:: FDIFF_2 semantic presentation

REAL is non empty V49() V72() V73() V74() V78() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V72() V73() V74() V75() V76() V77() V78() Element of K19(REAL)
K19(REAL) is set
COMPLEX is non empty V49() V72() V78() set
omega is non empty epsilon-transitive epsilon-connected ordinal V72() V73() V74() V75() V76() V77() V78() set
K19(omega) is set
K20(NAT,REAL) is complex-valued ext-real-valued real-valued set
K19(K20(NAT,REAL)) is set
K19(K19(REAL)) is set
{} is set
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
{{},1} is set
K20(REAL,REAL) is complex-valued ext-real-valued real-valued set
K19(K20(REAL,REAL)) is set
RAT is non empty V49() V72() V73() V74() V75() V78() set
INT is non empty V49() V72() V73() V74() V75() V76() V78() set
K20(COMPLEX,COMPLEX) is complex-valued set
K19(K20(COMPLEX,COMPLEX)) is set
K20(K20(COMPLEX,COMPLEX),COMPLEX) is complex-valued set
K19(K20(K20(COMPLEX,COMPLEX),COMPLEX)) is set
K20(K20(REAL,REAL),REAL) is complex-valued ext-real-valued real-valued set
K19(K20(K20(REAL,REAL),REAL)) is set
K20(RAT,RAT) is V5( RAT ) complex-valued ext-real-valued real-valued set
K19(K20(RAT,RAT)) is set
K20(K20(RAT,RAT),RAT) is V5( RAT ) complex-valued ext-real-valued real-valued set
K19(K20(K20(RAT,RAT),RAT)) is set
K20(INT,INT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued set
K19(K20(INT,INT)) is set
K20(K20(INT,INT),INT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued set
K19(K20(K20(INT,INT),INT)) is set
K20(NAT,NAT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued natural-valued set
K20(K20(NAT,NAT),NAT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued natural-valued set
K19(K20(K20(NAT,NAT),NAT)) is set
K19(NAT) is set
0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
- 1 is non empty V22() real ext-real non positive negative Element of REAL
{0} is V72() V73() V74() V75() V76() V77() set
K19(K20(NAT,NAT)) is set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
[#] REAL is closed open V72() V73() V74() Element of K19(REAL)
-infty is non empty non real ext-real non positive negative set
+infty is non empty non real ext-real positive non negative set
x0 is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
- x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- 1 is non empty V22() real ext-real non positive negative set
(- 1) (#) x0 is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim x0 is V22() real ext-real Element of REAL
f is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim f is V22() real ext-real Element of REAL
h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim h is V22() real ext-real Element of REAL
c is V22() real ext-real set
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * fp is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * fp) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
max ((2 * fm),((2 * fp) + 1)) is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * h) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h . a is V22() real ext-real Element of REAL
(h . a) - (lim x0) is V22() real ext-real Element of REAL
abs ((h . a) - (lim x0)) is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
(x0 . h) - (lim x0) is V22() real ext-real Element of REAL
abs ((x0 . h) - (lim x0)) is V22() real ext-real Element of REAL
h . a is V22() real ext-real Element of REAL
(h . a) - (lim x0) is V22() real ext-real Element of REAL
abs ((h . a) - (lim x0)) is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
(f . h) - (lim x0) is V22() real ext-real Element of REAL
abs ((f . h) - (lim x0)) is V22() real ext-real Element of REAL
h . a is V22() real ext-real Element of REAL
(h . a) - (lim x0) is V22() real ext-real Element of REAL
abs ((h . a) - (lim x0)) is V22() real ext-real Element of REAL
h . a is V22() real ext-real Element of REAL
(h . a) - (lim x0) is V22() real ext-real Element of REAL
abs ((h . a) - (lim x0)) is V22() real ext-real Element of REAL
x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . (f + 1) is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
2 * f is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * f) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * f) + 0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * (f + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . (f + 1) is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
f is set
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . h is V22() real ext-real Element of REAL
2 * h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . f is V22() real ext-real Element of REAL
dom x0 is V72() V73() V74() V75() V76() V77() Element of K19(NAT)
x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
f + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . (f + 1) is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
2 * f is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * f) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((2 * f) + 1) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((2 * f) + 1) + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * (f + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * (f + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . (f + 1) is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
f is set
dom x0 is V72() V73() V74() V75() V76() V77() Element of K19(NAT)
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . h is V22() real ext-real Element of REAL
2 * h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * h) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . f is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
h is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng h is V72() V73() V74() Element of K19(REAL)
lim h is V22() real ext-real Element of REAL
f + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim (f + h) is V22() real ext-real Element of REAL
lim f is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
0 + x0 is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng f is V72() V73() V74() Element of K19(REAL)
h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng h is V72() V73() V74() Element of K19(REAL)
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
f . c is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
h is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
f * h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 . c is V22() real ext-real Element of REAL
h . c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
f . (h . c) is V22() real ext-real Element of REAL
lim f is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim x0 is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
h " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
h + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (h + fm) is V72() V73() V74() Element of K19(REAL)
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
f /* (h + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (h + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h ") (#) ((f /* (h + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((h ") (#) ((f /* (h + fm)) - (f /* fm))) is V22() real ext-real Element of REAL
f /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((f /* (c + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((c ") (#) ((f /* (c + fm)) - (f /* fm))) is V22() real ext-real Element of REAL
fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * a) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . n is V22() real ext-real Element of REAL
h . a is V22() real ext-real Element of REAL
fp . n is V22() real ext-real Element of REAL
c . a is V22() real ext-real Element of REAL
fp . n is V22() real ext-real Element of REAL
fp . n is V22() real ext-real Element of REAL
lim h is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim c is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim fp is V22() real ext-real Element of REAL
n is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
n + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (n + fm) is V72() V73() V74() Element of K19(REAL)
a is set
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(n + fm) . h is V22() real ext-real Element of REAL
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
2 * c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * c) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h + fm) . c is V22() real ext-real Element of REAL
n . h is V22() real ext-real Element of REAL
fm . h is V22() real ext-real Element of REAL
(n . h) + (fm . h) is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
(h . c) + (fm . h) is V22() real ext-real Element of REAL
fm . c is V22() real ext-real Element of REAL
(h . c) + (fm . c) is V22() real ext-real Element of REAL
(c + fm) . c is V22() real ext-real Element of REAL
n . h is V22() real ext-real Element of REAL
fm . h is V22() real ext-real Element of REAL
(n . h) + (fm . h) is V22() real ext-real Element of REAL
c . c is V22() real ext-real Element of REAL
(c . c) + (fm . h) is V22() real ext-real Element of REAL
fm . c is V22() real ext-real Element of REAL
(c . c) + (fm . c) is V22() real ext-real Element of REAL
n " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (n + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) ((f /* (n + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
((n ") (#) ((f /* (n + fm)) - (f /* fm))) * h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((n ") (#) ((f /* (n + fm)) - (f /* fm))) * h) . c is V22() real ext-real Element of REAL
h . c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((n ") (#) ((f /* (n + fm)) - (f /* fm))) . (h . c) is V22() real ext-real Element of REAL
2 * c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(2 * c) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((n ") (#) ((f /* (n + fm)) - (f /* fm))) . ((2 * c) + 1) is V22() real ext-real Element of REAL
(n ") . ((2 * c) + 1) is V22() real ext-real Element of REAL
((f /* (n + fm)) - (f /* fm)) . ((2 * c) + 1) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * (((f /* (n + fm)) - (f /* fm)) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
(f /* (n + fm)) . ((2 * c) + 1) is V22() real ext-real Element of REAL
(f /* fm) . ((2 * c) + 1) is V22() real ext-real Element of REAL
((f /* (n + fm)) . ((2 * c) + 1)) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * (((f /* (n + fm)) . ((2 * c) + 1)) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(n + fm) . ((2 * c) + 1) is V22() real ext-real Element of REAL
f . ((n + fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
(f . ((n + fm) . ((2 * c) + 1))) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * ((f . ((n + fm) . ((2 * c) + 1))) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
n . ((2 * c) + 1) is V22() real ext-real Element of REAL
fm . ((2 * c) + 1) is V22() real ext-real Element of REAL
(n . ((2 * c) + 1)) + (fm . ((2 * c) + 1)) is V22() real ext-real Element of REAL
f . ((n . ((2 * c) + 1)) + (fm . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(f . ((n . ((2 * c) + 1)) + (fm . ((2 * c) + 1)))) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * ((f . ((n . ((2 * c) + 1)) + (fm . ((2 * c) + 1)))) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
c . c is V22() real ext-real Element of REAL
(c . c) + (fm . ((2 * c) + 1)) is V22() real ext-real Element of REAL
f . ((c . c) + (fm . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(f . ((c . c) + (fm . ((2 * c) + 1)))) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * ((f . ((c . c) + (fm . ((2 * c) + 1)))) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
fm . c is V22() real ext-real Element of REAL
(c . c) + (fm . c) is V22() real ext-real Element of REAL
f . ((c . c) + (fm . c)) is V22() real ext-real Element of REAL
(f . ((c . c) + (fm . c))) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * ((f . ((c . c) + (fm . c))) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(c + fm) . c is V22() real ext-real Element of REAL
f . ((c + fm) . c) is V22() real ext-real Element of REAL
(f . ((c + fm) . c)) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * ((f . ((c + fm) . c)) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(f /* (c + fm)) . c is V22() real ext-real Element of REAL
((f /* (c + fm)) . c) - ((f /* fm) . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((n ") . ((2 * c) + 1)) * (((f /* (c + fm)) . c) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(n . ((2 * c) + 1)) " is V22() real ext-real Element of REAL
((n . ((2 * c) + 1)) ") * (((f /* (c + fm)) . c) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(c . c) " is V22() real ext-real Element of REAL
((c . c) ") * (((f /* (c + fm)) . c) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
(c ") . c is V22() real ext-real Element of REAL
((c ") . c) * (((f /* (c + fm)) . c) - ((f /* fm) . ((2 * c) + 1))) is V22() real ext-real Element of REAL
f . (fm . ((2 * c) + 1)) is V22() real ext-real Element of REAL
((f /* (c + fm)) . c) - (f . (fm . ((2 * c) + 1))) is V22() real ext-real Element of REAL
((c ") . c) * (((f /* (c + fm)) . c) - (f . (fm . ((2 * c) + 1)))) is V22() real ext-real Element of REAL
f . (fm . c) is V22() real ext-real Element of REAL
((f /* (c + fm)) . c) - (f . (fm . c)) is V22() real ext-real Element of REAL
((c ") . c) * (((f /* (c + fm)) . c) - (f . (fm . c))) is V22() real ext-real Element of REAL
(f /* fm) . c is V22() real ext-real Element of REAL
((f /* (c + fm)) . c) - ((f /* fm) . c) is V22() real ext-real Element of REAL
((c ") . c) * (((f /* (c + fm)) . c) - ((f /* fm) . c)) is V22() real ext-real Element of REAL
((f /* (c + fm)) - (f /* fm)) . c is V22() real ext-real Element of REAL
((c ") . c) * (((f /* (c + fm)) - (f /* fm)) . c) is V22() real ext-real Element of REAL
((c ") (#) ((f /* (c + fm)) - (f /* fm))) . c is V22() real ext-real Element of REAL
lim (((n ") (#) ((f /* (n + fm)) - (f /* fm))) * h) is V22() real ext-real Element of REAL
lim ((n ") (#) ((f /* (n + fm)) - (f /* fm))) is V22() real ext-real Element of REAL
c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
((n ") (#) ((f /* (n + fm)) - (f /* fm))) * a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((n ") (#) ((f /* (n + fm)) - (f /* fm))) * a) . b is V22() real ext-real Element of REAL
a . b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((n ") (#) ((f /* (n + fm)) - (f /* fm))) . (a . b) is V22() real ext-real Element of REAL
2 * b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((n ") (#) ((f /* (n + fm)) - (f /* fm))) . (2 * b) is V22() real ext-real Element of REAL
(n ") . (2 * b) is V22() real ext-real Element of REAL
((f /* (n + fm)) - (f /* fm)) . (2 * b) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * (((f /* (n + fm)) - (f /* fm)) . (2 * b)) is V22() real ext-real Element of REAL
(f /* (n + fm)) . (2 * b) is V22() real ext-real Element of REAL
(f /* fm) . (2 * b) is V22() real ext-real Element of REAL
((f /* (n + fm)) . (2 * b)) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * (((f /* (n + fm)) . (2 * b)) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(n + fm) . (2 * b) is V22() real ext-real Element of REAL
f . ((n + fm) . (2 * b)) is V22() real ext-real Element of REAL
(f . ((n + fm) . (2 * b))) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * ((f . ((n + fm) . (2 * b))) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
n . (2 * b) is V22() real ext-real Element of REAL
fm . (2 * b) is V22() real ext-real Element of REAL
(n . (2 * b)) + (fm . (2 * b)) is V22() real ext-real Element of REAL
f . ((n . (2 * b)) + (fm . (2 * b))) is V22() real ext-real Element of REAL
(f . ((n . (2 * b)) + (fm . (2 * b)))) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * ((f . ((n . (2 * b)) + (fm . (2 * b)))) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
(h . b) + (fm . (2 * b)) is V22() real ext-real Element of REAL
f . ((h . b) + (fm . (2 * b))) is V22() real ext-real Element of REAL
(f . ((h . b) + (fm . (2 * b)))) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * ((f . ((h . b) + (fm . (2 * b)))) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
fm . b is V22() real ext-real Element of REAL
(h . b) + (fm . b) is V22() real ext-real Element of REAL
f . ((h . b) + (fm . b)) is V22() real ext-real Element of REAL
(f . ((h . b) + (fm . b))) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * ((f . ((h . b) + (fm . b))) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(h + fm) . b is V22() real ext-real Element of REAL
f . ((h + fm) . b) is V22() real ext-real Element of REAL
(f . ((h + fm) . b)) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * ((f . ((h + fm) . b)) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(f /* (h + fm)) . b is V22() real ext-real Element of REAL
((f /* (h + fm)) . b) - ((f /* fm) . (2 * b)) is V22() real ext-real Element of REAL
((n ") . (2 * b)) * (((f /* (h + fm)) . b) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(n . (2 * b)) " is V22() real ext-real Element of REAL
((n . (2 * b)) ") * (((f /* (h + fm)) . b) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(h . b) " is V22() real ext-real Element of REAL
((h . b) ") * (((f /* (h + fm)) . b) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
(h ") . b is V22() real ext-real Element of REAL
((h ") . b) * (((f /* (h + fm)) . b) - ((f /* fm) . (2 * b))) is V22() real ext-real Element of REAL
f . (fm . (2 * b)) is V22() real ext-real Element of REAL
((f /* (h + fm)) . b) - (f . (fm . (2 * b))) is V22() real ext-real Element of REAL
((h ") . b) * (((f /* (h + fm)) . b) - (f . (fm . (2 * b)))) is V22() real ext-real Element of REAL
f . (fm . b) is V22() real ext-real Element of REAL
((f /* (h + fm)) . b) - (f . (fm . b)) is V22() real ext-real Element of REAL
((h ") . b) * (((f /* (h + fm)) . b) - (f . (fm . b))) is V22() real ext-real Element of REAL
