f is non empty Relation-like set
x \/ g is non empty Relation-like set
dom C is non empty complex-membered ext-real-membered real-membered set
(dom r) \/ (dom f) is non empty complex-membered ext-real-membered real-membered set
dom f2 is non empty complex-membered ext-real-membered real-membered set
x \/ c is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
f0 is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
R^1 | f0 is strict TopSpace-like real-membered SubSpace of R^1
[:(R^1 | f0),I[01]:] is strict TopSpace-like TopStruct
[#] (R^1 | x) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | x)
bool the carrier of (R^1 | x) is set
[#] (R^1 | c) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | c)
bool the carrier of (R^1 | c) is set
([#] (R^1 | x)) \/ ([#] (R^1 | c)) is non empty complex-membered ext-real-membered real-membered set
x \/ ([#] (R^1 | c)) is non empty complex-membered ext-real-membered real-membered set
[#] (R^1 | f0) is non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | f0)
the carrier of (R^1 | f0) is complex-membered ext-real-membered real-membered set
bool the carrier of (R^1 | f0) is set
[#] [:(R^1 | x),I[01]:] is non empty non proper closed Element of bool the carrier of [:(R^1 | x),I[01]:]
bool the carrier of [:(R^1 | x),I[01]:] is set
[#] [:(R^1 | c),I[01]:] is non empty non proper closed Element of bool the carrier of [:(R^1 | c),I[01]:]
bool the carrier of [:(R^1 | c),I[01]:] is set
([#] [:(R^1 | x),I[01]:]) \/ ([#] [:(R^1 | c),I[01]:]) is non empty set
[#] I[01] is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
[:([#] (R^1 | x)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | x),I[01]:]
[:([#] (R^1 | x)),([#] I[01]):] \/ ([#] [:(R^1 | c),I[01]:]) is non empty set
[:([#] (R^1 | c)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | c),I[01]:]
[:([#] (R^1 | x)),([#] I[01]):] \/ [:([#] (R^1 | c)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued set
[:([#] (R^1 | f0)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | f0),I[01]:]
the carrier of [:(R^1 | f0),I[01]:] is set
bool the carrier of [:(R^1 | f0),I[01]:] is set
[#] [:(R^1 | f0),I[01]:] is non proper closed Element of bool the carrier of [:(R^1 | f0),I[01]:]
Closed-Interval-TSpace ((inf (dom r)),(sup (dom r))) is non empty strict TopSpace-like real-membered SubSpace of R^1
Closed-Interval-TSpace ((inf (dom f)),(sup (dom f))) is non empty strict TopSpace-like real-membered SubSpace of R^1
[:R^1,I[01]:] is non empty strict TopSpace-like T_0 T_1 T_2 TopStruct
([#] [:(R^1 | x),I[01]:]) /\ ([#] [:(R^1 | c),I[01]:]) is Element of bool the carrier of [:(R^1 | c),I[01]:]
ci1 is set
p . ci1 is set
fc1 . ci1 is set
[:([#] (R^1 | x)),([#] I[01]):] /\ ([#] [:(R^1 | c),I[01]:]) is Relation-like Element of bool the carrier of [:(R^1 | c),I[01]:]
[:([#] (R^1 | x)),([#] I[01]):] /\ [:([#] (R^1 | c)),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | c),I[01]:]
([#] (R^1 | x)) /\ ([#] (R^1 | c)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | c)
[:(([#] (R^1 | x)) /\ ([#] (R^1 | c))),([#] I[01]):] is Relation-like complex-yielding ext-real-valued real-valued Element of bool the carrier of [:(R^1 | c),I[01]:]
x /\ ([#] (R^1 | c)) is complex-membered ext-real-membered real-membered Element of bool the carrier of (R^1 | c)
x /\ c is complex-membered ext-real-membered real-membered Element of bool the carrier of R^1
{(sup (dom r))} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
di1 is set
di1 is set
[di1,di1] is non empty set
{di1,di1} is non empty finite set
{di1} is non empty trivial finite set
{{di1,di1},{di1}} is non empty finite V29() set
p3 is real V101() ext-real Element of the carrier of I[01]
p . ((sup x),p3) is set
p . ((sup x),0) is set
fc1 . ((inf c),0) is set
fc1 . ((inf c),p3) is set
[: the carrier of [:(R^1 | f0),I[01]:], the carrier of n:] is Relation-like set
bool [: the carrier of [:(R^1 | f0),I[01]:], the carrier of n:] is set
p +* fc1 is Relation-like Function-like set
ci1 is Relation-like the carrier of [:(R^1 | f0),I[01]:] -defined the carrier of n -valued Function-like total quasi_total Element of bool [: the carrier of [:(R^1 | f0),I[01]:], the carrier of n:]
di1 is real V101() ext-real Element of the carrier of (R^1 | f0)
ci1 . (di1,0) is set
C . di1 is set
ci1 . (di1,1) is set
f2 . di1 is set
[di1,0] is non empty set
{di1,0} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{di1} is non empty trivial finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{di1,0},{di1}} is non empty finite V29() set
dom ci1 is Element of bool the carrier of [:(R^1 | f0),I[01]:]
dom p is non empty Element of bool the carrier of [:(R^1 | x),I[01]:]
dom fc1 is non empty Element of bool the carrier of [:(R^1 | c),I[01]:]
(dom p) \/ (dom fc1) is non empty set
[di1,1] is non empty set
{di1,1} is non empty finite complex-membered ext-real-membered real-membered left_end right_end bounded_below bounded_above real-bounded set
{{di1,1},{di1}} is non empty finite V29() set
f . di1 is set
[di1,(f . di1)] is non empty set
{di1,(f . di1)} is non empty finite set
{{di1,(f . di1)},{di1}} is non empty finite V29() set
ci1 . [di1,0] is set
fc1 . [di1,0] is set
fc1 . (di1,0) is set
(dom x) \/ (dom g) is non empty complex-membered ext-real-membered real-membered set
g . di1 is set
[di1,(g . di1)] is non empty set
{di1,(g . di1)} is non empty finite set
{{di1,(g . di1)},{di1}} is non empty finite V29() set
ci1 . [di1,1] is set
fc1 . [di1,1] is set
fc1 . (di1,1) is set
r . di1 is set
[di1,(r . di1)] is non empty set
{di1,(r . di1)} is non empty finite set
{{di1,(r . di1)},{di1}} is non empty finite V29() set
ci1 . [di1,0] is set
p . [di1,0] is set
p . (di1,0) is set
(dom x) \/ (dom g) is non empty complex-membered ext-real-membered real-membered set
x . di1 is set
[di1,(x . di1)] is non empty set
{di1,(x . di1)} is non empty finite set
{{di1,(x . di1)},{di1}} is non empty finite V29() set
ci1 . [di1,1] is set
p . [di1,1] is set
p . (di1,1) is set
inf f0 is ext-real set
sup f0 is ext-real set
di1 is real V101() ext-real Element of the carrier of I[01]
ci1 . ((inf f0),di1) is set
ci1 . ((sup f0),di1) is set
[.(inf (dom r)),(sup (dom f)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
inf [.(inf (dom r)),(sup (dom f)).] is ext-real set
[(inf x),di1] is non empty set
{(inf x),di1} is non empty finite ext-real-membered left_end right_end set
{(inf x)} is non empty trivial finite ext-real-membered left_end right_end set
{{(inf x),di1},{(inf x)}} is non empty finite V29() set
dom p is non empty Element of bool the carrier of [:(R^1 | x),I[01]:]
[(inf f0),di1] is non empty set
{(inf f0),di1} is non empty finite ext-real-membered left_end right_end set
{(inf f0)} is non empty trivial finite ext-real-membered left_end right_end set
{{(inf f0),di1},{(inf f0)}} is non empty finite V29() set
dom fc1 is non empty Element of bool the carrier of [:(R^1 | c),I[01]:]
(dom p) \/ (dom fc1) is non empty set
p . ((inf x),0) is set
fc1 . ((inf c),0) is set
ci1 . [(inf f0),di1] is set
fc1 . [(inf f0),di1] is set
fc1 . ((inf c),di1) is set
ci1 . [(inf f0),di1] is set
p . [(inf f0),di1] is set
p . ((inf f0),di1) is set
sup [.(inf (dom r)),(sup (dom f)).] is ext-real set
[(sup c),di1] is non empty set
{(sup c),di1} is non empty finite ext-real-membered left_end right_end set
{(sup c)} is non empty trivial finite ext-real-membered left_end right_end set
{{(sup c),di1},{(sup c)}} is non empty finite V29() set
[(sup f0),di1] is non empty set
{(sup f0),di1} is non empty finite ext-real-membered left_end right_end set
{(sup f0)} is non empty trivial finite ext-real-membered left_end right_end set
{{(sup f0),di1},{(sup f0)}} is non empty finite V29() set
ci1 . [(sup f0),di1] is set
fc1 . [(sup f0),di1] is set
fc1 . ((sup c),di1) is set
n is TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
r . 1 is Relation-like Function-like set
r /. 1 is Relation-like Function-like Element of (n)
<*(r /. 1)*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x . 1 is Relation-like Function-like set
f is ordinal natural real V101() ext-real non negative set
f + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x . (f + 1) is Relation-like Function-like set
x /. f is Relation-like Function-like Element of (n)
r /. (f + 1) is Relation-like Function-like Element of (n)
(n,(x /. f),(r /. (f + 1))) is Relation-like Function-like Element of (n)
f is ordinal natural real V101() ext-real non negative set
f + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(f + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(f + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
g is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
g . 1 is Relation-like Function-like set
g is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
g . 1 is Relation-like Function-like set
g /. (f + 1) is Relation-like Function-like Element of (n)
r /. ((f + 1) + 1) is Relation-like Function-like Element of (n)
(n,(g /. (f + 1)),(r /. ((f + 1) + 1))) is Relation-like Function-like Element of (n)
<*(n,(g /. (f + 1)),(r /. ((f + 1) + 1)))*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
g ^ <*(n,(g /. (f + 1)),(r /. ((f + 1) + 1)))*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
Seg (len g) is finite V32( len g) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom g is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
C is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len C is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*(n,(g /. (f + 1)),(r /. ((f + 1) + 1)))*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len g) + (len <*(n,(g /. (f + 1)),(r /. ((f + 1) + 1)))*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
f2 is ordinal natural real V101() ext-real non negative set
f2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C . (f2 + 1) is Relation-like Function-like set
C /. f2 is Relation-like Function-like Element of (n)
r /. (f2 + 1) is Relation-like Function-like Element of (n)
(n,(C /. f2),(r /. (f2 + 1))) is Relation-like Function-like Element of (n)
g . (f2 + 1) is Relation-like Function-like set
C . f2 is Relation-like Function-like set
g . f2 is Relation-like Function-like set
g /. f2 is Relation-like Function-like Element of (n)
C . f2 is Relation-like Function-like set
g . f2 is Relation-like Function-like set
g /. f2 is Relation-like Function-like Element of (n)
C . 1 is Relation-like Function-like set
(f + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(f + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(f + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
g is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
g . 1 is Relation-like Function-like set
C is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len C is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
C . 1 is Relation-like Function-like set
(len r) -' 1 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len r) - 1 is real V101() ext-real set
((len r) -' 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is ordinal natural real V101() ext-real non negative set
x + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