(f /* fm) . b is V22() real ext-real Element of REAL
((f /* (h + fm)) . b) - ((f /* fm) . b) is V22() real ext-real Element of REAL
((h ") . b) * (((f /* (h + fm)) . b) - ((f /* fm) . b)) is V22() real ext-real Element of REAL
((f /* (h + fm)) - (f /* fm)) . b is V22() real ext-real Element of REAL
((h ") . b) * (((f /* (h + fm)) - (f /* fm)) . b) is V22() real ext-real Element of REAL
((h ") (#) ((f /* (h + fm)) - (f /* fm))) . b is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
h is open V72() V73() V74() Neighbourhood of x0
NAT --> x0 is V1() V4( REAL ) V4( NAT ) V5( REAL ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued non-decreasing non-increasing V79() Element of K19(K20(REAL,REAL))
fm is V22() real ext-real set
x0 - fm is V22() real ext-real Element of REAL
x0 + fm is V22() real ext-real Element of REAL
].(x0 - fm),(x0 + fm).[ is open V72() V73() V74() Element of K19(REAL)
c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim n is V22() real ext-real Element of REAL
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm / (a + 2) is V22() real ext-real Element of REAL
n . a is V22() real ext-real Element of REAL
a is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
fp is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fp is V72() V73() V74() Element of K19(REAL)
a + fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + fp) is V72() V73() V74() Element of K19(REAL)
h is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . c is V22() real ext-real Element of REAL
h is set
fp . 0 is V22() real ext-real Element of REAL
h is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + fp) . c is V22() real ext-real Element of REAL
c + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm * (c + 2) is V22() real ext-real Element of REAL
fm * 1 is V22() real ext-real Element of REAL
(c + 2) " is non empty V22() real ext-real positive non negative Element of REAL
(fm * (c + 2)) * ((c + 2) ") is V22() real ext-real Element of REAL
fm * ((c + 2) ") is V22() real ext-real Element of REAL
(c + 2) * ((c + 2) ") is non empty V22() real ext-real positive non negative Element of REAL
fm * ((c + 2) * ((c + 2) ")) is V22() real ext-real Element of REAL
fm / (c + 2) is V22() real ext-real Element of REAL
x0 + (fm / (c + 2)) is V22() real ext-real Element of REAL
x0 - 0 is V22() real ext-real Element of REAL
x0 + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 - fm & not x0 + fm <= b₁ ) } is set
a . c is V22() real ext-real Element of REAL
fp . c is V22() real ext-real Element of REAL
(a . c) + (fp . c) is V22() real ext-real Element of REAL
(fm / (c + 2)) + (fp . c) is V22() real ext-real Element of REAL
(fm / (c + 2)) + x0 is V22() real ext-real Element of REAL
h is set
x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng x0 is V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f * h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (f * h) is V72() V73() V74() Element of K19(REAL)
dom h is V72() V73() V74() Element of K19(REAL)
h /* x0 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (h /* x0) is V72() V73() V74() Element of K19(REAL)
h .: (rng x0) is V72() V73() V74() Element of K19(REAL)
F₁() is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
x0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . x0 is V22() real ext-real Element of REAL
x0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
F₁() . x0 is V22() real ext-real Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . c is V22() real ext-real Element of REAL
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . fm is V22() real ext-real Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . fm is V22() real ext-real Element of REAL
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
F₁() . fm is V22() real ext-real Element of REAL
fp is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . n is V22() real ext-real Element of REAL
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . a is V22() real ext-real Element of REAL
f is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(NAT,NAT))
h . 0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
rng h is V72() V73() V74() V75() V76() V77() Element of K19(NAT)
dom h is V72() V73() V74() V75() V76() V77() Element of K19(NAT)
c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . fm is V22() real ext-real Element of REAL
rng c is V72() V73() V74() Element of K19(REAL)
fm is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . (fm + 1) is V22() real ext-real Element of REAL
c . fm is V22() real ext-real Element of REAL
fm is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
fp is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . fp is V22() real ext-real Element of REAL
fp is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
F₁() . fp is V22() real ext-real Element of REAL
fm . 0 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
F₁() . n is V22() real ext-real Element of REAL
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
F₁() . n is V22() real ext-real Element of REAL
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . a is V22() real ext-real Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . (a + 1) is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . (fm . (a + 1)) is V22() real ext-real Element of REAL
F₁() * fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(F₁() * fm) . n is V22() real ext-real Element of REAL
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(F₁() * fm) . (n + 1) is V22() real ext-real Element of REAL
fm . n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . (n + 1) is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . h is V22() real ext-real Element of REAL
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . c is V22() real ext-real Element of REAL
F₁() . (fm . (n + 1)) is V22() real ext-real Element of REAL
(F₁() * fm) . 0 is V22() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
F₁() . n is V22() real ext-real Element of REAL
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h . x0 is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
c is open V72() V73() V74() Neighbourhood of x0
fm is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
fp is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
diff (f,x0) is V22() real ext-real Element of REAL
h is open V72() V73() V74() Neighbourhood of x0
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((f /* (c + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V22() real ext-real set
x0 - c is V22() real ext-real Element of REAL
x0 + c is V22() real ext-real Element of REAL
].(x0 - c),(x0 + c).[ is open V72() V73() V74() Element of K19(REAL)
fp is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fp is V72() V73() V74() Element of K19(REAL)
fm is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
fm + fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (fm + fp) is V72() V73() V74() Element of K19(REAL)
fm " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (fm + fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (fm + fp)) - (f /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (fm + fp)) + (- (f /* fp)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(fm ") (#) ((f /* (fm + fp)) - (f /* fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp))) is V22() real ext-real Element of REAL
a is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom a is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
a . h is V22() real ext-real Element of REAL
(lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) * h is V22() real ext-real Element of REAL
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
f * h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . x0 is V22() real ext-real Element of REAL
c is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom c is V72() V73() V74() Element of K19(REAL)
c - a is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- a is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) a is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
c + (- a) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
- c is V22() real ext-real set
].(- c),c.[ is open V72() V73() V74() Element of K19(REAL)
b is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom b is V72() V73() V74() Element of K19(REAL)
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . b is V22() real ext-real Element of REAL
b is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
lim b is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
b ^\ n is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of b
r2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
r2 + n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
b . (r2 + n) is V22() real ext-real Element of REAL
(b . (r2 + n)) - 0 is V22() real ext-real Element of REAL
abs ((b . (r2 + n)) - 0) is V22() real ext-real Element of REAL
0 - c is V22() real ext-real Element of REAL
0 + c is V22() real ext-real Element of REAL
].(0 - c),(0 + c).[ is open V72() V73() V74() Element of K19(REAL)
(b ^\ n) . r2 is V22() real ext-real Element of REAL
(b ^\ n) + fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng ((b ^\ n) + fp) is V72() V73() V74() Element of K19(REAL)
r2 is set
c2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((b ^\ n) + fp) . c2 is V22() real ext-real Element of REAL
(b ^\ n) . c2 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= - c & not c <= b₁ ) } is set
((b ^\ n) . c2) + x0 is V22() real ext-real Element of REAL
c2 is V22() real ext-real Element of REAL
x0 + (- c) is V22() real ext-real Element of REAL
c2 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 - c & not x0 + c <= b₁ ) } is set
fp . c2 is V22() real ext-real Element of REAL
((b ^\ n) . c2) + (fp . c2) is V22() real ext-real Element of REAL
(b ^\ n) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
a /* (b ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ^\ n) ") (#) (a /* (b ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c /* (b ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ^\ n) ") (#) (c /* (b ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b /* b is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(b ") (#) (b /* b) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ") (#) (b /* b)) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (b ") (#) (b /* b)
(b ") ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of b "
(b /* b) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of b /* b
((b ") ^\ n) (#) ((b /* b) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ^\ n) ") (#) ((b /* b) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b /* (b ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ^\ n) ") (#) (b /* (b ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((b ^\ n) ") (#) (c /* (b ^\ n))) - (((b ^\ n) ") (#) (a /* (b ^\ n))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((b ^\ n) ") (#) (a /* (b ^\ n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((b ^\ n) ") (#) (a /* (b ^\ n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((b ^\ n) ") (#) (c /* (b ^\ n))) + (- (((b ^\ n) ") (#) (a /* (b ^\ n)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c /* (b ^\ n)) - (a /* (b ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (a /* (b ^\ n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (a /* (b ^\ n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c /* (b ^\ n)) + (- (a /* (b ^\ n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((b ^\ n) ") (#) ((c /* (b ^\ n)) - (a /* (b ^\ n))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c - a is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- a is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) a is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
c + (- a) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(c - a) /* (b ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((b ^\ n) ") (#) ((c - a) /* (b ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(b ^\ n) . c2 is V22() real ext-real Element of REAL
((((b ^\ n) ") (#) (c /* (b ^\ n))) - (((b ^\ n) ") (#) (a /* (b ^\ n)))) . c2 is V22() real ext-real Element of REAL
((b ^\ n) ") . c2 is V22() real ext-real Element of REAL
((c - a) /* (b ^\ n)) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (((c - a) /* (b ^\ n)) . c2) is V22() real ext-real Element of REAL
(c - a) . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((c - a) . ((b ^\ n) . c2)) is V22() real ext-real Element of REAL
b . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (b . ((b ^\ n) . c2)) is V22() real ext-real Element of REAL
(b /* (b ^\ n)) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((b /* (b ^\ n)) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") (#) (b /* (b ^\ n))) . c2 is V22() real ext-real Element of REAL
c2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
(b ^\ n) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") (#) (a /* (b ^\ n))) . c2 is V22() real ext-real Element of REAL
((b ^\ n) ") . c2 is V22() real ext-real Element of REAL
(a /* (b ^\ n)) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((a /* (b ^\ n)) . c2) is V22() real ext-real Element of REAL
a . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (a . ((b ^\ n) . c2)) is V22() real ext-real Element of REAL
((b ^\ n) . c2) * (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (((b ^\ n) . c2) * (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp))))) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((b ^\ n) . c2) is V22() real ext-real Element of REAL
((((b ^\ n) ") . c2) * ((b ^\ n) . c2)) * (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) is V22() real ext-real Element of REAL
((b ^\ n) . c2) " is V22() real ext-real Element of REAL
(((b ^\ n) . c2) ") * ((b ^\ n) . c2) is V22() real ext-real Element of REAL
((((b ^\ n) . c2) ") * ((b ^\ n) . c2)) * (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) is V22() real ext-real Element of REAL
1 * (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) is V22() real ext-real Element of REAL
c2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") (#) (c /* (b ^\ n))) . c2 is V22() real ext-real Element of REAL
((b ^\ n) ") . c2 is V22() real ext-real Element of REAL
(c /* (b ^\ n)) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((c /* (b ^\ n)) . c2) is V22() real ext-real Element of REAL
(b ^\ n) . c2 is V22() real ext-real Element of REAL
c . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (c . ((b ^\ n) . c2)) is V22() real ext-real Element of REAL
(f * h) . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
((f * h) . ((b ^\ n) . c2)) - (f . x0) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (((f * h) . ((b ^\ n) . c2)) - (f . x0)) is V22() real ext-real Element of REAL
h . ((b ^\ n) . c2) is V22() real ext-real Element of REAL
f . (h . ((b ^\ n) . c2)) is V22() real ext-real Element of REAL
(f . (h . ((b ^\ n) . c2))) - (f . x0) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((f . (h . ((b ^\ n) . c2))) - (f . x0)) is V22() real ext-real Element of REAL
((b ^\ n) . c2) + x0 is V22() real ext-real Element of REAL
f . (((b ^\ n) . c2) + x0) is V22() real ext-real Element of REAL
(f . (((b ^\ n) . c2) + x0)) - (f . x0) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((f . (((b ^\ n) . c2) + x0)) - (f . x0)) is V22() real ext-real Element of REAL
((b ^\ n) + fp) . c2 is V22() real ext-real Element of REAL
f . (((b ^\ n) + fp) . c2) is V22() real ext-real Element of REAL
f . (fp . c2) is V22() real ext-real Element of REAL
(f . (((b ^\ n) + fp) . c2)) - (f . (fp . c2)) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((f . (((b ^\ n) + fp) . c2)) - (f . (fp . c2))) is V22() real ext-real Element of REAL
(f /* fp) . c2 is V22() real ext-real Element of REAL
(f . (((b ^\ n) + fp) . c2)) - ((f /* fp) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * ((f . (((b ^\ n) + fp) . c2)) - ((f /* fp) . c2)) is V22() real ext-real Element of REAL
f /* ((b ^\ n) + fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((b ^\ n) + fp)) . c2 is V22() real ext-real Element of REAL
((f /* ((b ^\ n) + fp)) . c2) - ((f /* fp) . c2) is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (((f /* ((b ^\ n) + fp)) . c2) - ((f /* fp) . c2)) is V22() real ext-real Element of REAL
(f /* ((b ^\ n) + fp)) - (f /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((b ^\ n) + fp)) + (- (f /* fp)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* ((b ^\ n) + fp)) - (f /* fp)) . c2 is V22() real ext-real Element of REAL
(((b ^\ n) ") . c2) * (((f /* ((b ^\ n) + fp)) - (f /* fp)) . c2) is V22() real ext-real Element of REAL
((b ^\ n) ") (#) ((f /* ((b ^\ n) + fp)) - (f /* fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((b ^\ n) ") (#) ((f /* ((b ^\ n) + fp)) - (f /* fp))) . c2 is V22() real ext-real Element of REAL
lim (((b ^\ n) ") (#) (c /* (b ^\ n))) is V22() real ext-real Element of REAL
lim (((b ^\ n) ") (#) (a /* (b ^\ n))) is V22() real ext-real Element of REAL
(((b ^\ n) ") (#) (a /* (b ^\ n))) . 0 is V22() real ext-real Element of REAL
lim ((((b ^\ n) ") (#) (c /* (b ^\ n))) - (((b ^\ n) ") (#) (a /* (b ^\ n)))) is V22() real ext-real Element of REAL
(lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) - (lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) is V22() real ext-real Element of REAL
lim (((b ^\ n) ") (#) (b /* (b ^\ n))) is V22() real ext-real Element of REAL
lim ((b ") (#) (b /* b)) is V22() real ext-real Element of REAL
n is open V72() V73() V74() Neighbourhood of x0
b is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
r1 . 1 is V22() real ext-real Element of REAL
(lim ((fm ") (#) ((f /* (fm + fp)) - (f /* fp)))) * 1 is V22() real ext-real Element of REAL
c2 is V22() real ext-real Element of REAL