r . (x + 1) is Relation-like Function-like set
r /. x is Relation-like Function-like Element of (n)
r /. (x + 1) is Relation-like Function-like Element of (n)
(n,(r /. x),(r /. (x + 1))) is Relation-like Function-like Element of (n)
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x . 1 is Relation-like Function-like set
f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
f . 1 is Relation-like Function-like set
g is ordinal natural real V101() ext-real non negative set
x . g is Relation-like Function-like set
f . g is Relation-like Function-like set
g + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x . (g + 1) is Relation-like Function-like set
f . (g + 1) is Relation-like Function-like set
f /. g is Relation-like Function-like Element of (n)
r /. (g + 1) is Relation-like Function-like Element of (n)
(n,(f /. g),(r /. (g + 1))) is Relation-like Function-like Element of (n)
x /. g is Relation-like Function-like Element of (n)
(n,(x /. g),(r /. (g + 1))) is Relation-like Function-like Element of (n)
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x . 0 is Relation-like Function-like set
f . 0 is Relation-like Function-like set
n is TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non proper Element of bool the carrier of n
the carrier of n is set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,r) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,r) . (len r) is Relation-like Function-like set
len (n,r) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
dom (n,r) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
rng (n,r) is functional finite Element of bool (n)
bool (n) is set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
<*r*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,<*r*>) is Relation-like Function-like Element of (n)
len <*r*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,<*r*>) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,<*r*>) . 1 is Relation-like Function-like set
<*r*> . 1 is Relation-like Function-like set
n is non empty TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
r ^ x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(r ^ x)) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(r ^ x)) . (len r) is Relation-like Function-like set
(n,r) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,r) . (len r) is Relation-like Function-like set
len (n,(r ^ x)) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,(r ^ x))) is finite V32( len (n,(r ^ x))) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,(r ^ x)) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
len (n,r) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,r)) is finite V32( len (n,r)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,r) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
r is ordinal natural real V101() ext-real non negative set
r + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x ^ f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(x ^ f)) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(x ^ f)) . (len x) is Relation-like Function-like set
(n,x) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,x) . (len x) is Relation-like Function-like set
g is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
C is Relation-like Function-like Element of (n)
<*C*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
g ^ <*C*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
<*C*> ^ f is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
g ^ (<*C*> ^ f) is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len g) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(x ^ f) . 1 is Relation-like Function-like set
x . 1 is Relation-like Function-like set
len (<*C*> ^ f) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*C*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len <*C*>) + (len f) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
1 + (len f) is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
len (g ^ (<*C*> ^ f)) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
r + (len (<*C*> ^ f)) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (g ^ (<*C*> ^ f))) is finite V32( len (g ^ (<*C*> ^ f))) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(n,(g ^ (<*C*> ^ f))) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len (n,(g ^ (<*C*> ^ f))) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,(g ^ (<*C*> ^ f)))) is finite V32( len (n,(g ^ (<*C*> ^ f)))) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,(g ^ (<*C*> ^ f))) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len g) is finite V32( len g) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(n,g) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len (n,g) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,g)) is finite V32( len (n,g)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,g) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len x) is finite V32( len x) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
len (n,x) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,x)) is finite V32( len (n,x)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,x) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(n,(g ^ (<*C*> ^ f))) /. r is Relation-like Function-like Element of (n)
(n,(g ^ (<*C*> ^ f))) . r is Relation-like Function-like set
(n,g) . r is Relation-like Function-like set
(n,g) /. r is Relation-like Function-like Element of (n)
(n,x) /. r is Relation-like Function-like Element of (n)
(n,x) . r is Relation-like Function-like set
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
0 + (len x) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len x) + (len f) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len (x ^ f) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (x ^ f)) is finite V32( len (x ^ f)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (x ^ f) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom x is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(x ^ f) /. (r + 1) is Relation-like Function-like Element of (n)
(x ^ f) . (r + 1) is Relation-like Function-like set
x . (r + 1) is Relation-like Function-like set
x /. (r + 1) is Relation-like Function-like Element of (n)
(n,((n,x) /. r),(x /. (r + 1))) is Relation-like Function-like Element of (n)
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
r ^ x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(r ^ x)) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,(r ^ x)) . (len r) is Relation-like Function-like set
(n,r) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,r) . (len r) is Relation-like Function-like set
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like Function-like Element of (n)
<*r*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x ^ <*r*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(x ^ <*r*>)) is Relation-like Function-like Element of (n)
(n,x) is Relation-like Function-like Element of (n)
(n,(n,x),r) is Relation-like Function-like Element of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,<*r*>) is Relation-like Function-like Element of (n)
f is Relation-like Function-like Element of (n)
f \/ r is Relation-like set
(n,f,r) is Relation-like Function-like Element of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len (x ^ <*r*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*r*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len x) + (len <*r*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len x) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(n,(x ^ <*r*>)) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,(x ^ <*r*>)) . (len (x ^ <*r*>)) is Relation-like Function-like set
0 + (len x) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (x ^ <*r*>)) is finite V32( len (x ^ <*r*>)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
len (n,(x ^ <*r*>)) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Seg (len (n,(x ^ <*r*>))) is finite V32( len (n,(x ^ <*r*>))) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (n,(x ^ <*r*>)) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(n,(x ^ <*r*>)) /. (len x) is Relation-like Function-like Element of (n)
(n,(x ^ <*r*>)) . (len x) is Relation-like Function-like set
(n,x) is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
(n,x) . (len x) is Relation-like Function-like set
dom (x ^ <*r*>) is non empty finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
(x ^ <*r*>) /. ((len x) + 1) is Relation-like Function-like Element of (n)
(x ^ <*r*>) . ((len x) + 1) is Relation-like Function-like set
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
n is non empty TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is set
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,x) is Relation-like Function-like Element of (n)
rng (n,x) is set
x is ordinal natural real V101() ext-real non negative set
x + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,f) is Relation-like Function-like Element of (n)
rng (n,f) is set
g is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
C is Relation-like Function-like Element of (n)
<*C*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
g ^ <*C*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*C*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len g) + (len <*C*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len g) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(n,g) is Relation-like Function-like Element of (n)
(n,(n,g),C) is Relation-like Function-like Element of (n)
(n,g) \/ C is Relation-like set
(n,g) \/ C is Relation-like set
f2 is ordinal natural real V101() ext-real non negative set
g /. f2 is Relation-like Function-like Element of (n)
rng (g /. f2) is set
f2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f /. f2 is Relation-like Function-like Element of (n)
rng (f /. f2) is set
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f . f2 is Relation-like Function-like set
rng (f . f2) is set
Seg (len g) is finite V32( len g) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom g is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
g . f2 is Relation-like Function-like set
rng (n,g) is set
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f . (len f) is Relation-like Function-like set
f /. (len f) is Relation-like Function-like Element of (n)
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
rng C is set
(rng (n,g)) \/ (rng C) is set
(n,g) \/ C is Relation-like set
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,x) is Relation-like Function-like Element of (n)
rng (n,x) is set
n is non empty TopSpace-like TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,r) is Relation-like Function-like Element of (n)
r /. 1 is Relation-like Function-like Element of (n)
dom (r /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (r /. 1)) is ext-real set
r /. (len r) is Relation-like Function-like Element of (n)
dom (r /. (len r)) is complex-membered ext-real-membered real-membered set
sup (dom (r /. (len r))) is ext-real set
[.(inf (dom (r /. 1))),(sup (dom (r /. (len r)))).] is interval set
(r /. 1) . (inf (dom (r /. 1))) is set