c2 - x0 is V22() real ext-real Element of REAL
r1 . (c2 - x0) is V22() real ext-real Element of REAL
r2 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
r2 . (c2 - x0) is V22() real ext-real Element of REAL
(r1 . (c2 - x0)) + (r2 . (c2 - x0)) is V22() real ext-real Element of REAL
c - r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- r1 is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) r1 is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
c + (- r1) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(c - r1) . (c2 - x0) is V22() real ext-real Element of REAL
(r1 . (c2 - x0)) + ((c - r1) . (c2 - x0)) is V22() real ext-real Element of REAL
c . (c2 - x0) is V22() real ext-real Element of REAL
(c . (c2 - x0)) - (r1 . (c2 - x0)) is V22() real ext-real Element of REAL
(r1 . (c2 - x0)) + ((c . (c2 - x0)) - (r1 . (c2 - x0))) is V22() real ext-real Element of REAL
(f * h) . (c2 - x0) is V22() real ext-real Element of REAL
((f * h) . (c2 - x0)) - (f . x0) is V22() real ext-real Element of REAL
h . (c2 - x0) is V22() real ext-real Element of REAL
f . (h . (c2 - x0)) is V22() real ext-real Element of REAL
(f . (h . (c2 - x0))) - (f . x0) is V22() real ext-real Element of REAL
(c2 - x0) + x0 is V22() real ext-real Element of REAL
f . ((c2 - x0) + x0) is V22() real ext-real Element of REAL
(f . ((c2 - x0) + x0)) - (f . x0) is V22() real ext-real Element of REAL
f . c2 is V22() real ext-real Element of REAL
(f . c2) - (f . x0) is V22() real ext-real Element of REAL
n is open V72() V73() V74() Neighbourhood of x0
r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
r1 . 1 is V22() real ext-real Element of REAL
r2 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
n is open V72() V73() V74() Neighbourhood of x0
r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
r1 . 1 is V22() real ext-real Element of REAL
r2 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
r1 . 1 is V22() real ext-real Element of REAL
r2 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
c2 is V22() real ext-real Element of REAL
f . c2 is V22() real ext-real Element of REAL
(f . c2) - (f . x0) is V22() real ext-real Element of REAL
c2 - x0 is V22() real ext-real Element of REAL
r1 . (c2 - x0) is V22() real ext-real Element of REAL
r2 . (c2 - x0) is V22() real ext-real Element of REAL
(r1 . (c2 - x0)) + (r2 . (c2 - x0)) is V22() real ext-real Element of REAL
n is open V72() V73() V74() Neighbourhood of x0
r1 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
r1 . 1 is V22() real ext-real Element of REAL
r2 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
n is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
n " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
r1 is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng r1 is V72() V73() V74() Element of K19(REAL)
n + r1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (n + r1) is V72() V73() V74() Element of K19(REAL)
f /* (n + r1) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* r1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n + r1)) - (f /* r1) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* r1) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* r1) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (n + r1)) + (- (f /* r1)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) ((f /* (n + r1)) - (f /* r1)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((n ") (#) ((f /* (n + r1)) - (f /* r1))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f . x0 is V22() real ext-real Element of REAL
h is open V72() V73() V74() Neighbourhood of x0
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
f /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((f /* (c + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim c is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
fp is V22() real ext-real set
x0 - fp is V22() real ext-real Element of REAL
x0 + fp is V22() real ext-real Element of REAL
].(x0 - fp),(x0 + fp).[ is open V72() V73() V74() Element of K19(REAL)
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c ^\ n is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of c
(c ^\ n) + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng ((c ^\ n) + fm) is V72() V73() V74() Element of K19(REAL)
h is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((c ^\ n) + fm) . c is V22() real ext-real Element of REAL
fm . c is V22() real ext-real Element of REAL
(c ^\ n) . c is V22() real ext-real Element of REAL
((c ^\ n) . c) + x0 is V22() real ext-real Element of REAL
c + n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . (c + n) is V22() real ext-real Element of REAL
(c . (c + n)) + x0 is V22() real ext-real Element of REAL
(c . (c + n)) - 0 is V22() real ext-real Element of REAL
abs ((c . (c + n)) - 0) is V22() real ext-real Element of REAL
0 - fp is V22() real ext-real Element of REAL
0 + fp is V22() real ext-real Element of REAL
].(0 - fp),(0 + fp).[ is open V72() V73() V74() Element of K19(REAL)
- fp is V22() real ext-real set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= - fp & not fp <= b₁ ) } is set
a is V22() real ext-real Element of REAL
x0 + (- fp) is V22() real ext-real Element of REAL
a is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 - fp & not x0 + fp <= b₁ ) } is set
(c ^\ n) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* ((c ^\ n) + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((c ^\ n) + fm)) - (f /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((c ^\ n) + fm)) + (- (f /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((c ^\ n) ") (#) ((f /* ((c ^\ n) + fm)) - (f /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h is set
fm ^\ n is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent subsequence of fm
(c + fm) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of c + fm
f /* ((c + fm) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (fm ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((c + fm) ^\ n)) - (f /* (fm ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* (fm ^\ n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* (fm ^\ n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* ((c + fm) ^\ n)) + (- (f /* (fm ^\ n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((c ^\ n) ") (#) ((f /* ((c + fm) ^\ n)) - (f /* (fm ^\ n))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + fm)) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* (c + fm)
((f /* (c + fm)) ^\ n) - (f /* (fm ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (c + fm)) ^\ n) + (- (f /* (fm ^\ n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((c ^\ n) ") (#) (((f /* (c + fm)) ^\ n) - (f /* (fm ^\ n))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* fm) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* fm
((f /* (c + fm)) ^\ n) - ((f /* fm) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* fm) ^\ n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* fm) ^\ n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (c + fm)) ^\ n) + (- ((f /* fm) ^\ n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((c ^\ n) ") (#) (((f /* (c + fm)) ^\ n) - ((f /* fm) ^\ n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (c + fm)) - (f /* fm)) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (f /* (c + fm)) - (f /* fm)
((c ^\ n) ") (#) (((f /* (c + fm)) - (f /* fm)) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(c ") ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of c "
((c ") ^\ n) (#) (((f /* (c + fm)) - (f /* fm)) ^\ n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((c ") (#) ((f /* (c + fm)) - (f /* fm))) ^\ n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (c ") (#) ((f /* (c + fm)) - (f /* fm))
h is open V72() V73() V74() Neighbourhood of x0
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V22() real ext-real Element of REAL
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
diff (h,x0) is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (c + fm)) - (h /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (c + fm)) + (- (h /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((h /* (c + fm)) - (h /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (c + fm)) - (h /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (c + fm)) + (- (h /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((h /* (c + fm)) - (h /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((c ") (#) ((h /* (c + fm)) - (h /* fm))) is V22() real ext-real Element of REAL
fp is open V72() V73() V74() Neighbourhood of x0
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (c + fm)) - (h /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (c + fm)) + (- (h /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((h /* (c + fm)) - (h /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is open V72() V73() V74() Neighbourhood of x0
c is open V72() V73() V74() Neighbourhood of x0
fm is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fm is V72() V73() V74() Element of K19(REAL)
c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
c + fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (c + fm) is V72() V73() V74() Element of K19(REAL)
c " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (c + fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (c + fm)) - (h /* fm) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* fm) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (c + fm)) + (- (h /* fm)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(c ") (#) ((h /* (c + fm)) - (h /* fm)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((c ") (#) ((h /* (c + fm)) - (h /* fm))) is V22() real ext-real Element of REAL
fp is open V72() V73() V74() Neighbourhood of x0
x0 is V22() real ext-real Element of REAL
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f * h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (f * h) is V72() V73() V74() Element of K19(REAL)
h . x0 is V22() real ext-real Element of REAL
diff ((f * h),x0) is V22() real ext-real Element of REAL
diff (f,(h . x0)) is V22() real ext-real Element of REAL
diff (h,x0) is V22() real ext-real Element of REAL
(diff (f,(h . x0))) * (diff (h,x0)) is V22() real ext-real Element of REAL
c is open V72() V73() V74() Neighbourhood of x0
{x0} is V72() V73() V74() set
fm is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
fm " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fp is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fp is V72() V73() V74() Element of K19(REAL)
fm + fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (fm + fp) is V72() V73() V74() Element of K19(REAL)
(f * h) /* (fm + fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f * h) /* fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f * h) /* (fm + fp)) - ((f * h) /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f * h) /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f * h) /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f * h) /* (fm + fp)) + (- ((f * h) /* fp)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
h /* fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . a is V22() real ext-real Element of REAL
a is set
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . h is V22() real ext-real Element of REAL
h /* (fm + fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (fm + fp)) - (h /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (fm + fp)) + (- (h /* fp)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
lim fm is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim fp is V22() real ext-real Element of REAL
fp . 0 is V22() real ext-real Element of REAL
lim (fm + fp) is V22() real ext-real Element of REAL
0 + x0 is V22() real ext-real Element of REAL
lim (h /* (fm + fp)) is V22() real ext-real Element of REAL
rng (h /* (fm + fp)) is V72() V73() V74() Element of K19(REAL)
dom f is V72() V73() V74() Element of K19(REAL)
h is set
rng (h /* fp) is V72() V73() V74() Element of K19(REAL)
{(h . x0)} is V72() V73() V74() set
h is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h /* fp) . c is V22() real ext-real Element of REAL
fp . c is V22() real ext-real Element of REAL
h is set
(h /* fp) . 0 is V22() real ext-real Element of REAL
h is set
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative set
(h /* fp) . h is V22() real ext-real Element of REAL
h + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V22() real ext-real positive non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h /* fp) . (h + 1) is V22() real ext-real Element of REAL
h is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
h . 0 is V22() real ext-real Element of REAL
rng h is V72() V73() V74() Element of K19(REAL)
lim h is V22() real ext-real Element of REAL
lim ((h /* (fm + fp)) - (h /* fp)) is V22() real ext-real Element of REAL
(h . x0) - (h . x0) is V22() real ext-real Element of REAL
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((h /* (fm + fp)) - (h /* fp)) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (h /* (fm + fp)) - (h /* fp)
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((h /* (fm + fp)) - (h /* fp)) ^\ c) . a is V22() real ext-real Element of REAL
a + c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((h /* (fm + fp)) - (h /* fp)) . (a + c) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . (a + c) is V22() real ext-real Element of REAL
(h /* fp) . (a + c) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (a + c)) - ((h /* fp) . (a + c)) is V22() real ext-real Element of REAL
fp . (a + c) is V22() real ext-real Element of REAL
h . (fp . (a + c)) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (a + c)) - (h . (fp . (a + c))) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (a + c)) - (h . x0) is V22() real ext-real Element of REAL
fp ^\ c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent subsequence of fp
fm ^\ c is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of fm
h ^\ c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent subsequence of h
(fm ^\ c) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(fm ^\ c) + (fp ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* ((fm ^\ c) + (fp ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (fp ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm ^\ c) + (fp ^\ c))) - (h /* (fp ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* (fp ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* (fp ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* ((fm ^\ c) + (fp ^\ c))) + (- (h /* (fp ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((fm ^\ c) ") (#) ((h /* ((fm ^\ c) + (fp ^\ c))) - (h /* (fp ^\ c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) - (h /* fp)) + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
r1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((h /* (fm + fp)) - (h /* fp)) + h) . r1 is V22() real ext-real Element of REAL
((h /* (fm + fp)) - (h /* fp)) . r1 is V22() real ext-real Element of REAL
h . r1 is V22() real ext-real Element of REAL
(((h /* (fm + fp)) - (h /* fp)) . r1) + (h . r1) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . r1 is V22() real ext-real Element of REAL
((h /* (fm + fp)) . r1) - (h . r1) is V22() real ext-real Element of REAL
(((h /* (fm + fp)) . r1) - (h . r1)) + (h . r1) is V22() real ext-real Element of REAL
lim (((h /* (fm + fp)) - (h /* fp)) ^\ c) is V22() real ext-real Element of REAL
r1 is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
r1 " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
r1 + (h ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (r1 + (h ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (h ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* (h ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* (h ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (r1 + (h ^\ c))) + (- (f /* (h ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((h /* (fm + fp)) - (h /* fp)) + h) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of ((h /* (fm + fp)) - (h /* fp)) + h
(h /* (fm + fp)) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of h /* (fm + fp)
rng ((h /* (fm + fp)) ^\ c) is V72() V73() V74() Element of K19(REAL)
rng (r1 + (h ^\ c)) is V72() V73() V74() Element of K19(REAL)
rng (h ^\ c) is V72() V73() V74() Element of K19(REAL)
lim ((r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)))) is V22() real ext-real Element of REAL
(fm + fp) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of fm + fp
rng ((fm + fp) ^\ c) is V72() V73() V74() Element of K19(REAL)
rng ((fm ^\ c) + (fp ^\ c)) is V72() V73() V74() Element of K19(REAL)
rng (fp ^\ c) is V72() V73() V74() Element of K19(REAL)
((r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)))) (#) (((fm ^\ c) ") (#) ((h /* ((fm ^\ c) + (fp ^\ c))) - (h /* (fp ^\ c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* ((fm + fp) ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm + fp) ^\ c)) - (h /* (fp ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm + fp) ^\ c)) + (- (h /* (fp ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* ((fm + fp) ^\ c)) - (h /* (fp ^\ c))) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)))) (#) (((h /* ((fm + fp) ^\ c)) - (h /* (fp ^\ c))) (#) ((fm ^\ c) ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) ^\ c) - (h /* (fp ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) ^\ c) + (- (h /* (fp ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h /* (fm + fp)) ^\ c) - (h /* (fp ^\ c))) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)))) (#) ((((h /* (fm + fp)) ^\ c) - (h /* (fp ^\ c))) (#) ((fm ^\ c) ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* fp) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of h /* fp
((h /* (fm + fp)) ^\ c) - ((h /* fp) ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* fp) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* fp) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (fm + fp)) ^\ c) + (- ((h /* fp) ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h /* (fm + fp)) ^\ c) - ((h /* fp) ^\ c)) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((r1 ") (#) ((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c)))) (#) ((((h /* (fm + fp)) ^\ c) - ((h /* fp) ^\ c)) (#) ((fm ^\ c) ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) /" r1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
r1 " is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) (#) (r1 ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
r1 (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) /" r1) (#) (r1 (#) ((fm ^\ c) ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) /" r1) (#) r1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) /" r1) (#) r1) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (r1 + (h ^\ c))) - (f /* (h ^\ c))) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (h /* (fm + fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h /* (fm + fp))) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* (h /* (fm + fp))
((f /* (h /* (fm + fp))) ^\ c) - (f /* (h ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (h /* (fm + fp))) ^\ c) + (- (f /* (h ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f /* (h /* (fm + fp))) ^\ c) - (f /* (h ^\ c))) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f * h) /* (fm + fp)) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (f * h) /* (fm + fp)
(((f * h) /* (fm + fp)) ^\ c) - (f /* (h ^\ c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) ^\ c) + (- (f /* (h ^\ c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) ^\ c) - (f /* (h ^\ c))) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* h) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* h
(((f * h) /* (fm + fp)) ^\ c) - ((f /* h) ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* h) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* h) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f * h) /* (fm + fp)) ^\ c) + (- ((f /* h) ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) ^\ c) - ((f /* h) ^\ c)) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f * h) /* fp) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (f * h) /* fp
(((f * h) /* (fm + fp)) ^\ c) - (((f * h) /* fp) ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((f * h) /* fp) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((f * h) /* fp) ^\ c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f * h) /* (fm + fp)) ^\ c) + (- (((f * h) /* fp) ^\ c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) ^\ c) - (((f * h) /* fp) ^\ c)) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) - ((f * h) /* fp)) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of ((f * h) /* (fm + fp)) - ((f * h) /* fp)
((((f * h) /* (fm + fp)) - ((f * h) /* fp)) ^\ c) (#) ((fm ^\ c) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(fm ") ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of fm "
((((f * h) /* (fm + fp)) - ((f * h) /* fp)) ^\ c) (#) ((fm ") ^\ c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) ^\ c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))
lim (((fm ^\ c) ") (#) ((h /* ((fm ^\ c) + (fp ^\ c))) - (h /* (fp ^\ c)))) is V22() real ext-real Element of REAL
lim (((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) ^\ c) is V22() real ext-real Element of REAL
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
(h /* (fm + fp)) * c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fm * c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fp * c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng (fp * c) is V72() V73() V74() Element of K19(REAL)
n is V22() real ext-real set
r1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
r2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
a " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
a + b is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (a + b) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* b is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (a + b)) - (h /* b) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* b) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* b) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (a + b)) + (- (h /* b)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(a ") (#) ((h /* (a + b)) - (h /* b)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((a ") (#) ((h /* (a + b)) - (h /* b))) . r2 is V22() real ext-real Element of REAL
(((a ") (#) ((h /* (a + b)) - (h /* b))) . r2) - 0 is V22() real ext-real Element of REAL
abs ((((a ") (#) ((h /* (a + b)) - (h /* b))) . r2) - 0) is V22() real ext-real Element of REAL
(a ") . r2 is V22() real ext-real Element of REAL
((h /* (a + b)) - (h /* b)) . r2 is V22() real ext-real Element of REAL
((a ") . r2) * (((h /* (a + b)) - (h /* b)) . r2) is V22() real ext-real Element of REAL
abs (((a ") . r2) * (((h /* (a + b)) - (h /* b)) . r2)) is V22() real ext-real Element of REAL
(h /* (a + b)) . r2 is V22() real ext-real Element of REAL
(h /* b) . r2 is V22() real ext-real Element of REAL
((h /* (a + b)) . r2) - ((h /* b) . r2) is V22() real ext-real Element of REAL
((a ") . r2) * (((h /* (a + b)) . r2) - ((h /* b) . r2)) is V22() real ext-real Element of REAL
abs (((a ") . r2) * (((h /* (a + b)) . r2) - ((h /* b) . r2))) is V22() real ext-real Element of REAL
fp . r2 is V22() real ext-real Element of REAL
h . (fp . r2) is V22() real ext-real Element of REAL
((h /* (a + b)) . r2) - (h . (fp . r2)) is V22() real ext-real Element of REAL
((a ") . r2) * (((h /* (a + b)) . r2) - (h . (fp . r2))) is V22() real ext-real Element of REAL
abs (((a ") . r2) * (((h /* (a + b)) . r2) - (h . (fp . r2)))) is V22() real ext-real Element of REAL
((h /* (a + b)) . r2) - (h . x0) is V22() real ext-real Element of REAL
((a ") . r2) * (((h /* (a + b)) . r2) - (h . x0)) is V22() real ext-real Element of REAL
abs (((a ") . r2) * (((h /* (a + b)) . r2) - (h . x0))) is V22() real ext-real Element of REAL
(fm + fp) * c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* ((fm + fp) * c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm + fp) * c)) . r2 is V22() real ext-real Element of REAL
((h /* ((fm + fp) * c)) . r2) - (h . x0) is V22() real ext-real Element of REAL
((a ") . r2) * (((h /* ((fm + fp) * c)) . r2) - (h . x0)) is V22() real ext-real Element of REAL
abs (((a ") . r2) * (((h /* ((fm + fp) * c)) . r2) - (h . x0))) is V22() real ext-real Element of REAL
((h /* (fm + fp)) * c) . r2 is V22() real ext-real Element of REAL
(((h /* (fm + fp)) * c) . r2) - (h . x0) is V22() real ext-real Element of REAL
((a ") . r2) * ((((h /* (fm + fp)) * c) . r2) - (h . x0)) is V22() real ext-real Element of REAL
abs (((a ") . r2) * ((((h /* (fm + fp)) * c) . r2) - (h . x0))) is V22() real ext-real Element of REAL
((a ") . r2) * ((h . x0) - (h . x0)) is V22() real ext-real Element of REAL
abs (((a ") . r2) * ((h . x0) - (h . x0))) is V22() real ext-real Element of REAL
rng ((fm + fp) * c) is V72() V73() V74() Element of K19(REAL)
rng (a + b) is V72() V73() V74() Element of K19(REAL)
lim ((a ") (#) ((h /* (a + b)) - (h /* b))) is V22() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
r1 is V22() real ext-real set
r2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h /* (fm + fp)) . c2 is V22() real ext-real Element of REAL
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . c2 is V22() real ext-real Element of REAL
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . c2) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs ((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . c2) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
(fm ") . c2 is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) - ((f * h) /* fp)) . c2 is V22() real ext-real Element of REAL
((fm ") . c2) * ((((f * h) /* (fm + fp)) - ((f * h) /* fp)) . c2) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((((f * h) /* (fm + fp)) - ((f * h) /* fp)) . c2)) is V22() real ext-real Element of REAL
((f * h) /* (fm + fp)) . c2 is V22() real ext-real Element of REAL
((f * h) /* fp) . c2 is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . c2) - (((f * h) /* fp) . c2) is V22() real ext-real Element of REAL
((fm ") . c2) * ((((f * h) /* (fm + fp)) . c2) - (((f * h) /* fp) . c2)) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((((f * h) /* (fm + fp)) . c2) - (((f * h) /* fp) . c2))) is V22() real ext-real Element of REAL
f /* (h /* (fm + fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h /* (fm + fp))) . c2 is V22() real ext-real Element of REAL
((f /* (h /* (fm + fp))) . c2) - (((f * h) /* fp) . c2) is V22() real ext-real Element of REAL
((fm ") . c2) * (((f /* (h /* (fm + fp))) . c2) - (((f * h) /* fp) . c2)) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * (((f /* (h /* (fm + fp))) . c2) - (((f * h) /* fp) . c2))) is V22() real ext-real Element of REAL
f . ((h /* (fm + fp)) . c2) is V22() real ext-real Element of REAL
(f . ((h /* (fm + fp)) . c2)) - (((f * h) /* fp) . c2) is V22() real ext-real Element of REAL
((fm ") . c2) * ((f . ((h /* (fm + fp)) . c2)) - (((f * h) /* fp) . c2)) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((f . ((h /* (fm + fp)) . c2)) - (((f * h) /* fp) . c2))) is V22() real ext-real Element of REAL
f . (h . x0) is V22() real ext-real Element of REAL
f /* (h /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h /* fp)) . c2 is V22() real ext-real Element of REAL
(f . (h . x0)) - ((f /* (h /* fp)) . c2) is V22() real ext-real Element of REAL
((fm ") . c2) * ((f . (h . x0)) - ((f /* (h /* fp)) . c2)) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((f . (h . x0)) - ((f /* (h /* fp)) . c2))) is V22() real ext-real Element of REAL
(h /* fp) . c2 is V22() real ext-real Element of REAL
f . ((h /* fp) . c2) is V22() real ext-real Element of REAL
(f . (h . x0)) - (f . ((h /* fp) . c2)) is V22() real ext-real Element of REAL
((fm ") . c2) * ((f . (h . x0)) - (f . ((h /* fp) . c2))) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((f . (h . x0)) - (f . ((h /* fp) . c2)))) is V22() real ext-real Element of REAL
fp . c2 is V22() real ext-real Element of REAL
h . (fp . c2) is V22() real ext-real Element of REAL
f . (h . (fp . c2)) is V22() real ext-real Element of REAL
(f . (h . x0)) - (f . (h . (fp . c2))) is V22() real ext-real Element of REAL
((fm ") . c2) * ((f . (h . x0)) - (f . (h . (fp . c2)))) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((f . (h . x0)) - (f . (h . (fp . c2))))) is V22() real ext-real Element of REAL
(f . (h . x0)) - (f . (h . x0)) is V22() real ext-real Element of REAL
((fm ") . c2) * ((f . (h . x0)) - (f . (h . x0))) is V22() real ext-real Element of REAL
abs (((fm ") . c2) * ((f . (h . x0)) - (f . (h . x0)))) is V22() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is V1() V4( NAT ) V5( NAT ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued natural-valued increasing non-decreasing Element of K19(K20(NAT,NAT))
(h /* (fm + fp)) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) - (h /* fp)) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
r1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((h /* (fm + fp)) - (h /* fp)) * n) . r1 is V22() real ext-real Element of REAL
n . r1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((h /* (fm + fp)) - (h /* fp)) . (n . r1) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . (n . r1) is V22() real ext-real Element of REAL
(h /* fp) . (n . r1) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (n . r1)) - ((h /* fp) . (n . r1)) is V22() real ext-real Element of REAL
fp . (n . r1) is V22() real ext-real Element of REAL
h . (fp . (n . r1)) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (n . r1)) - (h . (fp . (n . r1))) is V22() real ext-real Element of REAL
((h /* (fm + fp)) . (n . r1)) - (h . x0) is V22() real ext-real Element of REAL
((h /* (fm + fp)) * n) . r1 is V22() real ext-real Element of REAL
(((h /* (fm + fp)) * n) . r1) - (h . x0) is V22() real ext-real Element of REAL
fm * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h * n is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
fp * n is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
r1 is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
r1 " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c2 is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
r1 + c2 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (r1 + c2) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* c2 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (r1 + c2)) - (h /* c2) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* c2) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* c2) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (r1 + c2)) + (- (h /* c2)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(r1 ") (#) ((h /* (r1 + c2)) - (h /* c2)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim (((h /* (fm + fp)) - (h /* fp)) * n) is V22() real ext-real Element of REAL
d1 is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
d1 " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
d1 + (h * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (d1 + (h * n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (h * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (d1 + (h * n))) - (f /* (h * n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* (h * n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* (h * n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (d1 + (h * n))) + (- (f /* (h * n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (h * n) is V72() V73() V74() Element of K19(REAL)
((h /* (fm + fp)) - (h /* fp)) + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((h /* (fm + fp)) - (h /* fp)) + h) . a1 is V22() real ext-real Element of REAL
((h /* (fm + fp)) - (h /* fp)) . a1 is V22() real ext-real Element of REAL
h . a1 is V22() real ext-real Element of REAL
(((h /* (fm + fp)) - (h /* fp)) . a1) + (h . a1) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . a1 is V22() real ext-real Element of REAL
((h /* (fm + fp)) . a1) - (h . a1) is V22() real ext-real Element of REAL
(((h /* (fm + fp)) . a1) - (h . a1)) + (h . a1) is V22() real ext-real Element of REAL
(((h /* (fm + fp)) - (h /* fp)) + h) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n)))) (#) ((r1 ") (#) ((h /* (r1 + c2)) - (h /* c2))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(fm + fp) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* ((fm + fp) * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm + fp) * n)) - (h /* c2) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* ((fm + fp) * n)) + (- (h /* c2)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* ((fm + fp) * n)) - (h /* c2)) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n)))) (#) (((h /* ((fm + fp) * n)) - (h /* c2)) (#) (r1 ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) * n) - (h /* c2) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) * n) + (- (h /* c2)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h /* (fm + fp)) * n) - (h /* c2)) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n)))) (#) ((((h /* (fm + fp)) * n) - (h /* c2)) (#) (r1 ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* fp) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (fm + fp)) * n) - ((h /* fp) * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* fp) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* fp) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (fm + fp)) * n) + (- ((h /* fp) * n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h /* (fm + fp)) * n) - ((h /* fp) * n)) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n)))) (#) ((((h /* (fm + fp)) * n) - ((h /* fp) * n)) (#) (r1 ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (d1 + (h * n))) - (f /* (h * n))) /" d1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
d1 " is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (d1 + (h * n))) - (f /* (h * n))) (#) (d1 ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
d1 (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f /* (d1 + (h * n))) - (f /* (h * n))) /" d1) (#) (d1 (#) (r1 ")) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f /* (d1 + (h * n))) - (f /* (h * n))) /" d1) (#) d1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((((f /* (d1 + (h * n))) - (f /* (h * n))) /" d1) (#) d1) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (d1 + (h * n))) - (f /* (h * n))) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (h /* (fm + fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h /* (fm + fp))) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (h /* (fm + fp))) * n) - (f /* (h * n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (h /* (fm + fp))) * n) + (- (f /* (h * n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f /* (h /* (fm + fp))) * n) - (f /* (h * n))) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f * h) /* (fm + fp)) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) * n) - (f /* (h * n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) * n) + (- (f /* (h * n))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) * n) - (f /* (h * n))) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* h) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) * n) - ((f /* h) * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* h) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* h) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f * h) /* (fm + fp)) * n) + (- ((f /* h) * n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) * n) - ((f /* h) * n)) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f * h) /* fp) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) * n) - (((f * h) /* fp) * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((f * h) /* fp) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((f * h) /* fp) * n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f * h) /* (fm + fp)) * n) + (- (((f * h) /* fp) * n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f * h) /* (fm + fp)) * n) - (((f * h) /* fp) * n)) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f * h) /* (fm + fp)) - ((f * h) /* fp)) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((((f * h) /* (fm + fp)) - ((f * h) /* fp)) * n) (#) (r1 ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(fm ") * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((((f * h) /* (fm + fp)) - ((f * h) /* fp)) * n) (#) ((fm ") * n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) * n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng ((h /* (fm + fp)) * n) is V72() V73() V74() Element of K19(REAL)