(r /. (len r)) . (sup (dom (r /. (len r)))) is set
r is ordinal natural real V101() ext-real non negative set
r + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,x) is Relation-like Function-like Element of (n)
x /. 1 is Relation-like Function-like Element of (n)
dom (x /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (x /. 1)) is ext-real set
x /. (len x) is Relation-like Function-like Element of (n)
dom (x /. (len x)) is complex-membered ext-real-membered real-membered set
sup (dom (x /. (len x))) is ext-real set
[.(inf (dom (x /. 1))),(sup (dom (x /. (len x)))).] is interval set
(x /. 1) . (inf (dom (x /. 1))) is set
(x /. (len x)) . (sup (dom (x /. (len x)))) is set
f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
g is Relation-like Function-like Element of (n)
<*g*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
f ^ <*g*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*g*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len f) + (len <*g*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len f) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len x) is finite V32( len x) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom x is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x . (len x) is Relation-like Function-like set
f2 is ordinal natural real V101() ext-real non negative set
f /. f2 is Relation-like Function-like Element of (n)
dom (f /. f2) is complex-membered ext-real-membered real-membered set
sup (dom (f /. f2)) is ext-real set
(f /. f2) . (sup (dom (f /. f2))) is set
f2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f /. (f2 + 1) is Relation-like Function-like Element of (n)
dom (f /. (f2 + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (f /. (f2 + 1))) is ext-real set
(f /. (f2 + 1)) . (inf (dom (f /. (f2 + 1)))) is set
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. f2 is Relation-like Function-like Element of (n)
x . f2 is Relation-like Function-like set
f . f2 is Relation-like Function-like set
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x /. (f2 + 1) is Relation-like Function-like Element of (n)
x . (f2 + 1) is Relation-like Function-like set
f . (f2 + 1) is Relation-like Function-like set
f2 is ordinal natural real V101() ext-real non negative set
f /. f2 is Relation-like Function-like Element of (n)
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. f2 is Relation-like Function-like Element of (n)
x . f2 is Relation-like Function-like set
f . f2 is Relation-like Function-like set
C is non empty Relation-like Function-like (n) (n) (n) Element of (n)
<*C*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
dom C is non empty complex-membered ext-real-membered real-membered set
(n,C) is Element of the carrier of n
inf (dom C) is real V101() ext-real set
C . (inf (dom C)) is set
(n,C) is Element of the carrier of n
sup (dom C) is real V101() ext-real set
C . (sup (dom C)) is set
x . 1 is Relation-like Function-like set
(n,f) is Relation-like Function-like Element of (n)
f /. 1 is Relation-like Function-like Element of (n)
dom (f /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (f /. 1)) is ext-real set
f /. (len f) is Relation-like Function-like Element of (n)
dom (f /. (len f)) is complex-membered ext-real-membered real-membered set
sup (dom (f /. (len f))) is ext-real set
[.(inf (dom (f /. 1))),(sup (dom (f /. (len f)))).] is interval set
(f /. 1) . (inf (dom (f /. 1))) is set
(f /. (len f)) . (sup (dom (f /. (len f)))) is set
f2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom f2 is non empty complex-membered ext-real-membered real-membered set
(n,f2) is Element of the carrier of n
inf (dom f2) is real V101() ext-real set
f2 . (inf (dom f2)) is set
(n,f2) is Element of the carrier of n
sup (dom f2) is real V101() ext-real set
f2 . (sup (dom f2)) is set
C is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,f2,C) is Relation-like Function-like Element of (n)
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x /. (len f) is Relation-like Function-like Element of (n)
dom (x /. (len f)) is complex-membered ext-real-membered real-membered set
sup (dom (x /. (len f))) is ext-real set
(x /. (len f)) . (sup (dom (x /. (len f)))) is set
x /. ((len f) + 1) is Relation-like Function-like Element of (n)
dom (x /. ((len f) + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (x /. ((len f) + 1))) is ext-real set
(x /. ((len f) + 1)) . (inf (dom (x /. ((len f) + 1)))) is set
x . ((len f) + 1) is Relation-like Function-like set
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f . (len f) is Relation-like Function-like set
x . (len f) is Relation-like Function-like set
dom C is non empty complex-membered ext-real-membered real-membered set
inf (dom C) is real V101() ext-real set
(n,C) is Element of the carrier of n
C . (inf (dom C)) is set
dom (n,f2,C) is complex-membered ext-real-membered real-membered set
sup (dom C) is real V101() ext-real set
[.(inf (dom f2)),(sup (dom C)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(n,f2,C) . (inf (dom f2)) is set
(n,f2,C) . (sup (dom C)) is set
(n,C) is Element of the carrier of n
C . (sup (dom C)) is set
f . 1 is Relation-like Function-like set
x . 1 is Relation-like Function-like set
p is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom p is non empty complex-membered ext-real-membered real-membered set
(n,p) is Element of the carrier of n
inf (dom p) is real V101() ext-real set
p . (inf (dom p)) is set
(n,p) is Element of the carrier of n
sup (dom p) is real V101() ext-real set
p . (sup (dom p)) is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,r) is Relation-like Function-like Element of (n)
r /. 1 is Relation-like Function-like Element of (n)
dom (r /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (r /. 1)) is ext-real set
r /. (len r) is Relation-like Function-like Element of (n)
dom (r /. (len r)) is complex-membered ext-real-membered real-membered set
sup (dom (r /. (len r))) is ext-real set
[.(inf (dom (r /. 1))),(sup (dom (r /. (len r)))).] is interval set
(r /. 1) . (inf (dom (r /. 1))) is set
(r /. (len r)) . (sup (dom (r /. (len r)))) is set
n is non empty TopSpace-like TopStruct
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
[#] n is non empty non proper closed Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,r) is Relation-like Function-like Element of (n)
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,x) is Relation-like Function-like Element of (n)
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
r is ordinal natural real V101() ext-real non negative set
r + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
f is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,x) is Relation-like Function-like Element of (n)
(n,f) is Relation-like Function-like Element of (n)
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
C is non empty Relation-like Function-like (n) (n) (n) Element of (n)
f2 is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
x is Relation-like Function-like Element of (n)
<*x*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
f2 ^ <*x*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len f2 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*x*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len f2) + (len <*x*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len f2) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
p is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
U is Relation-like Function-like Element of (n)
<*U*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
p ^ <*U*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len p is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
len <*U*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len p) + (len <*U*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len p) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
dom x is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len x) is finite V32( len x) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. (len x) is Relation-like Function-like Element of (n)
x . (len x) is Relation-like Function-like set
f /. (len x) is Relation-like Function-like Element of (n)
V is non empty Relation-like Function-like (n) (n) (n) Element of (n)
c is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom V is non empty complex-membered ext-real-membered real-membered set
dom c is non empty complex-membered ext-real-membered real-membered set
f . (len f) is Relation-like Function-like set
c0 is ordinal natural real V101() ext-real non negative set
f2 /. c0 is Relation-like Function-like Element of (n)
dom (f2 /. c0) is complex-membered ext-real-membered real-membered set
sup (dom (f2 /. c0)) is ext-real set
(f2 /. c0) . (sup (dom (f2 /. c0))) is set
c0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f2 /. (c0 + 1) is Relation-like Function-like Element of (n)
dom (f2 /. (c0 + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (f2 /. (c0 + 1))) is ext-real set
(f2 /. (c0 + 1)) . (inf (dom (f2 /. (c0 + 1)))) is set
Seg (len f2) is finite V32( len f2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. c0 is Relation-like Function-like Element of (n)
x . c0 is Relation-like Function-like set
f2 . c0 is Relation-like Function-like set
x /. (c0 + 1) is Relation-like Function-like Element of (n)
x . (c0 + 1) is Relation-like Function-like set
f2 . (c0 + 1) is Relation-like Function-like set
c0 is ordinal natural real V101() ext-real non negative set
f2 /. c0 is Relation-like Function-like Element of (n)
c0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len f2) is finite V32( len f2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. c0 is Relation-like Function-like Element of (n)
f /. c0 is Relation-like Function-like Element of (n)
x . c0 is Relation-like Function-like set
f2 . c0 is Relation-like Function-like set
f0 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
c1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom f0 is non empty complex-membered ext-real-membered real-membered set
dom c1 is non empty complex-membered ext-real-membered real-membered set
(n,f2) is Relation-like Function-like Element of (n)
f2 /. 1 is Relation-like Function-like Element of (n)
dom (f2 /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (f2 /. 1)) is ext-real set
f2 /. (len f2) is Relation-like Function-like Element of (n)
dom (f2 /. (len f2)) is complex-membered ext-real-membered real-membered set
sup (dom (f2 /. (len f2))) is ext-real set
[.(inf (dom (f2 /. 1))),(sup (dom (f2 /. (len f2)))).] is interval set
(f2 /. 1) . (inf (dom (f2 /. 1))) is set
(f2 /. (len f2)) . (sup (dom (f2 /. (len f2)))) is set
c0 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom c0 is non empty complex-membered ext-real-membered real-membered set
(n,c0) is Element of the carrier of n
inf (dom c0) is real V101() ext-real set
c0 . (inf (dom c0)) is set
(n,c0) is Element of the carrier of n
sup (dom c0) is real V101() ext-real set
c0 . (sup (dom c0)) is set
f0 is ordinal natural real V101() ext-real non negative set
p /. f0 is Relation-like Function-like Element of (n)