a1 is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
d1 + a1 is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (d1 + a1) is V72() V73() V74() Element of K19(REAL)
rng ((fm + fp) * n) is V72() V73() V74() Element of K19(REAL)
rng (r1 + c2) is V72() V73() V74() Element of K19(REAL)
rng c2 is V72() V73() V74() Element of K19(REAL)
lim ((r1 ") (#) ((h /* (r1 + c2)) - (h /* c2))) is V22() real ext-real Element of REAL
lim ((d1 ") (#) ((f /* (d1 + (h * n))) - (f /* (h * n)))) is V22() real ext-real Element of REAL
lim (((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) * n) is V22() real ext-real Element of REAL
g is V22() real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n . k is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
m is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h /* (fm + fp)) . m is V22() real ext-real Element of REAL
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m is V22() real ext-real Element of REAL
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs ((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
(fm ") . m is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) - ((f * h) /* fp)) . m is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) - ((f * h) /* fp)) . m) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) - ((f * h) /* fp)) . m)) is V22() real ext-real Element of REAL
((f * h) /* (fm + fp)) . m is V22() real ext-real Element of REAL
((f * h) /* fp) . m is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . m) - (((f * h) /* fp) . m) is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (((f * h) /* fp) . m)) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (((f * h) /* fp) . m))) is V22() real ext-real Element of REAL
f /* (h /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h /* fp)) . m is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . m) - ((f /* (h /* fp)) . m) is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - ((f /* (h /* fp)) . m)) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - ((f /* (h /* fp)) . m))) is V22() real ext-real Element of REAL
(h /* fp) . m is V22() real ext-real Element of REAL
f . ((h /* fp) . m) is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . m) - (f . ((h /* fp) . m)) is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . ((h /* fp) . m))) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . ((h /* fp) . m)))) is V22() real ext-real Element of REAL
fp . m is V22() real ext-real Element of REAL
h . (fp . m) is V22() real ext-real Element of REAL
f . (h . (fp . m)) is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . m) - (f . (h . (fp . m))) is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . (h . (fp . m)))) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . (h . (fp . m))))) is V22() real ext-real Element of REAL
f . (h . x0) is V22() real ext-real Element of REAL
(((f * h) /* (fm + fp)) . m) - (f . (h . x0)) is V22() real ext-real Element of REAL
((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . (h . x0))) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((((f * h) /* (fm + fp)) . m) - (f . (h . x0)))) is V22() real ext-real Element of REAL
(f /* (h /* (fm + fp))) . m is V22() real ext-real Element of REAL
((f /* (h /* (fm + fp))) . m) - (f . (h . x0)) is V22() real ext-real Element of REAL
((fm ") . m) * (((f /* (h /* (fm + fp))) . m) - (f . (h . x0))) is V22() real ext-real Element of REAL
abs (((fm ") . m) * (((f /* (h /* (fm + fp))) . m) - (f . (h . x0)))) is V22() real ext-real Element of REAL
(f . (h . x0)) - (f . (h . x0)) is V22() real ext-real Element of REAL
((fm ") . m) * ((f . (h . x0)) - (f . (h . x0))) is V22() real ext-real Element of REAL
abs (((fm ") . m) * ((f . (h . x0)) - (f . (h . x0)))) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . m is V22() real ext-real Element of REAL
l is V22() real ext-real Element of REAL
l is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n . l is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
dom n is V72() V73() V74() V75() V76() V77() Element of K19(NAT)
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) * n) . l is V22() real ext-real Element of REAL
((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) * n) . l) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs (((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) * n) . l) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m is V22() real ext-real Element of REAL
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs ((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
(h /* (fm + fp)) . m is V22() real ext-real Element of REAL
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m is V22() real ext-real Element of REAL
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs ((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m is V22() real ext-real Element of REAL
(((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0))) is V22() real ext-real Element of REAL
abs ((((fm ") (#) (((f * h) /* (fm + fp)) - ((f * h) /* fp))) . m) - ((diff (f,(h . x0))) * (diff (h,x0)))) is V22() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
x0 is V22() real ext-real Element of REAL
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . x0 is V22() real ext-real Element of REAL
diff (f,x0) is V22() real ext-real Element of REAL
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h * f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
diff ((h * f),x0) is V22() real ext-real Element of REAL
diff (h,(f . x0)) is V22() real ext-real Element of REAL
(diff (h,(f . x0))) * (diff (f,x0)) is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
c is open V72() V73() V74() Neighbourhood of f . x0
fm is open V72() V73() V74() Neighbourhood of x0
f .: fm is V72() V73() V74() Element of K19(REAL)
dom f is V72() V73() V74() Element of K19(REAL)
fp is open V72() V73() V74() Neighbourhood of x0
n is open V72() V73() V74() Neighbourhood of x0
dom (h * f) is V72() V73() V74() Element of K19(REAL)
a is set
h is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . x0 is V22() real ext-real Element of REAL
diff (f,x0) is V22() real ext-real Element of REAL
(f . x0) ^2 is V22() real ext-real Element of REAL
(f . x0) * (f . x0) is V22() real ext-real set
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h / f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
diff ((h / f),x0) is V22() real ext-real Element of REAL
diff (h,x0) is V22() real ext-real Element of REAL
(diff (h,x0)) * (f . x0) is V22() real ext-real Element of REAL
h . x0 is V22() real ext-real Element of REAL
(diff (f,x0)) * (h . x0) is V22() real ext-real Element of REAL
((diff (h,x0)) * (f . x0)) - ((diff (f,x0)) * (h . x0)) is V22() real ext-real Element of REAL
(((diff (h,x0)) * (f . x0)) - ((diff (f,x0)) * (h . x0))) / ((f . x0) ^2) is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
c is open V72() V73() V74() Neighbourhood of x0
dom f is V72() V73() V74() Element of K19(REAL)
fm is open V72() V73() V74() Neighbourhood of x0
fm is open V72() V73() V74() Neighbourhood of x0
fp is open V72() V73() V74() Neighbourhood of x0
f " {0} is V72() V73() V74() Element of K19(REAL)
(dom f) \ (f " {0}) is V72() V73() V74() Element of K19(REAL)
n is set
a is V22() real ext-real Element of REAL
f . a is V22() real ext-real Element of REAL
(dom h) /\ ((dom f) \ (f " {0})) is V72() V73() V74() Element of K19(REAL)
{x0} is V72() V73() V74() set
dom (h / f) is V72() V73() V74() Element of K19(REAL)
f ^ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (f ^) is V72() V73() V74() Element of K19(REAL)
n is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
n " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng a is V72() V73() V74() Element of K19(REAL)
n + a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (n + a) is V72() V73() V74() Element of K19(REAL)
(h / f) /* (n + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h / f) /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h / f) /* (n + a)) - ((h / f) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h / f) /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h / f) /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h / f) /* (n + a)) + (- ((h / f) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h / f) /* (n + a)) - ((h / f) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((n ") (#) (((h / f) /* (n + a)) - ((h / f) /* a))) is V22() real ext-real Element of REAL
f /* (n + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim a is V22() real ext-real Element of REAL
f /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n + a)) - (f /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (n + a)) + (- (f /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) ((f /* (n + a)) - (f /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h /* (n + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (n + a)) - (h /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (n + a)) + (- (h /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) ((h /* (n + a)) - (h /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(dom h) /\ (dom (f ^)) is V72() V73() V74() Element of K19(REAL)
r1 is set
h (#) (f ^) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(h (#) (f ^)) /* (n + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h (#) (f ^)) /* (n + a)) - ((h / f) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h (#) (f ^)) /* (n + a)) + (- ((h / f) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h (#) (f ^)) /* (n + a)) - ((h / f) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h (#) (f ^)) /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h (#) (f ^)) /* (n + a)) - ((h (#) (f ^)) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h (#) (f ^)) /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h (#) (f ^)) /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h (#) (f ^)) /* (n + a)) + (- ((h (#) (f ^)) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h (#) (f ^)) /* (n + a)) - ((h (#) (f ^)) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f ^) /* (n + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (n + a)) (#) ((f ^) /* (n + a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (n + a)) (#) ((f ^) /* (n + a))) - ((h (#) (f ^)) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (n + a)) (#) ((f ^) /* (n + a))) + (- ((h (#) (f ^)) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h /* (n + a)) (#) ((f ^) /* (n + a))) - ((h (#) (f ^)) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (n + a)) /" (f /* (n + a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n + a)) " is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (n + a)) (#) ((f /* (n + a)) ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (n + a)) /" (f /* (n + a))) - ((h (#) (f ^)) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (n + a)) /" (f /* (n + a))) + (- ((h (#) (f ^)) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h /* (n + a)) /" (f /* (n + a))) - ((h (#) (f ^)) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f ^) /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* a) (#) ((f ^) /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (n + a)) /" (f /* (n + a))) - ((h /* a) (#) ((f ^) /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* a) (#) ((f ^) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* a) (#) ((f ^) /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (n + a)) /" (f /* (n + a))) + (- ((h /* a) (#) ((f ^) /* a))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h /* (n + a)) /" (f /* (n + a))) - ((h /* a) (#) ((f ^) /* a))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* a) /" (f /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* a) " is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* a) (#) ((f /* a) ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (n + a)) /" (f /* (n + a))) - ((h /* a) /" (f /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* a) /" (f /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* a) /" (f /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (n + a)) /" (f /* (n + a))) + (- ((h /* a) /" (f /* a))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) (((h /* (n + a)) /" (f /* (n + a))) - ((h /* a) /" (f /* a))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (n + a)) (#) (f /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* a) (#) (f /* (n + a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* a) (#) (f /* (n + a))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* a) (#) (f /* (n + a))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (n + a)) (#) (f /* a)) + (- ((h /* a) (#) (f /* (n + a)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (n + a)) (#) (f /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) /" ((f /* (n + a)) (#) (f /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (n + a)) (#) (f /* a)) " is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) (#) (((f /* (n + a)) (#) (f /* a)) ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(n ") (#) ((((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) /" ((f /* (n + a)) (#) (f /* a))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(n ") (#) (((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((n ") (#) (((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a))))) /" ((f /* (n + a)) (#) (f /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((n ") (#) (((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a))))) (#) (((f /* (n + a)) (#) (f /* a)) ") is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
lim (h /* a) is V22() real ext-real Element of REAL
(h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((n ") (#) ((f /* (n + a)) - (f /* a))) is V22() real ext-real Element of REAL
lim ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) is V22() real ext-real Element of REAL
lim (n + a) is V22() real ext-real Element of REAL
lim (f /* a) is V22() real ext-real Element of REAL
((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim (f /* (n + a)) is V22() real ext-real Element of REAL
lim ((f /* (n + a)) (#) (f /* a)) is V22() real ext-real Element of REAL
r2 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((n ") (#) (((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a))))) . r2 is V22() real ext-real Element of REAL
(n ") . r2 is V22() real ext-real Element of REAL
(((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) . r2 is V22() real ext-real Element of REAL
((n ") . r2) * ((((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a)))) . r2) is V22() real ext-real Element of REAL
((h /* (n + a)) (#) (f /* a)) . r2 is V22() real ext-real Element of REAL
((h /* a) (#) (f /* (n + a))) . r2 is V22() real ext-real Element of REAL
(((h /* (n + a)) (#) (f /* a)) . r2) - (((h /* a) (#) (f /* (n + a))) . r2) is V22() real ext-real Element of REAL
((n ") . r2) * ((((h /* (n + a)) (#) (f /* a)) . r2) - (((h /* a) (#) (f /* (n + a))) . r2)) is V22() real ext-real Element of REAL
(h /* (n + a)) . r2 is V22() real ext-real Element of REAL
(f /* a) . r2 is V22() real ext-real Element of REAL
((h /* (n + a)) . r2) * ((f /* a) . r2) is V22() real ext-real Element of REAL
(((h /* (n + a)) . r2) * ((f /* a) . r2)) - (((h /* a) (#) (f /* (n + a))) . r2) is V22() real ext-real Element of REAL
((n ") . r2) * ((((h /* (n + a)) . r2) * ((f /* a) . r2)) - (((h /* a) (#) (f /* (n + a))) . r2)) is V22() real ext-real Element of REAL
(h /* a) . r2 is V22() real ext-real Element of REAL
((h /* (n + a)) . r2) - ((h /* a) . r2) is V22() real ext-real Element of REAL
(((h /* (n + a)) . r2) - ((h /* a) . r2)) * ((f /* a) . r2) is V22() real ext-real Element of REAL
((h /* a) . r2) * ((f /* a) . r2) is V22() real ext-real Element of REAL
((((h /* (n + a)) . r2) - ((h /* a) . r2)) * ((f /* a) . r2)) + (((h /* a) . r2) * ((f /* a) . r2)) is V22() real ext-real Element of REAL
(f /* (n + a)) . r2 is V22() real ext-real Element of REAL
((h /* a) . r2) * ((f /* (n + a)) . r2) is V22() real ext-real Element of REAL
(((((h /* (n + a)) . r2) - ((h /* a) . r2)) * ((f /* a) . r2)) + (((h /* a) . r2) * ((f /* a) . r2))) - (((h /* a) . r2) * ((f /* (n + a)) . r2)) is V22() real ext-real Element of REAL
((n ") . r2) * ((((((h /* (n + a)) . r2) - ((h /* a) . r2)) * ((f /* a) . r2)) + (((h /* a) . r2) * ((f /* a) . r2))) - (((h /* a) . r2) * ((f /* (n + a)) . r2))) is V22() real ext-real Element of REAL
((n ") . r2) * (((h /* (n + a)) . r2) - ((h /* a) . r2)) is V22() real ext-real Element of REAL
(((n ") . r2) * (((h /* (n + a)) . r2) - ((h /* a) . r2))) * ((f /* a) . r2) is V22() real ext-real Element of REAL
((f /* (n + a)) . r2) - ((f /* a) . r2) is V22() real ext-real Element of REAL
((n ") . r2) * (((f /* (n + a)) . r2) - ((f /* a) . r2)) is V22() real ext-real Element of REAL