dom (p /. f0) is complex-membered ext-real-membered real-membered set
sup (dom (p /. f0)) is ext-real set
(p /. f0) . (sup (dom (p /. f0))) is set
f0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
p /. (f0 + 1) is Relation-like Function-like Element of (n)
dom (p /. (f0 + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (p /. (f0 + 1))) is ext-real set
(p /. (f0 + 1)) . (inf (dom (p /. (f0 + 1)))) is set
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len p) is finite V32( len p) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom p is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f /. f0 is Relation-like Function-like Element of (n)
f . f0 is Relation-like Function-like set
p . f0 is Relation-like Function-like set
f /. (f0 + 1) is Relation-like Function-like Element of (n)
f . (f0 + 1) is Relation-like Function-like set
p . (f0 + 1) is Relation-like Function-like set
f0 is ordinal natural real V101() ext-real non negative set
p /. f0 is Relation-like Function-like Element of (n)
f0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len p) is finite V32( len p) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom p is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. f0 is Relation-like Function-like Element of (n)
f /. f0 is Relation-like Function-like Element of (n)
f . f0 is Relation-like Function-like set
p . f0 is Relation-like Function-like set
c1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
c2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom c1 is non empty complex-membered ext-real-membered real-membered set
dom c2 is non empty complex-membered ext-real-membered real-membered set
(n,p) is Relation-like Function-like Element of (n)
p /. 1 is Relation-like Function-like Element of (n)
dom (p /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (p /. 1)) is ext-real set
p /. (len p) is Relation-like Function-like Element of (n)
dom (p /. (len p)) is complex-membered ext-real-membered real-membered set
sup (dom (p /. (len p))) is ext-real set
[.(inf (dom (p /. 1))),(sup (dom (p /. (len p)))).] is interval set
(p /. 1) . (inf (dom (p /. 1))) is set
(p /. (len p)) . (sup (dom (p /. (len p)))) is set
f0 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom f0 is non empty complex-membered ext-real-membered real-membered set
(n,f0) is Element of the carrier of n
inf (dom f0) is real V101() ext-real set
f0 . (inf (dom f0)) is set
(n,f0) is Element of the carrier of n
sup (dom f0) is real V101() ext-real set
f0 . (sup (dom f0)) is set
c1 is ordinal natural real V101() ext-real non negative set
f2 /. c1 is Relation-like Function-like Element of (n)
p /. c1 is Relation-like Function-like Element of (n)
c1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len f2) is finite V32( len f2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len p) is finite V32( len p) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom p is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
x /. c1 is Relation-like Function-like Element of (n)
f /. c1 is Relation-like Function-like Element of (n)
c2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
ci1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom c2 is non empty complex-membered ext-real-membered real-membered set
dom ci1 is non empty complex-membered ext-real-membered real-membered set
x . c1 is Relation-like Function-like set
f2 . c1 is Relation-like Function-like set
f . c1 is Relation-like Function-like set
p . c1 is Relation-like Function-like set
fc1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,c0,fc1) is Relation-like Function-like Element of (n)
fc2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,f0,fc2) is Relation-like Function-like Element of (n)
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len f2) is finite V32( len f2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f2 . (len f2) is Relation-like Function-like set
x . (len f2) is Relation-like Function-like set
x /. (len f2) is Relation-like Function-like Element of (n)
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len p) is finite V32( len p) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom p is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
p . (len p) is Relation-like Function-like set
f . (len p) is Relation-like Function-like set
f /. (len p) is Relation-like Function-like Element of (n)
f2 . 1 is Relation-like Function-like set
x . 1 is Relation-like Function-like set
x /. 1 is Relation-like Function-like Element of (n)
p . 1 is Relation-like Function-like set
f . 1 is Relation-like Function-like set
f /. 1 is Relation-like Function-like Element of (n)
f /. (len f2) is Relation-like Function-like Element of (n)
(n,fc1) is Element of the carrier of n
dom fc1 is non empty complex-membered ext-real-membered real-membered set
inf (dom fc1) is real V101() ext-real set
fc1 . (inf (dom fc1)) is set
dom (x /. (len f2)) is complex-membered ext-real-membered real-membered set
sup (dom (x /. (len f2))) is ext-real set
x /. ((len f2) + 1) is Relation-like Function-like Element of (n)
dom (x /. ((len f2) + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (x /. ((len f2) + 1))) is ext-real set
c1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
c2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom c1 is non empty complex-membered ext-real-membered real-membered set
dom c2 is non empty complex-membered ext-real-membered real-membered set
ci1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
ci1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom ci1 is non empty complex-membered ext-real-membered real-membered set
dom ci1 is non empty complex-membered ext-real-membered real-membered set
fc1 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
<*fc1*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
fc2 is non empty Relation-like Function-like (n) (n) (n) Element of (n)
<*fc2*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
r is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len r is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,r) is Relation-like Function-like Element of (n)
f is non empty Relation-like Function-like (n) (n) (n) Element of (n)
(n,x) is Relation-like Function-like Element of (n)
g is non empty Relation-like Function-like (n) (n) (n) Element of (n)
n is non empty TopStruct
[#] n is non empty non proper Element of bool the carrier of n
the carrier of n is non empty set
bool the carrier of n is set
PFuncs (REAL,([#] n)) is non empty functional set
(n) is non empty functional Element of bool (PFuncs (REAL,([#] n)))
bool (PFuncs (REAL,([#] n))) is set
[: the carrier of R^1, the carrier of n:] is Relation-like set
bool [: the carrier of R^1, the carrier of n:] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] n)) : b1 is Relation-like the carrier of R^1 -defined the carrier of n -valued Function-like (n) Element of bool [: the carrier of R^1, the carrier of n:] } is set
x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x . 1 is real V101() ext-real set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
x . (len x) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
(len x) - 1 is real V101() ext-real set
r is ordinal natural real V101() ext-real non negative set
r + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
x is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom x is non empty complex-membered ext-real-membered real-membered set
inf (dom x) is real V101() ext-real set
sup (dom x) is real V101() ext-real set
f is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
len f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
f . 1 is real V101() ext-real set
f . (len f) is real V101() ext-real set
(len f) - 1 is real V101() ext-real set
g is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
C is real V101() ext-real Element of REAL
<*C*> is non empty Relation-like NAT -defined REAL -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
g ^ <*C*> is non empty Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
len g is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len g) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f . r is real V101() ext-real set
f2 is real V101() ext-real set
[.(inf (dom x)),f2.] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x | [.(inf (dom x)),f2.] is Relation-like Function-like set
[.f2,(sup (dom x)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x | [.f2,(sup (dom x)).] is Relation-like Function-like set
x is Relation-like Function-like Element of (n)
p is Relation-like Function-like Element of (n)
(n,x,p) is Relation-like Function-like Element of (n)
1 + r is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
Seg (len f) is finite V32( len f) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom f is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
<*x*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len <*x*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,<*x*>) is Relation-like Function-like Element of (n)
V is ordinal natural real V101() ext-real non negative set
<*x*> /. V is Relation-like Function-like Element of (n)
f /. V is real V101() ext-real Element of REAL
V + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f /. (V + 1) is real V101() ext-real Element of REAL
[.(f /. V),(f /. (V + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x | [.(f /. V),(f /. (V + 1)).] is Relation-like Function-like set
Seg (len <*x*>) is finite V32( len <*x*>) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom <*x*> is non empty finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
<*x*> . V is Relation-like Function-like set
x | (dom x) is Relation-like Function-like set
f . (r + 1) is real V101() ext-real set
[.(inf (dom x)),(sup (dom x)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
dom x is complex-membered ext-real-membered real-membered set
(dom x) /\ [.(inf (dom x)),f2.] is complex-membered ext-real-membered real-membered Element of bool REAL
sup (dom x) is ext-real set
inf (dom x) is ext-real set
dom g is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
f | (dom g) is Relation-like NAT -defined dom g -defined NAT -defined REAL -valued Function-like finite FinSubsequence-like complex-yielding ext-real-valued real-valued Element of bool [:NAT,REAL:]
[:NAT,REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:NAT,REAL:] is set
Seg r is finite V32(r) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
g . 1 is real V101() ext-real set
U is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom U is non empty complex-membered ext-real-membered real-membered set
inf (dom U) is real V101() ext-real set
g . (len g) is real V101() ext-real set
sup (dom U) is real V101() ext-real set
rng f is finite complex-membered ext-real-membered real-membered bounded_below bounded_above real-bounded Element of bool REAL
V is Relation-like REAL -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom V is complex-membered ext-real-membered real-membered Element of bool REAL
V | (dom V) is Relation-like REAL -defined dom V -defined REAL -defined REAL -valued Function-like complex-yielding ext-real-valued real-valued Element of bool [:REAL,REAL:]
Seg (len g) is finite V32( len g) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
(len g) - 1 is real V101() ext-real set
c is Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len c is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,c) is Relation-like Function-like Element of (n)
<*p*> is non empty Relation-like NAT -defined (n) -valued Function-like finite V32(1) FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
c ^ <*p*> is non empty Relation-like NAT -defined (n) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of (n)
len (c ^ <*p*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n,(c ^ <*p*>)) is Relation-like Function-like Element of (n)
len <*p*> is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len c) + (len <*p*>) is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(len c) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc2 is ordinal natural real V101() ext-real non negative set
(c ^ <*p*>) /. fc2 is Relation-like Function-like Element of (n)
f /. fc2 is real V101() ext-real Element of REAL
fc2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f /. (fc2 + 1) is real V101() ext-real Element of REAL
[.(f /. fc2),(f /. (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x | [.(f /. fc2),(f /. (fc2 + 1)).] is Relation-like Function-like set
Seg (len (c ^ <*p*>)) is finite V32( len (c ^ <*p*>)) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom (c ^ <*p*>) is non empty finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end right_end bounded_below bounded_above real-bounded Element of bool NAT
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(c ^ <*p*>) . fc2 is Relation-like Function-like set
Seg (len c) is finite V32( len c) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom c is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
g /. fc2 is real V101() ext-real Element of REAL
g . fc2 is real V101() ext-real set
(f | (dom g)) . fc2 is real V101() ext-real set
f . fc2 is real V101() ext-real set
g /. (fc2 + 1) is real V101() ext-real Element of REAL
g . (fc2 + 1) is real V101() ext-real set
(f | (dom g)) . (fc2 + 1) is real V101() ext-real set
f . (fc2 + 1) is real V101() ext-real set
(c ^ <*p*>) . fc2 is Relation-like Function-like set
c . fc2 is Relation-like Function-like set
c /. fc2 is Relation-like Function-like Element of (n)
[.(g /. fc2),(g /. (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(x | [.(inf (dom x)),f2.]) | [.(g /. fc2),(g /. (fc2 + 1)).] is Relation-like Function-like set
x | [.(g /. fc2),(g /. (fc2 + 1)).] is Relation-like Function-like set
x is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
len x is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
x . 1 is real V101() ext-real set
r is non empty Relation-like Function-like (n) (n) (n) Element of (n)
dom r is non empty complex-membered ext-real-membered real-membered set
inf (dom r) is real V101() ext-real set
x . (len x) is real V101() ext-real set
sup (dom r) is real V101() ext-real set
(len x) - 1 is real V101() ext-real set
n is ordinal natural real V101() ext-real non negative set
TUnitSphere n is non empty TopSpace-like T_0 T_1 T_2 n -locally_euclidean n -manifold manifold-like V359() TopStruct
the carrier of (TUnitSphere n) is non empty set
r is Element of the carrier of (TUnitSphere n)
x is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total continuous Path of r,r
rng x is non empty Element of bool the carrier of (TUnitSphere n)
bool the carrier of (TUnitSphere n) is set
f is set
f is set
n + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
g is ordinal natural real V101() ext-real non negative set
Tunit_circle g is TopSpace-like SubSpace of TOP-REAL g
TOP-REAL g is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() g -locally_euclidean V359() () RLTopStruct
[#] (Tunit_circle g) is non proper closed Element of bool the carrier of (Tunit_circle g)
the carrier of (Tunit_circle g) is set
bool the carrier of (Tunit_circle g) is set
[#] (TOP-REAL g) is non empty non proper closed Element of bool the carrier of (TOP-REAL g)
the carrier of (TOP-REAL g) is non empty set
bool the carrier of (TOP-REAL g) is set
C is Relation-like NAT -defined Function-like finite V32(g) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL g)
0. (TOP-REAL g) is Relation-like NAT -defined Function-like finite V32(g) V45( TOP-REAL g) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL g)
the ZeroF of (TOP-REAL g) is Relation-like NAT -defined Function-like finite V32(g) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL g)
Tcircle ((0. (TOP-REAL g)),1) is TopSpace-like SubSpace of TOP-REAL g
the carrier of (Tcircle ((0. (TOP-REAL g)),1)) is set
Sphere ((0. (TOP-REAL g)),1) is closed Element of bool the carrier of (TOP-REAL g)
- C is Relation-like NAT -defined Function-like finite V32(g) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL g)
- C is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
{C} is non empty trivial functional finite V29() set
(Sphere ((0. (TOP-REAL g)),1)) \ {C} is Element of bool the carrier of (TOP-REAL g)
(TOP-REAL g) | ((Sphere ((0. (TOP-REAL g)),1)) \ {C}) is strict TopSpace-like SubSpace of TOP-REAL g
f2 is non empty TopSpace-like SubSpace of TOP-REAL g
[#] f2 is non empty non proper closed Element of bool the carrier of f2
the carrier of f2 is non empty set
bool the carrier of f2 is set
TPlane (C,(0. (TOP-REAL g))) is non empty TopSpace-like SubSpace of TOP-REAL g
stereographic_projection (f2,C) is non empty Relation-like the carrier of f2 -defined the carrier of (TPlane (C,(0. (TOP-REAL g)))) -valued Function-like total quasi_total Element of bool [: the carrier of f2, the carrier of (TPlane (C,(0. (TOP-REAL g)))):]
the carrier of (TPlane (C,(0. (TOP-REAL g)))) is non empty set
[: the carrier of f2, the carrier of (TPlane (C,(0. (TOP-REAL g)))):] is Relation-like set
bool [: the carrier of f2, the carrier of (TPlane (C,(0. (TOP-REAL g)))):] is set
dom x is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
x . 0 is set
x . 1 is set
x is non empty TopSpace-like SubSpace of TUnitSphere n
the carrier of x is non empty set
[: the carrier of I[01], the carrier of x:] is Relation-like set
bool [: the carrier of I[01], the carrier of x:] is set
p is Element of the carrier of x
U is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of x:]
V is non empty Relation-like the carrier of I[01] -defined the carrier of x -valued Function-like total quasi_total continuous Path of p,p
n is ordinal natural real V101() ext-real non negative set
TUnitSphere n is non empty TopSpace-like T_0 T_1 T_2 n -locally_euclidean n -manifold manifold-like V359() TopStruct
the carrier of (TUnitSphere n) is non empty set
r is Element of the carrier of (TUnitSphere n)
x is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total continuous Path of r,r
rng x is non empty Element of bool the carrier of (TUnitSphere n)
bool the carrier of (TUnitSphere n) is set
n + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
f is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
Tunit_circle f is TopSpace-like SubSpace of TOP-REAL f
TOP-REAL f is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() f -locally_euclidean V359() () RLTopStruct
[#] (Tunit_circle f) is non proper closed Element of bool the carrier of (Tunit_circle f)
the carrier of (Tunit_circle f) is set
bool the carrier of (Tunit_circle f) is set
[#] (TOP-REAL f) is non empty non proper closed Element of bool the carrier of (TOP-REAL f)
the carrier of (TOP-REAL f) is non empty set
bool the carrier of (TOP-REAL f) is set
dom x is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
bool the carrier of I[01] is set
[: the carrier of I[01], the carrier of (TOP-REAL f):] is Relation-like set
bool [: the carrier of I[01], the carrier of (TOP-REAL f):] is set
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TOP-REAL f) -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of (TOP-REAL f):]
Euclid f is non empty strict Reflexive discerning V91() triangle MetrStruct
the carrier of (Euclid f) is non empty set
bool the carrier of (Euclid f) is set
C is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
C . 1 is real V101() ext-real set
len C is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
C . (len C) is real V101() ext-real set
rng C is finite complex-membered ext-real-membered real-membered bounded_below bounded_above real-bounded Element of bool REAL
x * C is Relation-like NAT -defined the carrier of (TUnitSphere n) -valued Function-like finite Element of bool [:NAT, the carrier of (TUnitSphere n):]
[:NAT, the carrier of (TUnitSphere n):] is Relation-like set
bool [:NAT, the carrier of (TUnitSphere n):] is set
rng (x * C) is finite Element of bool the carrier of (TUnitSphere n)
x is set
x is set
p is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
0. (TOP-REAL f) is Relation-like NAT -defined Function-like finite V32(f) V45( TOP-REAL f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
the ZeroF of (TOP-REAL f) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
Tcircle ((0. (TOP-REAL f)),1) is TopSpace-like SubSpace of TOP-REAL f
the carrier of (Tcircle ((0. (TOP-REAL f)),1)) is set
Sphere ((0. (TOP-REAL f)),1) is closed bounded Element of bool the carrier of (TOP-REAL f)
- p is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
- p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
{p} is non empty trivial functional finite V29() set
(Sphere ((0. (TOP-REAL f)),1)) \ {p} is Element of bool the carrier of (TOP-REAL f)
(TOP-REAL f) | ((Sphere ((0. (TOP-REAL f)),1)) \ {p}) is strict TopSpace-like SubSpace of TOP-REAL f
U is non empty TopSpace-like SubSpace of TOP-REAL f
[#] U is non empty non proper closed Element of bool the carrier of U
the carrier of U is non empty set
bool the carrier of U is set
- (- p) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
- (- p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
{(- p)} is non empty trivial functional finite V29() set
(Sphere ((0. (TOP-REAL f)),1)) \ {(- p)} is Element of bool the carrier of (TOP-REAL f)
(TOP-REAL f) | ((Sphere ((0. (TOP-REAL f)),1)) \ {(- p)}) is strict TopSpace-like SubSpace of TOP-REAL f
V is non empty TopSpace-like SubSpace of TOP-REAL f
[#] V is non empty non proper closed Element of bool the carrier of V
the carrier of V is non empty set
bool the carrier of V is set
c is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
C /. c is real V101() ext-real Element of REAL
c + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (c + 1) is real V101() ext-real Element of REAL
[.(C /. c),(C /. (c + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x .: [.(C /. c),(C /. (c + 1)).] is Element of bool the carrier of (TUnitSphere n)
Seg (len C) is finite V32( len C) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
dom C is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc2 is ordinal natural real V101() ext-real non negative set
fc1 is Relation-like NAT -defined Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued set