((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) . r2) - ((f /* a) . r2))) is V22() real ext-real Element of REAL
((((n ") . r2) * (((h /* (n + a)) . r2) - ((h /* a) . r2))) * ((f /* a) . r2)) - (((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) . r2) - ((f /* a) . r2)))) is V22() real ext-real Element of REAL
((h /* (n + a)) - (h /* a)) . r2 is V22() real ext-real Element of REAL
((n ") . r2) * (((h /* (n + a)) - (h /* a)) . r2) is V22() real ext-real Element of REAL
(((n ") . r2) * (((h /* (n + a)) - (h /* a)) . r2)) * ((f /* a) . r2) is V22() real ext-real Element of REAL
((((n ") . r2) * (((h /* (n + a)) - (h /* a)) . r2)) * ((f /* a) . r2)) - (((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) . r2) - ((f /* a) . r2)))) is V22() real ext-real Element of REAL
((f /* (n + a)) - (f /* a)) . r2 is V22() real ext-real Element of REAL
((n ") . r2) * (((f /* (n + a)) - (f /* a)) . r2) is V22() real ext-real Element of REAL
((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) - (f /* a)) . r2)) is V22() real ext-real Element of REAL
((((n ") . r2) * (((h /* (n + a)) - (h /* a)) . r2)) * ((f /* a) . r2)) - (((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) - (f /* a)) . r2))) is V22() real ext-real Element of REAL
((n ") (#) ((h /* (n + a)) - (h /* a))) . r2 is V22() real ext-real Element of REAL
(((n ") (#) ((h /* (n + a)) - (h /* a))) . r2) * ((f /* a) . r2) is V22() real ext-real Element of REAL
((((n ") (#) ((h /* (n + a)) - (h /* a))) . r2) * ((f /* a) . r2)) - (((h /* a) . r2) * (((n ") . r2) * (((f /* (n + a)) - (f /* a)) . r2))) is V22() real ext-real Element of REAL
((n ") (#) ((f /* (n + a)) - (f /* a))) . r2 is V22() real ext-real Element of REAL
((h /* a) . r2) * (((n ") (#) ((f /* (n + a)) - (f /* a))) . r2) is V22() real ext-real Element of REAL
((((n ") (#) ((h /* (n + a)) - (h /* a))) . r2) * ((f /* a) . r2)) - (((h /* a) . r2) * (((n ") (#) ((f /* (n + a)) - (f /* a))) . r2)) is V22() real ext-real Element of REAL
(((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) . r2 is V22() real ext-real Element of REAL
((((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) . r2) - (((h /* a) . r2) * (((n ") (#) ((f /* (n + a)) - (f /* a))) . r2)) is V22() real ext-real Element of REAL
((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) . r2 is V22() real ext-real Element of REAL
((((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) . r2) - (((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) . r2) is V22() real ext-real Element of REAL
(((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) - ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) + (- ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a))))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) - ((h /* a) (#) ((n ") (#) ((f /* (n + a)) - (f /* a))))) . r2 is V22() real ext-real Element of REAL
lim ((n ") (#) ((h /* (n + a)) - (h /* a))) is V22() real ext-real Element of REAL
lim (((n ") (#) ((h /* (n + a)) - (h /* a))) (#) (f /* a)) is V22() real ext-real Element of REAL
lim ((n ") (#) (((h /* (n + a)) (#) (f /* a)) - ((h /* a) (#) (f /* (n + a))))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . x0 is V22() real ext-real Element of REAL
f ^ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
diff ((f ^),x0) is V22() real ext-real Element of REAL
diff (f,x0) is V22() real ext-real Element of REAL
(f . x0) ^2 is V22() real ext-real Element of REAL
(f . x0) * (f . x0) is V22() real ext-real set
(diff (f,x0)) / ((f . x0) ^2) is V22() real ext-real Element of REAL
- ((diff (f,x0)) / ((f . x0) ^2)) is V22() real ext-real Element of REAL
dom f is V72() V73() V74() Element of K19(REAL)
K20((dom f),REAL) is complex-valued ext-real-valued real-valued set
K19(K20((dom f),REAL)) is set
(dom f) --> 1 is V1() non-empty V4( REAL ) V4( dom f) V5( NAT ) V5( RAT ) V5( INT ) Function-like constant total complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(REAL,NAT))
K20(REAL,NAT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued natural-valued set
K19(K20(REAL,NAT)) is set
h is V1() V4( dom f) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20((dom f),REAL))
dom h is V72() V73() V74() Element of K19((dom f))
K19((dom f)) is set
fm is open V72() V73() V74() Neighbourhood of x0
c is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom c is V72() V73() V74() Element of K19(REAL)
rng c is V72() V73() V74() Element of K19(REAL)
{1} is V72() V73() V74() V75() V76() V77() set
fp is set
c . x0 is V22() real ext-real Element of REAL
c `| fm is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(c `| fm) . x0 is V22() real ext-real Element of REAL
diff (c,x0) is V22() real ext-real Element of REAL
c / f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
diff ((c / f),x0) is V22() real ext-real Element of REAL
0 * (f . x0) is V22() real ext-real Element of REAL
c . x0 is V22() real ext-real Element of REAL
(diff (f,x0)) * (c . x0) is V22() real ext-real Element of REAL
(0 * (f . x0)) - ((diff (f,x0)) * (c . x0)) is V22() real ext-real Element of REAL
((0 * (f . x0)) - ((diff (f,x0)) * (c . x0))) / ((f . x0) ^2) is V22() real ext-real Element of REAL
- ((diff (f,x0)) * (c . x0)) is V22() real ext-real Element of REAL
(- ((diff (f,x0)) * (c . x0))) / ((f . x0) ^2) is V22() real ext-real Element of REAL
(diff (f,x0)) * 1 is V22() real ext-real Element of REAL
- ((diff (f,x0)) * 1) is V22() real ext-real Element of REAL
(- ((diff (f,x0)) * 1)) / ((f . x0) ^2) is V22() real ext-real Element of REAL
dom (c / f) is V72() V73() V74() Element of K19(REAL)
f " {0} is V72() V73() V74() Element of K19(REAL)
(dom f) \ (f " {0}) is V72() V73() V74() Element of K19(REAL)
(dom c) /\ ((dom f) \ (f " {0})) is V72() V73() V74() Element of K19(REAL)
dom (f ^) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
(c / f) . fp is V22() real ext-real Element of REAL
c . fp is V22() real ext-real Element of REAL
f . fp is V22() real ext-real Element of REAL
(f . fp) " is V22() real ext-real Element of REAL
(c . fp) * ((f . fp) ") is V22() real ext-real Element of REAL
1 * ((f . fp) ") is V22() real ext-real Element of REAL
(f ^) . fp is V22() real ext-real Element of REAL
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f | x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f | x0) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
(dom f) /\ x0 is V72() V73() V74() Element of K19(REAL)
dom (f | x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
(f | x0) | x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom ((f | x0) `| x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
c is open V72() V73() V74() Neighbourhood of h
f . h is V22() real ext-real Element of REAL
fm is open V72() V73() V74() Neighbourhood of h
fp is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
n is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
fp is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K19(K20(REAL,REAL))
n is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K19(K20(REAL,REAL))
a is open V72() V73() V74() Neighbourhood of h
h is V22() real ext-real Element of REAL
(f | x0) . h is V22() real ext-real Element of REAL
(f | x0) . h is V22() real ext-real Element of REAL
((f | x0) . h) - ((f | x0) . h) is V22() real ext-real Element of REAL
((f | x0) . h) - (f . h) is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
(f . h) - (f . h) is V22() real ext-real Element of REAL
h - h is V22() real ext-real Element of REAL
fp . (h - h) is V22() real ext-real Element of REAL
n . (h - h) is V22() real ext-real Element of REAL
(fp . (h - h)) + (n . (h - h)) is V22() real ext-real Element of REAL
(f `| x0) . h is V22() real ext-real Element of REAL
diff (f,h) is V22() real ext-real Element of REAL
fp . 1 is V22() real ext-real Element of REAL
diff ((f | x0),h) is V22() real ext-real Element of REAL
((f | x0) `| x0) . h is V22() real ext-real Element of REAL
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f + h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f + h) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f `| x0) + (h `| x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
dom f is V72() V73() V74() Element of K19(REAL)
(dom f) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom (f + h) is V72() V73() V74() Element of K19(REAL)
dom ((f + h) `| x0) is V72() V73() V74() Element of K19(REAL)
dom (h `| x0) is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
(dom (f `| x0)) /\ (dom (h `| x0)) is V72() V73() V74() Element of K19(REAL)
dom ((f `| x0) + (h `| x0)) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
((f + h) `| x0) . c is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
(diff (f,c)) + (diff (h,c)) is V22() real ext-real Element of REAL
(f `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) + (diff (h,c)) is V22() real ext-real Element of REAL
(h `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) + ((h `| x0) . c) is V22() real ext-real Element of REAL
((f `| x0) + (h `| x0)) . c is V22() real ext-real Element of REAL
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f - h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- h is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) h is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
f + (- h) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f - h) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f `| x0) - (h `| x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- (h `| x0) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (h `| x0) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f `| x0) + (- (h `| x0)) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
dom h is V72() V73() V74() Element of K19(REAL)
dom f is V72() V73() V74() Element of K19(REAL)
(dom f) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom (f - h) is V72() V73() V74() Element of K19(REAL)
dom ((f - h) `| x0) is V72() V73() V74() Element of K19(REAL)
dom (h `| x0) is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
(dom (f `| x0)) /\ (dom (h `| x0)) is V72() V73() V74() Element of K19(REAL)
dom ((f `| x0) - (h `| x0)) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
((f - h) `| x0) . c is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
(diff (f,c)) - (diff (h,c)) is V22() real ext-real Element of REAL
(f `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) - (diff (h,c)) is V22() real ext-real Element of REAL
(h `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) - ((h `| x0) . c) is V22() real ext-real Element of REAL
((f `| x0) - (h `| x0)) . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is open V72() V73() V74() Element of K19(REAL)
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
x0 (#) h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(x0 (#) h) `| f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
x0 (#) (h `| f) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
dom (x0 (#) h) is V72() V73() V74() Element of K19(REAL)
dom ((x0 (#) h) `| f) is V72() V73() V74() Element of K19(REAL)
dom (h `| f) is V72() V73() V74() Element of K19(REAL)
dom (x0 (#) (h `| f)) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
((x0 (#) h) `| f) . c is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
x0 * (diff (h,c)) is V22() real ext-real Element of REAL
(h `| f) . c is V22() real ext-real Element of REAL
x0 * ((h `| f) . c) is V22() real ext-real Element of REAL
(x0 (#) (h `| f)) . c is V22() real ext-real Element of REAL
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f (#) h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f (#) h) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f `| x0) (#) h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f (#) (h `| x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((f `| x0) (#) h) + (f (#) (h `| x0)) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
dom h is V72() V73() V74() Element of K19(REAL)
(dom f) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom (f (#) h) is V72() V73() V74() Element of K19(REAL)
dom ((f (#) h) `| x0) is V72() V73() V74() Element of K19(REAL)
dom (h `| x0) is V72() V73() V74() Element of K19(REAL)
(dom f) /\ (dom (h `| x0)) is V72() V73() V74() Element of K19(REAL)
dom (f (#) (h `| x0)) is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
(dom (f `| x0)) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom ((f `| x0) (#) h) is V72() V73() V74() Element of K19(REAL)
(dom ((f `| x0) (#) h)) /\ (dom (f (#) (h `| x0))) is V72() V73() V74() Element of K19(REAL)
dom (((f `| x0) (#) h) + (f (#) (h `| x0))) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
((f (#) h) `| x0) . c is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
(diff (f,c)) * (h . c) is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
(f . c) * (diff (h,c)) is V22() real ext-real Element of REAL
((diff (f,c)) * (h . c)) + ((f . c) * (diff (h,c))) is V22() real ext-real Element of REAL
(f `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) * (h . c) is V22() real ext-real Element of REAL
(((f `| x0) . c) * (h . c)) + ((f . c) * (diff (h,c))) is V22() real ext-real Element of REAL
(h `| x0) . c is V22() real ext-real Element of REAL
(f . c) * ((h `| x0) . c) is V22() real ext-real Element of REAL
(((f `| x0) . c) * (h . c)) + ((f . c) * ((h `| x0) . c)) is V22() real ext-real Element of REAL
((f `| x0) (#) h) . c is V22() real ext-real Element of REAL
(((f `| x0) (#) h) . c) + ((f . c) * ((h `| x0) . c)) is V22() real ext-real Element of REAL
(f (#) (h `| x0)) . c is V22() real ext-real Element of REAL
(((f `| x0) (#) h) . c) + ((f (#) (h `| x0)) . c) is V22() real ext-real Element of REAL
(((f `| x0) (#) h) + (f (#) (h `| x0))) . c is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
x0 (#) x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(x0 (#) x0) " {0} is V72() V73() V74() Element of K19(REAL)
x0 " {0} is V72() V73() V74() Element of K19(REAL)
f is set
h is V22() real ext-real Element of REAL
(x0 (#) x0) . h is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
(x0 . h) * (x0 . h) is V22() real ext-real Element of REAL
dom (x0 (#) x0) is V72() V73() V74() Element of K19(REAL)
dom x0 is V72() V73() V74() Element of K19(REAL)
(dom x0) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
f is set
h is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
(x0 . h) * (x0 . h) is V22() real ext-real Element of REAL
(x0 (#) x0) . h is V22() real ext-real Element of REAL
dom x0 is V72() V73() V74() Element of K19(REAL)
(dom x0) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
dom (x0 (#) x0) is V72() V73() V74() Element of K19(REAL)
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f / h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f / h) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f `| x0) (#) h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(h `| x0) (#) f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((f `| x0) (#) h) - ((h `| x0) (#) f) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- ((h `| x0) (#) f) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((h `| x0) (#) f) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f `| x0) (#) h) + (- ((h `| x0) (#) f)) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
h (#) h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(((f `| x0) (#) h) - ((h `| x0) (#) f)) / (h (#) h) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
dom h is V72() V73() V74() Element of K19(REAL)
h " {0} is V72() V73() V74() Element of K19(REAL)
(dom h) \ (h " {0}) is V72() V73() V74() Element of K19(REAL)
c is set
fm is V22() real ext-real Element of REAL
h . fm is V22() real ext-real Element of REAL
(dom f) /\ ((dom h) \ (h " {0})) is V72() V73() V74() Element of K19(REAL)
dom (f / h) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
c is V22() real ext-real Element of REAL
dom ((f / h) `| x0) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
dom (h `| x0) is V72() V73() V74() Element of K19(REAL)
(dom (h `| x0)) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
dom ((h `| x0) (#) f) is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
(dom (f `| x0)) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom ((f `| x0) (#) h) is V72() V73() V74() Element of K19(REAL)
(dom ((f `| x0) (#) h)) /\ (dom ((h `| x0) (#) f)) is V72() V73() V74() Element of K19(REAL)
dom (((f `| x0) (#) h) - ((h `| x0) (#) f)) is V72() V73() V74() Element of K19(REAL)
h . c is V22() real ext-real Element of REAL
(h . c) * (h . c) is V22() real ext-real Element of REAL
(h (#) h) . c is V22() real ext-real Element of REAL
(h (#) h) " {0} is V72() V73() V74() Element of K19(REAL)
(dom h) /\ (dom h) is V72() V73() V74() Element of K19(REAL)
dom (h (#) h) is V72() V73() V74() Element of K19(REAL)
(dom (h (#) h)) \ ((h (#) h) " {0}) is V72() V73() V74() Element of K19(REAL)
(dom (((f `| x0) (#) h) - ((h `| x0) (#) f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
dom ((((f `| x0) (#) h) - ((h `| x0) (#) f)) / (h (#) h)) is V72() V73() V74() Element of K19(REAL)
((f / h) `| x0) . c is V22() real ext-real Element of REAL
diff ((f / h),c) is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
(diff (f,c)) * (h . c) is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
(diff (h,c)) * (f . c) is V22() real ext-real Element of REAL
((diff (f,c)) * (h . c)) - ((diff (h,c)) * (f . c)) is V22() real ext-real Element of REAL
(h . c) ^2 is V22() real ext-real Element of REAL
(h . c) * (h . c) is V22() real ext-real set
(((diff (f,c)) * (h . c)) - ((diff (h,c)) * (f . c))) / ((h . c) ^2) is V22() real ext-real Element of REAL
(f `| x0) . c is V22() real ext-real Element of REAL
((f `| x0) . c) * (h . c) is V22() real ext-real Element of REAL
(((f `| x0) . c) * (h . c)) - ((diff (h,c)) * (f . c)) is V22() real ext-real Element of REAL