fc1 . (c + 1) is real V101() ext-real set
fc1 . 1 is real V101() ext-real set
fc1 . c is real V101() ext-real set
c0 is complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
x .: c0 is Element of bool the carrier of (TUnitSphere n)
g .: c0 is Element of bool the carrier of (TOP-REAL f)
f0 is Element of bool the carrier of (Euclid f)
diameter f0 is real V101() ext-real Element of REAL
c1 is Element of the carrier of (Euclid f)
c2 is Element of the carrier of (Euclid f)
dist (c1,c2) is real V101() ext-real Element of REAL
REAL f is non empty functional FinSequence-membered FinSequenceSet of REAL
Pitag_dist f is Relation-like [:(REAL f),(REAL f):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[:(REAL f),(REAL f):],REAL:]
[:(REAL f),(REAL f):] is Relation-like set
[:[:(REAL f),(REAL f):],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[:(REAL f),(REAL f):],REAL:] is set
MetrStruct(# (REAL f),(Pitag_dist f) #) is strict MetrStruct
the distance of (Euclid f) is Relation-like [: the carrier of (Euclid f), the carrier of (Euclid f):] -defined REAL -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [:[: the carrier of (Euclid f), the carrier of (Euclid f):],REAL:]
[: the carrier of (Euclid f), the carrier of (Euclid f):] is Relation-like set
[:[: the carrier of (Euclid f), the carrier of (Euclid f):],REAL:] is Relation-like complex-yielding ext-real-valued real-valued set
bool [:[: the carrier of (Euclid f), the carrier of (Euclid f):],REAL:] is set
the distance of (Euclid f) . (c1,c2) is real V101() ext-real Element of REAL
ci1 is Relation-like NAT -defined REAL -valued Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL f
ci1 is Relation-like NAT -defined REAL -valued Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL f
ci1 - ci1 is Relation-like NAT -defined REAL -valued Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of REAL f
|.(ci1 - ci1).| is real V101() ext-real non negative Element of REAL
p - (- p) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p - (- p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p - (- p)).| is real V101() ext-real non negative Element of REAL
p + (- (- p)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p + (- (- p)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p + (- (- p))).| is real V101() ext-real non negative Element of REAL
di1 is real V101() ext-real set
di1 * p is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
di1 * p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
(di1 * p) + p is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
(di1 * p) + p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((di1 * p) + p).| is real V101() ext-real non negative Element of REAL
(di1 * p) + (di1 * p) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
(di1 * p) + (di1 * p) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((di1 * p) + (di1 * p)).| is real V101() ext-real non negative Element of REAL
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(1 + 1) * p is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
(1 + 1) * p is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.((1 + 1) * p).| is real V101() ext-real non negative Element of REAL
abs 2 is real V101() ext-real Element of REAL
|.p.| is real V101() ext-real non negative Element of REAL
(abs 2) * |.p.| is real V101() ext-real set
p - (0. (TOP-REAL f)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p - (0. (TOP-REAL f)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p - (0. (TOP-REAL f))).| is real V101() ext-real non negative Element of REAL
- (0. (TOP-REAL f)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
- (0. (TOP-REAL f)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
p + (- (0. (TOP-REAL f))) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p + (- (0. (TOP-REAL f))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p + (- (0. (TOP-REAL f)))).| is real V101() ext-real non negative Element of REAL
- 1 is real V101() ext-real non positive set
(- 1) * (0. (TOP-REAL f)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
(- 1) * (0. (TOP-REAL f)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
p + ((- 1) * (0. (TOP-REAL f))) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p + ((- 1) * (0. (TOP-REAL f))) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p + ((- 1) * (0. (TOP-REAL f)))).| is real V101() ext-real non negative Element of REAL
p + (0. (TOP-REAL f)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
p + (0. (TOP-REAL f)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(p + (0. (TOP-REAL f))).| is real V101() ext-real non negative Element of REAL
|.2.| is real V101() ext-real Element of REAL
[#] (TUnitSphere n) is non empty non proper closed Element of bool the carrier of (TUnitSphere n)
PFuncs (REAL,([#] (TUnitSphere n))) is non empty functional set
((TUnitSphere n)) is non empty functional Element of bool (PFuncs (REAL,([#] (TUnitSphere n))))
bool (PFuncs (REAL,([#] (TUnitSphere n)))) is set
[: the carrier of R^1, the carrier of (TUnitSphere n):] is Relation-like set
bool [: the carrier of R^1, the carrier of (TUnitSphere n):] is set
{ b1 where b1 is Relation-like Function-like Element of PFuncs (REAL,([#] (TUnitSphere n))) : b1 is Relation-like the carrier of R^1 -defined the carrier of (TUnitSphere n) -valued Function-like ( TUnitSphere n) Element of bool [: the carrier of R^1, the carrier of (TUnitSphere n):] } is set
inf (dom x) is ext-real set
sup (dom x) is ext-real set
(len C) - 1 is real V101() ext-real set
c is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
fc1 is Relation-like NAT -defined ((TUnitSphere n)) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of ((TUnitSphere n))
len fc1 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
((TUnitSphere n),fc1) is Relation-like Function-like Element of ((TUnitSphere n))
fc2 is ordinal natural real V101() ext-real non negative set
fc1 /. fc2 is Relation-like Function-like Element of ((TUnitSphere n))
rng (fc1 /. fc2) is set
((len C) - 1) + 1 is real V101() ext-real set
c0 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
C /. c0 is real V101() ext-real Element of REAL
c0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (c0 + 1) is real V101() ext-real Element of REAL
[.(C /. c0),(C /. (c0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
x .: [.(C /. c0),(C /. (c0 + 1)).] is Element of bool the carrier of (TUnitSphere n)
x | [.(C /. c0),(C /. (c0 + 1)).] is Relation-like the carrier of I[01] -defined [.(C /. c0),(C /. (c0 + 1)).] -defined the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like Element of bool [: the carrier of I[01], the carrier of (TUnitSphere n):]
[: the carrier of I[01], the carrier of (TUnitSphere n):] is Relation-like set
bool [: the carrier of I[01], the carrier of (TUnitSphere n):] is set
rng (x | [.(C /. c0),(C /. (c0 + 1)).]) is Element of bool the carrier of (TUnitSphere n)
fc2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng fc2 is non empty set
((TUnitSphere n),fc2) is Element of the carrier of (TUnitSphere n)
dom fc2 is non empty complex-membered ext-real-membered real-membered set
inf (dom fc2) is real V101() ext-real set
fc2 . (inf (dom fc2)) is set
((TUnitSphere n),fc2) is Element of the carrier of (TUnitSphere n)
sup (dom fc2) is real V101() ext-real set
fc2 . (sup (dom fc2)) is set
L[01] (0,1,(inf (dom fc2)),(sup (dom fc2))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))):]
Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2))) is non empty strict TopSpace-like real-membered SubSpace of R^1
the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) is non empty complex-membered ext-real-membered real-membered set
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))):] is set
(L[01] (0,1,(inf (dom fc2)),(sup (dom fc2)))) * fc2 is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
TPlane ((- p),(0. (TOP-REAL f))) is non empty TopSpace-like pathwise_connected convex () () SubSpace of TOP-REAL f
stereographic_projection (V,(- p)) is non empty Relation-like the carrier of V -defined the carrier of (TPlane ((- p),(0. (TOP-REAL f)))) -valued Function-like total quasi_total Element of bool [: the carrier of V, the carrier of (TPlane ((- p),(0. (TOP-REAL f)))):]
the carrier of (TPlane ((- p),(0. (TOP-REAL f)))) is non empty set
[: the carrier of V, the carrier of (TPlane ((- p),(0. (TOP-REAL f)))):] is Relation-like set
bool [: the carrier of V, the carrier of (TPlane ((- p),(0. (TOP-REAL f)))):] is set
(- p) - (0. (TOP-REAL f)) is Relation-like NAT -defined Function-like finite V32(f) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL f)
(- p) - (0. (TOP-REAL f)) is Relation-like NAT -defined REAL -valued Function-like finite FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued FinSequence of REAL
|.(0. (TOP-REAL f)).| is real V101() ext-real non negative Element of REAL
TOP-REAL n is non empty TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() () RLTopStruct
the carrier of (TOP-REAL n) is non empty set
[: the carrier of (TOP-REAL n), the carrier of V:] is Relation-like set
bool [: the carrier of (TOP-REAL n), the carrier of V:] is set
c2 is non empty Relation-like the carrier of (TOP-REAL n) -defined the carrier of V -valued Function-like total quasi_total Element of bool [: the carrier of (TOP-REAL n), the carrier of V:]
dom c2 is non empty Element of bool the carrier of (TOP-REAL n)
bool the carrier of (TOP-REAL n) is set
[#] (TOP-REAL n) is non empty non proper closed Element of bool the carrier of (TOP-REAL n)
rng c2 is non empty Element of bool the carrier of V
ci1 is Element of the carrier of V
{ci1} is non empty trivial finite set
([#] V) \ {ci1} is Element of bool the carrier of V
ci1 is non empty Element of bool the carrier of V
V | ci1 is non empty strict TopSpace-like SubSpace of V
[#] (V | ci1) is non empty non proper closed Element of bool the carrier of (V | ci1)
the carrier of (V | ci1) is non empty set
bool the carrier of (V | ci1) is set
di1 is Element of the carrier of (V | ci1)
di1 is Element of the carrier of (V | ci1)
[: the carrier of I[01], the carrier of (V | ci1):] is Relation-like set
bool [: the carrier of I[01], the carrier of (V | ci1):] is set
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (V | ci1) -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of (V | ci1):]
p3 . 0 is set
p3 . 1 is set
(TOP-REAL f) | (Sphere ((0. (TOP-REAL f)),1)) is strict TopSpace-like SubSpace of TOP-REAL f
S0 is non empty TopSpace-like SubSpace of TUnitSphere n
the carrier of S0 is non empty set
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (V | ci1) -valued Function-like total quasi_total Path of di1,di1
dom p3 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] I[01] is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
[#] S0 is non empty non proper closed Element of bool the carrier of S0
bool the carrier of S0 is set
rng p3 is non empty Element of bool the carrier of (V | ci1)
[: the carrier of I[01], the carrier of (TUnitSphere n):] is Relation-like set
bool [: the carrier of I[01], the carrier of (TUnitSphere n):] is set