((((f `| x0) . c) * (h . c)) - ((diff (h,c)) * (f . c))) / ((h . c) ^2) is V22() real ext-real Element of REAL
(h `| x0) . c is V22() real ext-real Element of REAL
((h `| x0) . c) * (f . c) is V22() real ext-real Element of REAL
(((f `| x0) . c) * (h . c)) - (((h `| x0) . c) * (f . c)) is V22() real ext-real Element of REAL
((((f `| x0) . c) * (h . c)) - (((h `| x0) . c) * (f . c))) / ((h . c) ^2) is V22() real ext-real Element of REAL
((f `| x0) (#) h) . c is V22() real ext-real Element of REAL
(((f `| x0) (#) h) . c) - (((h `| x0) . c) * (f . c)) is V22() real ext-real Element of REAL
((((f `| x0) (#) h) . c) - (((h `| x0) . c) * (f . c))) / ((h . c) ^2) is V22() real ext-real Element of REAL
((h `| x0) (#) f) . c is V22() real ext-real Element of REAL
(((f `| x0) (#) h) . c) - (((h `| x0) (#) f) . c) is V22() real ext-real Element of REAL
((((f `| x0) (#) h) . c) - (((h `| x0) (#) f) . c)) / ((h . c) ^2) is V22() real ext-real Element of REAL
(((f `| x0) (#) h) - ((h `| x0) (#) f)) . c is V22() real ext-real Element of REAL
((((f `| x0) (#) h) - ((h `| x0) (#) f)) . c) / ((h . c) * (h . c)) is V22() real ext-real Element of REAL
((((f `| x0) (#) h) - ((h `| x0) (#) f)) . c) / ((h (#) h) . c) is V22() real ext-real Element of REAL
((h (#) h) . c) " is V22() real ext-real Element of REAL
((((f `| x0) (#) h) - ((h `| x0) (#) f)) . c) * (((h (#) h) . c) ") is V22() real ext-real Element of REAL
((((f `| x0) (#) h) - ((h `| x0) (#) f)) / (h (#) h)) . c is V22() real ext-real Element of REAL
((dom ((f `| x0) (#) h)) /\ (dom ((h `| x0) (#) f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
((dom (f `| x0)) /\ (dom h)) /\ (dom ((h `| x0) (#) f)) is V72() V73() V74() Element of K19(REAL)
(((dom (f `| x0)) /\ (dom h)) /\ (dom ((h `| x0) (#) f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ (dom h) is V72() V73() V74() Element of K19(REAL)
(x0 /\ (dom h)) /\ (dom ((h `| x0) (#) f)) is V72() V73() V74() Element of K19(REAL)
((x0 /\ (dom h)) /\ (dom ((h `| x0) (#) f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ (dom ((h `| x0) (#) f)) is V72() V73() V74() Element of K19(REAL)
(x0 /\ (dom ((h `| x0) (#) f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ ((dom (h `| x0)) /\ (dom f)) is V72() V73() V74() Element of K19(REAL)
(x0 /\ ((dom (h `| x0)) /\ (dom f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ (dom f) is V72() V73() V74() Element of K19(REAL)
x0 /\ (x0 /\ (dom f)) is V72() V73() V74() Element of K19(REAL)
(x0 /\ (x0 /\ (dom f))) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ x0 is V72() V73() V74() Element of K19(REAL)
(x0 /\ x0) /\ ((dom (h (#) h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
((dom h) /\ (dom h)) \ ((h (#) h) " {0}) is V72() V73() V74() Element of K19(REAL)
x0 /\ (((dom h) /\ (dom h)) \ ((h (#) h) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ ((dom h) \ (h " {0})) is V72() V73() V74() Element of K19(REAL)
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f ^ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f ^) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f (#) f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f `| x0) / (f (#) f) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
- ((f `| x0) / (f (#) f)) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(- 1) (#) ((f `| x0) / (f (#) f)) is V1() V4( REAL ) Function-like complex-valued ext-real-valued real-valued set
h is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
dom f is V72() V73() V74() Element of K19(REAL)
f " {0} is V72() V73() V74() Element of K19(REAL)
(dom f) \ (f " {0}) is V72() V73() V74() Element of K19(REAL)
h is set
c is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
dom (f ^) is V72() V73() V74() Element of K19(REAL)
dom ((f ^) `| x0) is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
(f . h) * (f . h) is V22() real ext-real Element of REAL
(f (#) f) . h is V22() real ext-real Element of REAL
(f (#) f) " {0} is V72() V73() V74() Element of K19(REAL)
(dom f) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
dom (f (#) f) is V72() V73() V74() Element of K19(REAL)
(dom (f (#) f)) \ ((f (#) f) " {0}) is V72() V73() V74() Element of K19(REAL)
(dom (f `| x0)) /\ ((dom (f (#) f)) \ ((f (#) f) " {0})) is V72() V73() V74() Element of K19(REAL)
dom ((f `| x0) / (f (#) f)) is V72() V73() V74() Element of K19(REAL)
((f ^) `| x0) . h is V22() real ext-real Element of REAL
diff ((f ^),h) is V22() real ext-real Element of REAL
diff (f,h) is V22() real ext-real Element of REAL
(f . h) ^2 is V22() real ext-real Element of REAL
(f . h) * (f . h) is V22() real ext-real set
(diff (f,h)) / ((f . h) ^2) is V22() real ext-real Element of REAL
- ((diff (f,h)) / ((f . h) ^2)) is V22() real ext-real Element of REAL
(f `| x0) . h is V22() real ext-real Element of REAL
((f `| x0) . h) / ((f . h) * (f . h)) is V22() real ext-real Element of REAL
- (((f `| x0) . h) / ((f . h) * (f . h))) is V22() real ext-real Element of REAL
((f `| x0) . h) / ((f (#) f) . h) is V22() real ext-real Element of REAL
- (((f `| x0) . h) / ((f (#) f) . h)) is V22() real ext-real Element of REAL
((f (#) f) . h) " is V22() real ext-real Element of REAL
((f `| x0) . h) * (((f (#) f) . h) ") is V22() real ext-real Element of REAL
- (((f `| x0) . h) * (((f (#) f) . h) ")) is V22() real ext-real Element of REAL
((f `| x0) / (f (#) f)) . h is V22() real ext-real Element of REAL
- (((f `| x0) / (f (#) f)) . h) is V22() real ext-real Element of REAL
(- ((f `| x0) / (f (#) f))) . h is V22() real ext-real Element of REAL
dom (- ((f `| x0) / (f (#) f))) is V72() V73() V74() Element of K19(REAL)
x0 /\ ((dom (f (#) f)) \ ((f (#) f) " {0})) is V72() V73() V74() Element of K19(REAL)
((dom f) /\ (dom f)) \ ((f (#) f) " {0}) is V72() V73() V74() Element of K19(REAL)
x0 /\ (((dom f) /\ (dom f)) \ ((f (#) f) " {0})) is V72() V73() V74() Element of K19(REAL)
x0 /\ ((dom f) \ (f " {0})) is V72() V73() V74() Element of K19(REAL)
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f .: x0 is V72() V73() V74() Element of K19(REAL)
f `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h * f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(h * f) `| x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h `| (f .: x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(h `| (f .: x0)) * f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((h `| (f .: x0)) * f) (#) (f `| x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
dom h is V72() V73() V74() Element of K19(REAL)
dom (h * f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
dom ((h * f) `| x0) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
((h * f) `| x0) . c is V22() real ext-real Element of REAL
diff ((h * f),c) is V22() real ext-real Element of REAL
diff (h,(f . c)) is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
(diff (h,(f . c))) * (diff (f,c)) is V22() real ext-real Element of REAL
(f `| x0) . c is V22() real ext-real Element of REAL
(diff (h,(f . c))) * ((f `| x0) . c) is V22() real ext-real Element of REAL
(h `| (f .: x0)) . (f . c) is V22() real ext-real Element of REAL
((h `| (f .: x0)) . (f . c)) * ((f `| x0) . c) is V22() real ext-real Element of REAL
((h `| (f .: x0)) * f) . c is V22() real ext-real Element of REAL
(((h `| (f .: x0)) * f) . c) * ((f `| x0) . c) is V22() real ext-real Element of REAL
(((h `| (f .: x0)) * f) (#) (f `| x0)) . c is V22() real ext-real Element of REAL
dom (h `| (f .: x0)) is V72() V73() V74() Element of K19(REAL)
dom ((h `| (f .: x0)) * f) is V72() V73() V74() Element of K19(REAL)
(dom ((h `| (f .: x0)) * f)) /\ x0 is V72() V73() V74() Element of K19(REAL)
dom (f `| x0) is V72() V73() V74() Element of K19(REAL)
(dom ((h `| (f .: x0)) * f)) /\ (dom (f `| x0)) is V72() V73() V74() Element of K19(REAL)
dom (((h `| (f .: x0)) * f) (#) (f `| x0)) is V72() V73() V74() Element of K19(REAL)
x0 is open V72() V73() V74() Element of K19(REAL)
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
c is open V72() V73() V74() Neighbourhood of h
{h} is V72() V73() V74() set
NAT --> 0 is V1() V4( REAL ) V4( NAT ) V5( NAT ) V5( RAT ) V5( INT ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(REAL,NAT))
K20(REAL,NAT) is V5( RAT ) V5( INT ) complex-valued ext-real-valued real-valued natural-valued set
K19(K20(REAL,NAT)) is set
fp is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
fp " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng n is V72() V73() V74() Element of K19(REAL)
fp + n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (fp + n) is V72() V73() V74() Element of K19(REAL)
f /* (fp + n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (fp + n)) - (f /* n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (fp + n)) + (- (f /* n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(fp ") (#) ((f /* (fp + n)) - (f /* n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((fp ") (#) ((f /* (fp + n)) - (f /* n))) is V22() real ext-real Element of REAL
lim (fp + n) is V22() real ext-real Element of REAL
a is V22() real ext-real set
h - a is V22() real ext-real Element of REAL
h + a is V22() real ext-real Element of REAL
].(h - a),(h + a).[ is open V72() V73() V74() Element of K19(REAL)
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(fp + n) ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of fp + n
rng ((fp + n) ^\ h) is V72() V73() V74() Element of K19(REAL)
a is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
((fp + n) ^\ h) . b is V22() real ext-real Element of REAL
b + h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(fp + n) . (b + h) is V22() real ext-real Element of REAL
(((fp + n) ^\ h) . b) - h is V22() real ext-real Element of REAL
abs ((((fp + n) ^\ h) . b) - h) is V22() real ext-real Element of REAL
a is set
((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (fp ") (#) ((f /* (fp + n)) - (f /* n))
fp ^\ h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of fp
n ^\ h is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent subsequence of n
rng (n ^\ h) is V72() V73() V74() Element of K19(REAL)
n is set
abs (fp ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued convergent Element of K19(K20(NAT,REAL))
fm is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
abs (((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fm . n is V22() real ext-real Element of REAL
(abs (((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h)) . n is V22() real ext-real Element of REAL
(abs (fp ^\ h)) . n is V22() real ext-real Element of REAL
(n ^\ h) . n is V22() real ext-real Element of REAL
((fp + n) ^\ h) . n is V22() real ext-real Element of REAL
f . (((fp + n) ^\ h) . n) is V22() real ext-real Element of REAL
f . ((n ^\ h) . n) is V22() real ext-real Element of REAL
(f . (((fp + n) ^\ h) . n)) - (f . ((n ^\ h) . n)) is V22() real ext-real Element of REAL
abs ((f . (((fp + n) ^\ h) . n)) - (f . ((n ^\ h) . n))) is V22() real ext-real Element of REAL
(((fp + n) ^\ h) . n) - ((n ^\ h) . n) is V22() real ext-real Element of REAL
((((fp + n) ^\ h) . n) - ((n ^\ h) . n)) ^2 is V22() real ext-real Element of REAL
((((fp + n) ^\ h) . n) - ((n ^\ h) . n)) * ((((fp + n) ^\ h) . n) - ((n ^\ h) . n)) is V22() real ext-real set
abs ((((fp + n) ^\ h) . n) - ((n ^\ h) . n)) is V22() real ext-real Element of REAL
(abs ((((fp + n) ^\ h) . n) - ((n ^\ h) . n))) ^2 is V22() real ext-real Element of REAL
(abs ((((fp + n) ^\ h) . n) - ((n ^\ h) . n))) * (abs ((((fp + n) ^\ h) . n) - ((n ^\ h) . n))) is V22() real ext-real set
((abs (fp ^\ h)) . n) " is V22() real ext-real Element of REAL
((f /* (fp + n)) - (f /* n)) ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of (f /* (fp + n)) - (f /* n)
abs (((f /* (fp + n)) - (f /* n)) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs (((f /* (fp + n)) - (f /* n)) ^\ h)) . n is V22() real ext-real Element of REAL
(((abs (fp ^\ h)) . n) ") * ((abs (((f /* (fp + n)) - (f /* n)) ^\ h)) . n) is V22() real ext-real Element of REAL
(abs (fp ^\ h)) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((abs (fp ^\ h)) ") . n is V22() real ext-real Element of REAL
(((abs (fp ^\ h)) ") . n) * ((abs (((f /* (fp + n)) - (f /* n)) ^\ h)) . n) is V22() real ext-real Element of REAL
((abs (fp ^\ h)) ") (#) (abs (((f /* (fp + n)) - (f /* n)) ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((abs (fp ^\ h)) ") (#) (abs (((f /* (fp + n)) - (f /* n)) ^\ h))) . n is V22() real ext-real Element of REAL
(fp ^\ h) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
abs ((fp ^\ h) ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs ((fp ^\ h) ")) (#) (abs (((f /* (fp + n)) - (f /* n)) ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((abs ((fp ^\ h) ")) (#) (abs (((f /* (fp + n)) - (f /* n)) ^\ h))) . n is V22() real ext-real Element of REAL
((fp ^\ h) ") (#) (((f /* (fp + n)) - (f /* n)) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
abs (((fp ^\ h) ") (#) (((f /* (fp + n)) - (f /* n)) ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs (((fp ^\ h) ") (#) (((f /* (fp + n)) - (f /* n)) ^\ h))) . n is V22() real ext-real Element of REAL
(fp ") ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of fp "
((fp ") ^\ h) (#) (((f /* (fp + n)) - (f /* n)) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
abs (((fp ") ^\ h) (#) (((f /* (fp + n)) - (f /* n)) ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs (((fp ") ^\ h) (#) (((f /* (fp + n)) - (f /* n)) ^\ h))) . n is V22() real ext-real Element of REAL
(((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h) . n is V22() real ext-real Element of REAL
abs ((((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h) . n) is V22() real ext-real Element of REAL
(fp ^\ h) + (n ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((fp ^\ h) + (n ^\ h)) . n is V22() real ext-real Element of REAL
(((fp ^\ h) + (n ^\ h)) . n) - ((n ^\ h) . n) is V22() real ext-real Element of REAL
abs ((((fp ^\ h) + (n ^\ h)) . n) - ((n ^\ h) . n)) is V22() real ext-real Element of REAL
(abs ((((fp ^\ h) + (n ^\ h)) . n) - ((n ^\ h) . n))) ^2 is V22() real ext-real Element of REAL
(abs ((((fp ^\ h) + (n ^\ h)) . n) - ((n ^\ h) . n))) * (abs ((((fp ^\ h) + (n ^\ h)) . n) - ((n ^\ h) . n))) is V22() real ext-real set
(fp ^\ h) . n is V22() real ext-real Element of REAL
((fp ^\ h) . n) + ((n ^\ h) . n) is V22() real ext-real Element of REAL
(((fp ^\ h) . n) + ((n ^\ h) . n)) - ((n ^\ h) . n) is V22() real ext-real Element of REAL
abs ((((fp ^\ h) . n) + ((n ^\ h) . n)) - ((n ^\ h) . n)) is V22() real ext-real Element of REAL
(abs ((((fp ^\ h) . n) + ((n ^\ h) . n)) - ((n ^\ h) . n))) ^2 is V22() real ext-real Element of REAL
(abs ((((fp ^\ h) . n) + ((n ^\ h) . n)) - ((n ^\ h) . n))) * (abs ((((fp ^\ h) . n) + ((n ^\ h) . n)) - ((n ^\ h) . n))) is V22() real ext-real set
((abs (fp ^\ h)) . n) ^2 is V22() real ext-real Element of REAL
((abs (fp ^\ h)) . n) * ((abs (fp ^\ h)) . n) is V22() real ext-real set
((abs (fp ^\ h)) . n) * ((abs (fp ^\ h)) . n) is V22() real ext-real Element of REAL
abs ((fp ^\ h) . n) is V22() real ext-real Element of REAL
(((abs (fp ^\ h)) . n) * ((abs (fp ^\ h)) . n)) * (((abs (fp ^\ h)) . n) ") is V22() real ext-real Element of REAL
((abs (fp ^\ h)) . n) * (((abs (fp ^\ h)) . n) ") is V22() real ext-real Element of REAL
((abs (fp ^\ h)) . n) * (((abs (fp ^\ h)) . n) * (((abs (fp ^\ h)) . n) ")) is V22() real ext-real Element of REAL
((abs (fp ^\ h)) . n) * 1 is V22() real ext-real Element of REAL
f /* ((fp + n) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((fp + n) ^\ h)) . n is V22() real ext-real Element of REAL
((f /* ((fp + n) ^\ h)) . n) - (f . ((n ^\ h) . n)) is V22() real ext-real Element of REAL
abs (((f /* ((fp + n) ^\ h)) . n) - (f . ((n ^\ h) . n))) is V22() real ext-real Element of REAL
f /* (n ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (n ^\ h)) . n is V22() real ext-real Element of REAL
((f /* ((fp + n) ^\ h)) . n) - ((f /* (n ^\ h)) . n) is V22() real ext-real Element of REAL
abs (((f /* ((fp + n) ^\ h)) . n) - ((f /* (n ^\ h)) . n)) is V22() real ext-real Element of REAL
(f /* ((fp + n) ^\ h)) - (f /* (n ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* (n ^\ h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* (n ^\ h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* ((fp + n) ^\ h)) + (- (f /* (n ^\ h))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* ((fp + n) ^\ h)) - (f /* (n ^\ h))) . n is V22() real ext-real Element of REAL
abs (((f /* ((fp + n) ^\ h)) - (f /* (n ^\ h))) . n) is V22() real ext-real Element of REAL
abs ((f /* ((fp + n) ^\ h)) - (f /* (n ^\ h))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs ((f /* ((fp + n) ^\ h)) - (f /* (n ^\ h)))) . n is V22() real ext-real Element of REAL
(f /* (fp + n)) ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* (fp + n)
((f /* (fp + n)) ^\ h) - (f /* (n ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (fp + n)) ^\ h) + (- (f /* (n ^\ h))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
abs (((f /* (fp + n)) ^\ h) - (f /* (n ^\ h))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs (((f /* (fp + n)) ^\ h) - (f /* (n ^\ h)))) . n is V22() real ext-real Element of REAL
(f /* n) ^\ h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued subsequence of f /* n
((f /* (fp + n)) ^\ h) - ((f /* n) ^\ h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* n) ^\ h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* n) ^\ h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (fp + n)) ^\ h) + (- ((f /* n) ^\ h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
abs (((f /* (fp + n)) ^\ h) - ((f /* n) ^\ h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(abs (((f /* (fp + n)) ^\ h) - ((f /* n) ^\ h))) . n is V22() real ext-real Element of REAL
lim (fp ^\ h) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim (abs (fp ^\ h)) is V22() real ext-real Element of REAL