p3 is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total Element of bool [: the carrier of I[01], the carrier of (TUnitSphere n):]
c1 is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total Path of ((TUnitSphere n),fc2),((TUnitSphere n),fc2)
rng c1 is non empty Element of bool the carrier of (TUnitSphere n)
p2 is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total Path of ((TUnitSphere n),fc2),((TUnitSphere n),fc2)
rng p2 is non empty Element of bool the carrier of (TUnitSphere n)
s1 is Element of the carrier of S0
s2 is Element of the carrier of S0
Paths (s1,s2) is non empty set
EqRel (S0,s1,s2) is Relation-like Paths (s1,s2) -defined Paths (s1,s2) -valued Element of bool [:(Paths (s1,s2)),(Paths (s1,s2)):]
[:(Paths (s1,s2)),(Paths (s1,s2)):] is Relation-like set
bool [:(Paths (s1,s2)),(Paths (s1,s2)):] is set
p5 is non empty Relation-like the carrier of I[01] -defined the carrier of S0 -valued Function-like total quasi_total Path of s1,s2
Class ((EqRel (S0,s1,s2)),p5) is Element of bool (Paths (s1,s2))
bool (Paths (s1,s2)) is set
p6 is non empty Relation-like the carrier of I[01] -defined the carrier of S0 -valued Function-like total quasi_total Path of s1,s2
Class ((EqRel (S0,s1,s2)),p6) is Element of bool (Paths (s1,s2))
L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1) is non empty Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (Closed-Interval-TSpace (0,1)):]
[: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (Closed-Interval-TSpace (0,1)):] is Relation-like complex-yielding ext-real-valued real-valued set
bool [: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (Closed-Interval-TSpace (0,1)):] is set
p2 * (L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1)) is Relation-like the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) -defined the carrier of (TUnitSphere n) -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (TUnitSphere n):]
[: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (TUnitSphere n):] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))), the carrier of (TUnitSphere n):] is set
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c2 is non empty set
dom c2 is non empty complex-membered ext-real-membered real-membered set
rng (L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1)) is non empty complex-membered ext-real-membered real-membered Element of bool REAL
[#] (Closed-Interval-TSpace (0,1)) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace (0,1))
bool the carrier of (Closed-Interval-TSpace (0,1)) is set
dom p2 is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of I[01]
dom (L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1)) is non empty complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2))))
bool the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) is set
[#] (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2)))) is non empty non proper closed complex-membered ext-real-membered real-membered Element of bool the carrier of (Closed-Interval-TSpace ((inf (dom fc2)),(sup (dom fc2))))
[.(inf (dom fc2)),(sup (dom fc2)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
(L[01] (0,1,(inf (dom fc2)),(sup (dom fc2)))) * c2 is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined Function-like set
(L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1)) * (L[01] (0,1,(inf (dom fc2)),(sup (dom fc2)))) is non empty Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (Closed-Interval-TSpace (0,1)) -valued Function-like total quasi_total complex-yielding ext-real-valued real-valued Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (Closed-Interval-TSpace (0,1)):]
p2 * ((L[01] ((inf (dom fc2)),(sup (dom fc2)),0,1)) * (L[01] (0,1,(inf (dom fc2)),(sup (dom fc2))))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (TUnitSphere n) -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (TUnitSphere n):]
[: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (TUnitSphere n):] is Relation-like set
bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (TUnitSphere n):] is set
p2 * (id (Closed-Interval-TSpace (0,1))) is Relation-like the carrier of (Closed-Interval-TSpace (0,1)) -defined the carrier of (TUnitSphere n) -valued Function-like Element of bool [: the carrier of (Closed-Interval-TSpace (0,1)), the carrier of (TUnitSphere n):]
inf (dom c2) is real V101() ext-real set
sup (dom c2) is real V101() ext-real set
((Sphere ((0. (TOP-REAL f)),1)) \ {p}) \ {(- p)} is Element of bool the carrier of (TOP-REAL f)
([#] V) \ {p} is Element of bool the carrier of V
{(- p)} \/ {p} is non empty finite V29() set
(Sphere ((0. (TOP-REAL f)),1)) \ ({(- p)} \/ {p}) is Element of bool the carrier of (TOP-REAL f)
dom C is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc2 is ordinal natural real V101() ext-real non negative set
fc2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc1 /. fc2 is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc1 /. fc2) is complex-membered ext-real-membered real-membered set
C /. fc2 is real V101() ext-real Element of REAL
C /. (fc2 + 1) is real V101() ext-real Element of REAL
[.(C /. fc2),(C /. (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
1 + fc2 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
((len C) - 1) + 1 is real V101() ext-real set
Seg (len C) is finite V32( len C) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
C . fc2 is real V101() ext-real set
C . (fc2 + 1) is real V101() ext-real set
[.(C . fc2),(C . (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
dom c is non empty complex-membered ext-real-membered real-membered set
c | [.(C /. fc2),(C /. (fc2 + 1)).] is Relation-like Function-like set
fc2 is ordinal natural real V101() ext-real non negative set
fc1 /. fc2 is Relation-like Function-like Element of ((TUnitSphere n))
C /. fc2 is real V101() ext-real Element of REAL
fc2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (fc2 + 1) is real V101() ext-real Element of REAL
[.(C /. fc2),(C /. (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c | [.(C /. fc2),(C /. (fc2 + 1)).] is Relation-like Function-like set
C . (fc2 + 1) is real V101() ext-real set
C . fc2 is real V101() ext-real set
dom (fc1 /. fc2) is complex-membered ext-real-membered real-membered set
c0 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c0 is non empty complex-membered ext-real-membered real-membered set
inf (dom c0) is real V101() ext-real set
sup (dom c0) is real V101() ext-real set
[.(inf (dom c0)),(sup (dom c0)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
rng c0 is non empty set
rng c0 is non empty set
dom (x * C) is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
((TUnitSphere n),c0) is Element of the carrier of (TUnitSphere n)
c0 . (inf (dom c0)) is set
x . (C . fc2) is set
(x * C) . fc2 is set
((TUnitSphere n),c0) is Element of the carrier of (TUnitSphere n)
c0 . (sup (dom c0)) is set
x . (C . (fc2 + 1)) is set
(x * C) . (fc2 + 1) is set
f0 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng f0 is non empty set
dom f0 is non empty complex-membered ext-real-membered real-membered set
rng c0 is non empty set
Seg (len fc1) is finite V32( len fc1) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc2 is ordinal natural real V101() ext-real non negative set
fc1 /. fc2 is Relation-like Function-like Element of ((TUnitSphere n))
f0 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom f0 is non empty complex-membered ext-real-membered real-membered set
C /. fc2 is real V101() ext-real Element of REAL
fc2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (fc2 + 1) is real V101() ext-real Element of REAL
[.(C /. fc2),(C /. (fc2 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c1 is non empty set
dom c1 is non empty complex-membered ext-real-membered real-membered set
c2 is Relation-like Function-like Element of ((TUnitSphere n))
ci1 is ordinal natural real V101() ext-real non negative set
ci1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
fc1 /. ci1 is Relation-like Function-like Element of ((TUnitSphere n))
dom ci1 is non empty complex-membered ext-real-membered real-membered set
C /. ci1 is real V101() ext-real Element of REAL
ci1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (ci1 + 1) is real V101() ext-real Element of REAL
[.(C /. ci1),(C /. (ci1 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
fc2 is Relation-like NAT -defined ((TUnitSphere n)) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of ((TUnitSphere n))
dom fc2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc2 is Relation-like NAT -defined ((TUnitSphere n)) -valued Function-like finite FinSequence-like FinSubsequence-like Function-yielding V204() FinSequence of ((TUnitSphere n))
dom fc2 is finite complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
len fc2 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
2 - 1 is real V101() ext-real set
c0 is ordinal natural real V101() ext-real non negative set
fc2 /. c0 is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc2 /. c0) is complex-membered ext-real-membered real-membered set
sup (dom (fc2 /. c0)) is ext-real set
(fc2 /. c0) . (sup (dom (fc2 /. c0))) is set
c0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc2 /. (c0 + 1) is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc2 /. (c0 + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (fc2 /. (c0 + 1))) is ext-real set
(fc2 /. (c0 + 1)) . (inf (dom (fc2 /. (c0 + 1)))) is set
fc1 /. c0 is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . c0 is Relation-like Function-like set
c1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c1 is non empty complex-membered ext-real-membered real-membered set
C /. c0 is real V101() ext-real Element of REAL
C /. (c0 + 1) is real V101() ext-real Element of REAL
[.(C /. c0),(C /. (c0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c2 is non empty set
dom c2 is non empty complex-membered ext-real-membered real-membered set
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc1 /. (c0 + 1) is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . (c0 + 1) is Relation-like Function-like set
ci1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom ci1 is non empty complex-membered ext-real-membered real-membered set
(c0 + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. ((c0 + 1) + 1) is real V101() ext-real Element of REAL
[.(C /. (c0 + 1)),(C /. ((c0 + 1) + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
di1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng di1 is non empty set
dom di1 is non empty complex-membered ext-real-membered real-membered set
dom (fc1 /. c0) is complex-membered ext-real-membered real-membered set
dom (fc1 /. (c0 + 1)) is complex-membered ext-real-membered real-membered set
((TUnitSphere n),c2) is Element of the carrier of (TUnitSphere n)
sup (dom c2) is real V101() ext-real set
c2 . (sup (dom c2)) is set
((TUnitSphere n),c1) is Element of the carrier of (TUnitSphere n)
sup (dom c1) is real V101() ext-real set
c1 . (sup (dom c1)) is set
(fc1 /. c0) . (C /. (c0 + 1)) is set
c | [.(C /. c0),(C /. (c0 + 1)).] is Relation-like Function-like set
(c | [.(C /. c0),(C /. (c0 + 1)).]) . (C /. (c0 + 1)) is set
c . (C /. (c0 + 1)) is set
c | [.(C /. (c0 + 1)),(C /. ((c0 + 1) + 1)).] is Relation-like Function-like set
(c | [.(C /. (c0 + 1)),(C /. ((c0 + 1) + 1)).]) . (C /. (c0 + 1)) is set
(fc1 /. (c0 + 1)) . (C /. (c0 + 1)) is set
((TUnitSphere n),ci1) is Element of the carrier of (TUnitSphere n)
inf (dom ci1) is real V101() ext-real set
ci1 . (inf (dom ci1)) is set
((TUnitSphere n),di1) is Element of the carrier of (TUnitSphere n)
inf (dom di1) is real V101() ext-real set
di1 . (inf (dom di1)) is set
c0 + 2 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (c0 + 2) is real V101() ext-real Element of REAL
[.(C /. (c0 + 1)),(C /. (c0 + 2)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c0 is ordinal natural real V101() ext-real non negative set
fc2 /. c0 is Relation-like Function-like Element of ((TUnitSphere n))
fc1 /. c0 is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . c0 is Relation-like Function-like set
c1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c1 is non empty complex-membered ext-real-membered real-membered set
C /. c0 is real V101() ext-real Element of REAL
c0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (c0 + 1) is real V101() ext-real Element of REAL
[.(C /. c0),(C /. (c0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c2 is non empty set
dom c2 is non empty complex-membered ext-real-membered real-membered set
((TUnitSphere n),fc2) is Relation-like Function-like Element of ((TUnitSphere n))
fc2 /. 1 is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc2 /. 1) is complex-membered ext-real-membered real-membered set
inf (dom (fc2 /. 1)) is ext-real set
fc2 /. (len fc2) is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc2 /. (len fc2)) is complex-membered ext-real-membered real-membered set
sup (dom (fc2 /. (len fc2))) is ext-real set
[.(inf (dom (fc2 /. 1))),(sup (dom (fc2 /. (len fc2)))).] is interval set
(fc2 /. 1) . (inf (dom (fc2 /. 1))) is set
(fc2 /. (len fc2)) . (sup (dom (fc2 /. (len fc2)))) is set
c0 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c0 is non empty complex-membered ext-real-membered real-membered set
((TUnitSphere n),c0) is Element of the carrier of (TUnitSphere n)
inf (dom c0) is real V101() ext-real set
c0 . (inf (dom c0)) is set
((TUnitSphere n),c0) is Element of the carrier of (TUnitSphere n)
sup (dom c0) is real V101() ext-real set
c0 . (sup (dom c0)) is set
f0 is ordinal natural real V101() ext-real non negative set
fc1 /. f0 is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc1 /. f0) is complex-membered ext-real-membered real-membered set
sup (dom (fc1 /. f0)) is ext-real set
(fc1 /. f0) . (sup (dom (fc1 /. f0))) is set
f0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc1 /. (f0 + 1) is Relation-like Function-like Element of ((TUnitSphere n))
dom (fc1 /. (f0 + 1)) is complex-membered ext-real-membered real-membered set
inf (dom (fc1 /. (f0 + 1))) is ext-real set
(fc1 /. (f0 + 1)) . (inf (dom (fc1 /. (f0 + 1)))) is set
fc2 . f0 is Relation-like Function-like set
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c2 is non empty complex-membered ext-real-membered real-membered set
C /. f0 is real V101() ext-real Element of REAL
C /. (f0 + 1) is real V101() ext-real Element of REAL
[.(C /. f0),(C /. (f0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
ci1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng ci1 is non empty set
dom ci1 is non empty complex-membered ext-real-membered real-membered set
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc2 . (f0 + 1) is Relation-like Function-like set
di1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom di1 is non empty complex-membered ext-real-membered real-membered set
(f0 + 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. ((f0 + 1) + 1) is real V101() ext-real Element of REAL
[.(C /. (f0 + 1)),(C /. ((f0 + 1) + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
di1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng di1 is non empty set
dom di1 is non empty complex-membered ext-real-membered real-membered set
(fc1 /. f0) . (C /. (f0 + 1)) is set
c | [.(C /. f0),(C /. (f0 + 1)).] is Relation-like Function-like set
(c | [.(C /. f0),(C /. (f0 + 1)).]) . (C /. (f0 + 1)) is set
c . (C /. (f0 + 1)) is set
c | [.(C /. (f0 + 1)),(C /. ((f0 + 1) + 1)).] is Relation-like Function-like set
(c | [.(C /. (f0 + 1)),(C /. ((f0 + 1) + 1)).]) . (C /. (f0 + 1)) is set
(fc1 /. (f0 + 1)) . (C /. (f0 + 1)) is set
f0 is ordinal natural real V101() ext-real non negative set
fc2 /. f0 is Relation-like Function-like Element of ((TUnitSphere n))
fc1 /. f0 is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . f0 is Relation-like Function-like set
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c2 is non empty complex-membered ext-real-membered real-membered set
C /. f0 is real V101() ext-real Element of REAL
f0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (f0 + 1) is real V101() ext-real Element of REAL
[.(C /. f0),(C /. (f0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
ci1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng ci1 is non empty set
dom ci1 is non empty complex-membered ext-real-membered real-membered set
(len fc1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
fc1 /. 1 is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . 1 is Relation-like Function-like set
c1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c1 is non empty complex-membered ext-real-membered real-membered set
C /. 1 is real V101() ext-real Element of REAL
1 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (1 + 1) is real V101() ext-real Element of REAL
[.(C /. 1),(C /. (1 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c2 is non empty set
dom c2 is non empty complex-membered ext-real-membered real-membered set
Seg (len fc2) is finite V32( len fc2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
Seg (len C) is finite V32( len C) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc1 /. (len fc1) is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . (len fc1) is Relation-like Function-like set
ci1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom ci1 is non empty complex-membered ext-real-membered real-membered set
C /. (len fc1) is real V101() ext-real Element of REAL
C /. ((len fc1) + 1) is real V101() ext-real Element of REAL
[.(C /. (len fc1)),(C /. ((len fc1) + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
di1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng di1 is non empty set
dom di1 is non empty complex-membered ext-real-membered real-membered set
f0 is ordinal natural real V101() ext-real non negative set
fc2 /. f0 is Relation-like Function-like Element of ((TUnitSphere n))
rng (fc2 /. f0) is set
Seg (len fc2) is finite V32( len fc2) complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below bounded_above real-bounded Element of bool NAT
fc1 /. f0 is Relation-like Function-like Element of ((TUnitSphere n))
fc2 . f0 is Relation-like Function-like set
c1 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
dom c1 is non empty complex-membered ext-real-membered real-membered set
C /. f0 is real V101() ext-real Element of REAL
f0 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
C /. (f0 + 1) is real V101() ext-real Element of REAL
[.(C /. f0),(C /. (f0 + 1)).] is complex-membered ext-real-membered real-membered interval Element of bool REAL
c2 is non empty Relation-like Function-like ( TUnitSphere n) ( TUnitSphere n) ( TUnitSphere n) Element of ((TUnitSphere n))
rng c2 is non empty set
dom c2 is non empty complex-membered ext-real-membered real-membered set
rng c0 is non empty set
((TUnitSphere n),c) is Element of the carrier of (TUnitSphere n)
dom c is non empty complex-membered ext-real-membered real-membered set
inf (dom c) is real V101() ext-real set
c . (inf (dom c)) is set
((TUnitSphere n),c) is Element of the carrier of (TUnitSphere n)
sup (dom c) is real V101() ext-real set
c . (sup (dom c)) is set
f0 is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total continuous Path of r,r
rng f0 is non empty Element of bool the carrier of (TUnitSphere n)
n is ordinal natural real V101() ext-real non negative set
TUnitSphere n is non empty TopSpace-like T_0 T_1 T_2 n -locally_euclidean n -manifold manifold-like V359() TopStruct
the carrier of (TUnitSphere n) is non empty set
x is Element of the carrier of (TUnitSphere n)
f is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total continuous Path of x,x
rng f is non empty Element of bool the carrier of (TUnitSphere n)
bool the carrier of (TUnitSphere n) is set
rng f is non empty Element of bool the carrier of (TUnitSphere n)
bool the carrier of (TUnitSphere n) is set
g is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like total quasi_total continuous Path of x,x
rng g is non empty Element of bool the carrier of (TUnitSphere n)
C is non empty Relation-like the carrier of I[01] -defined the carrier of (TUnitSphere n) -valued Function-like constant total quasi_total continuous ( TUnitSphere n,x) Path of x,x
rng f is non empty Element of bool the carrier of (TUnitSphere n)
bool the carrier of (TUnitSphere n) is set
n is non empty ordinal natural real V101() ext-real positive non negative set
TOP-REAL n is non empty non trivial non finite TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() n -locally_euclidean V359() () RLTopStruct
the carrier of (TOP-REAL n) is non empty non trivial non finite set
r is non empty real V101() ext-real positive non negative set
x is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tcircle (x,r) is non empty strict TopSpace-like SubSpace of TOP-REAL n
3 - 1 is real V101() ext-real set
n - 1 is real V101() ext-real set
n -' 1 is ordinal natural real V101() ext-real non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered bounded_below Element of NAT
(n -' 1) + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
(n - 1) + 1 is real V101() ext-real set
2 + 1 is non empty ordinal natural real V101() ext-real positive non negative V153() V154() complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered left_end bounded_below Element of NAT
TUnitSphere (n -' 1) is non empty TopSpace-like T_0 T_1 T_2 n -' 1 -locally_euclidean n -' 1 -manifold manifold-like V359() TopStruct
Tunit_circle ((n -' 1) + 1) is non empty TopSpace-like SubSpace of TOP-REAL ((n -' 1) + 1)
TOP-REAL ((n -' 1) + 1) is non empty non trivial non finite TopSpace-like V114() V142() V143() V144() V145() V146() V147() V148() strict V243() V244() (n -' 1) + 1 -locally_euclidean V359() () RLTopStruct
Tunit_circle n is non empty TopSpace-like SubSpace of TOP-REAL n
0. (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) V45( TOP-REAL n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
the ZeroF of (TOP-REAL n) is Relation-like NAT -defined Function-like finite V32(n) FinSequence-like FinSubsequence-like complex-yielding ext-real-valued real-valued Element of the carrier of (TOP-REAL n)
Tcircle ((0. (TOP-REAL n)),1) is non empty strict TopSpace-like SubSpace of TOP-REAL n