abs 0 is V22() real ext-real V95() Element of REAL
lim fm is V22() real ext-real Element of REAL
fm . 0 is V22() real ext-real Element of REAL
lim (abs (((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h)) is V22() real ext-real Element of REAL
lim (((fp ") (#) ((f /* (fp + n)) - (f /* n))) ^\ h) is V22() real ext-real Element of REAL
diff (f,h) is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
diff (f,h) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
].x0,f.[ is open V72() V73() V74() Element of K19(REAL)
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
h | ].x0,f.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
c is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(left_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
min (h,c) is V22() real ext-real Element of REAL
(min (h,c)) - 1 is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ is open V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
n is V22() real ext-real Element of REAL
f . fp is V22() real ext-real Element of REAL
f . n is V22() real ext-real Element of REAL
(f . fp) - (f . n) is V22() real ext-real Element of REAL
abs ((f . fp) - (f . n)) is V22() real ext-real Element of REAL
fp - n is V22() real ext-real Element of REAL
(fp - n) ^2 is V22() real ext-real Element of REAL
(fp - n) * (fp - n) is V22() real ext-real set
{ b₁ where b₁ is V22() real ext-real Element of REAL : not x0 <= b₁ } is set
c - 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (h,c)) - 1 & not x0 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
h - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f | ].((min (h,c)) - 1),x0.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(right_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
max (h,c) is V22() real ext-real Element of REAL
(max (h,c)) + 1 is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
n is V22() real ext-real Element of REAL
f . fp is V22() real ext-real Element of REAL
f . n is V22() real ext-real Element of REAL
(f . fp) - (f . n) is V22() real ext-real Element of REAL
abs ((f . fp) - (f . n)) is V22() real ext-real Element of REAL
fp - n is V22() real ext-real Element of REAL
(fp - n) ^2 is V22() real ext-real Element of REAL
(fp - n) * (fp - n) is V22() real ext-real set
{ b₁ where b₁ is V22() real ext-real Element of REAL : not b₁ <= x0 } is set
c + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 & not (max (h,c)) + 1 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
h + 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f | ].x0,((max (h,c)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
f is V22() real ext-real Element of REAL
([#] REAL) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
max (f,h) is V22() real ext-real Element of REAL
min (f,h) is V22() real ext-real Element of REAL
(max (f,h)) + 1 is V22() real ext-real Element of REAL
f + 0 is V22() real ext-real Element of REAL
h + 0 is V22() real ext-real Element of REAL
h - 0 is V22() real ext-real Element of REAL
(min (f,h)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (f,h)) - 1 & not (max (f,h)) + 1 <= b₁ ) } is set
].((min (f,h)) - 1),((max (f,h)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].((min (f,h)) - 1),((max (f,h)) + 1).[ /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
f - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
n is V22() real ext-real Element of REAL
x0 . fp is V22() real ext-real Element of REAL
x0 . n is V22() real ext-real Element of REAL
(x0 . fp) - (x0 . n) is V22() real ext-real Element of REAL
abs ((x0 . fp) - (x0 . n)) is V22() real ext-real Element of REAL
fp - n is V22() real ext-real Element of REAL
(fp - n) ^2 is V22() real ext-real Element of REAL
(fp - n) * (fp - n) is V22() real ext-real set
x0 | ].((min (f,h)) - 1),((max (f,h)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
(x0 . f) - (x0 . h) is V22() real ext-real Element of REAL
abs ((x0 . f) - (x0 . h)) is V22() real ext-real Element of REAL
f - h is V22() real ext-real Element of REAL
(f - h) ^2 is V22() real ext-real Element of REAL
(f - h) * (f - h) is V22() real ext-real set
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(left_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
min (h,c) is V22() real ext-real Element of REAL
c - 0 is V22() real ext-real Element of REAL
(min (h,c)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not x0 <= b₁ } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (h,c)) - 1 & not x0 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ is open V72() V73() V74() Element of K19(REAL)
].((min (h,c)) - 1),x0.[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].((min (h,c)) - 1),x0.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(left_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
min (h,c) is V22() real ext-real Element of REAL
c - 0 is V22() real ext-real Element of REAL
(min (h,c)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not x0 <= b₁ } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (h,c)) - 1 & not x0 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ is open V72() V73() V74() Element of K19(REAL)
].((min (h,c)) - 1),x0.[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].((min (h,c)) - 1),x0.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(left_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
min (h,c) is V22() real ext-real Element of REAL
c - 0 is V22() real ext-real Element of REAL
(min (h,c)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not x0 <= b₁ } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (h,c)) - 1 & not x0 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ is open V72() V73() V74() Element of K19(REAL)
].((min (h,c)) - 1),x0.[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].((min (h,c)) - 1),x0.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(left_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
min (h,c) is V22() real ext-real Element of REAL
c - 0 is V22() real ext-real Element of REAL
(min (h,c)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not x0 <= b₁ } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (h,c)) - 1 & not x0 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].((min (h,c)) - 1),x0.[ is open V72() V73() V74() Element of K19(REAL)
].((min (h,c)) - 1),x0.[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].((min (h,c)) - 1),x0.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h - 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(right_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
max (h,c) is V22() real ext-real Element of REAL
(max (h,c)) + 1 is V22() real ext-real Element of REAL
c + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not b₁ <= x0 } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 & not (max (h,c)) + 1 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].x0,((max (h,c)) + 1).[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].x0,((max (h,c)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h + 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(right_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
max (h,c) is V22() real ext-real Element of REAL
(max (h,c)) + 1 is V22() real ext-real Element of REAL
c + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not b₁ <= x0 } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 & not (max (h,c)) + 1 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].x0,((max (h,c)) + 1).[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].x0,((max (h,c)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h + 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(right_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
max (h,c) is V22() real ext-real Element of REAL
(max (h,c)) + 1 is V22() real ext-real Element of REAL
c + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not b₁ <= x0 } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 & not (max (h,c)) + 1 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].x0,((max (h,c)) + 1).[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].x0,((max (h,c)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h + 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is V22() real ext-real Element of REAL
(right_open_halfline x0) /\ (dom f) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
max (h,c) is V22() real ext-real Element of REAL
(max (h,c)) + 1 is V22() real ext-real Element of REAL
c + 0 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : not b₁ <= x0 } is set
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= x0 & not (max (h,c)) + 1 <= b₁ ) } is set
fp is V22() real ext-real Element of REAL
].x0,((max (h,c)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].x0,((max (h,c)) + 1).[ /\ (dom f) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (f,fp) is V22() real ext-real Element of REAL
f | ].x0,((max (h,c)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h + 0 is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
f . c is V22() real ext-real Element of REAL
f . h is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f is V22() real ext-real Element of REAL
([#] REAL) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
max (f,h) is V22() real ext-real Element of REAL
min (f,h) is V22() real ext-real Element of REAL
(max (f,h)) + 1 is V22() real ext-real Element of REAL
h + 0 is V22() real ext-real Element of REAL
h - 0 is V22() real ext-real Element of REAL
(min (f,h)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (f,h)) - 1 & not (max (f,h)) + 1 <= b₁ ) } is set
].((min (f,h)) - 1),((max (f,h)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].((min (f,h)) - 1),((max (f,h)) + 1).[ /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (x0,fp) is V22() real ext-real Element of REAL
x0 | ].((min (f,h)) - 1),((max (f,h)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f + 0 is V22() real ext-real Element of REAL
f - 0 is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f is V22() real ext-real Element of REAL
([#] REAL) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
max (f,h) is V22() real ext-real Element of REAL
min (f,h) is V22() real ext-real Element of REAL
(max (f,h)) + 1 is V22() real ext-real Element of REAL
h + 0 is V22() real ext-real Element of REAL
h - 0 is V22() real ext-real Element of REAL
(min (f,h)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (f,h)) - 1 & not (max (f,h)) + 1 <= b₁ ) } is set
].((min (f,h)) - 1),((max (f,h)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].((min (f,h)) - 1),((max (f,h)) + 1).[ /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (x0,fp) is V22() real ext-real Element of REAL
x0 | ].((min (f,h)) - 1),((max (f,h)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f + 0 is V22() real ext-real Element of REAL
f - 0 is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f is V22() real ext-real Element of REAL
([#] REAL) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
max (f,h) is V22() real ext-real Element of REAL
min (f,h) is V22() real ext-real Element of REAL
(max (f,h)) + 1 is V22() real ext-real Element of REAL
h + 0 is V22() real ext-real Element of REAL
h - 0 is V22() real ext-real Element of REAL
(min (f,h)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (f,h)) - 1 & not (max (f,h)) + 1 <= b₁ ) } is set
].((min (f,h)) - 1),((max (f,h)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].((min (f,h)) - 1),((max (f,h)) + 1).[ /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (x0,fp) is V22() real ext-real Element of REAL
x0 | ].((min (f,h)) - 1),((max (f,h)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f + 0 is V22() real ext-real Element of REAL
f - 0 is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f is V22() real ext-real Element of REAL
([#] REAL) /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
h is V22() real ext-real Element of REAL
max (f,h) is V22() real ext-real Element of REAL
min (f,h) is V22() real ext-real Element of REAL
(max (f,h)) + 1 is V22() real ext-real Element of REAL
h + 0 is V22() real ext-real Element of REAL
h - 0 is V22() real ext-real Element of REAL
(min (f,h)) - 1 is V22() real ext-real Element of REAL
{ b₁ where b₁ is V22() real ext-real Element of REAL : ( not b₁ <= (min (f,h)) - 1 & not (max (f,h)) + 1 <= b₁ ) } is set
].((min (f,h)) - 1),((max (f,h)) + 1).[ is open V72() V73() V74() Element of K19(REAL)
].((min (f,h)) - 1),((max (f,h)) + 1).[ /\ (dom x0) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (x0,fp) is V22() real ext-real Element of REAL
x0 | ].((min (f,h)) - 1),((max (f,h)) + 1).[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f + 0 is V22() real ext-real Element of REAL
f - 0 is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
x0 . f is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
].x0,f.[ is open V72() V73() V74() Element of K19(REAL)
h is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
h | ].x0,f.[ is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
rng (h | ].x0,f.[) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
diff (h,c) is V22() real ext-real Element of REAL
fm is V22() real ext-real Element of REAL
diff (h,fm) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
rng (f | (left_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
fm is V22() real ext-real Element of REAL
diff (f,fm) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
rng (f | (right_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
c is V22() real ext-real Element of REAL
diff (f,c) is V22() real ext-real Element of REAL
fm is V22() real ext-real Element of REAL
diff (f,fm) is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
rng x0 is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
f is V22() real ext-real Element of REAL
diff (x0,f) is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
diff (x0,h) is V22() real ext-real Element of REAL
x0 is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom x0 is V72() V73() V74() Element of K19(REAL)
x0 " is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (x0 ") is V72() V73() V74() Element of K19(REAL)
rng x0 is V72() V73() V74() Element of K19(REAL)
rng (x0 ") is V72() V73() V74() Element of K19(REAL)
f is V22() real ext-real Element of REAL
diff ((x0 "),f) is V22() real ext-real Element of REAL
(x0 ") . f is V22() real ext-real Element of REAL
diff (x0,((x0 ") . f)) is V22() real ext-real Element of REAL
1 / (diff (x0,((x0 ") . f))) is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
{f} is V72() V73() V74() set
NAT --> ((x0 ") . f) is V1() V4( REAL ) V4( NAT ) V5( REAL ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued non-decreasing non-increasing V79() Element of K19(K20(REAL,REAL))
fm is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
fm " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
fp is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng fp is V72() V73() V74() Element of K19(REAL)
fm + fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (fm + fp) is V72() V73() V74() Element of K19(REAL)
(x0 ") /* (fm + fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(x0 ") /* fp is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((x0 ") /* (fm + fp)) - ((x0 ") /* fp) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((x0 ") /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((x0 ") /* fp) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((x0 ") /* (fm + fp)) + (- ((x0 ") /* fp)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(fm ") (#) (((x0 ") /* (fm + fp)) - ((x0 ") /* fp)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((fm ") (#) (((x0 ") /* (fm + fp)) - ((x0 ") /* fp))) is V22() real ext-real Element of REAL
lim (fm + fp) is V22() real ext-real Element of REAL
c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(fm + fp) . a is V22() real ext-real Element of REAL
n . a is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
x0 . h is V22() real ext-real Element of REAL
h - h is V22() real ext-real Element of REAL
c is V22() real ext-real Element of REAL
a is V22() real ext-real set
b is V22() real ext-real set
b + c is V22() real ext-real set
x0 . (b + c) is V22() real ext-real Element of REAL
(x0 ") . (x0 . h) is V22() real ext-real Element of REAL
b + c is V22() real ext-real Element of REAL
x0 . (b + c) is V22() real ext-real Element of REAL
a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . h is V22() real ext-real Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a . h is V22() real ext-real Element of REAL
(fm + fp) . h is V22() real ext-real Element of REAL
fm . h is V22() real ext-real Element of REAL
fp . h is V22() real ext-real Element of REAL
(fm . h) + (fp . h) is V22() real ext-real Element of REAL
(fm . h) + (x0 . h) is V22() real ext-real Element of REAL
n . h is V22() real ext-real Element of REAL
(n . h) + (a . h) is V22() real ext-real Element of REAL
x0 . ((n . h) + (a . h)) is V22() real ext-real Element of REAL
(x0 ") . (x0 . h) is V22() real ext-real Element of REAL
x0 . ((x0 ") . (x0 . h)) is V22() real ext-real Element of REAL
(x0 ") | (rng x0) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom ((x0 ") | (rng x0)) is V72() V73() V74() Element of K19(REAL)
x0 | ([#] REAL) is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(x0 ") | (dom (x0 ")) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
h is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a . h is V22() real ext-real Element of REAL
n . h is V22() real ext-real Element of REAL
(a . h) + (n . h) is V22() real ext-real Element of REAL
((x0 ") /* (fm + fp)) - n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- n is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) n is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((x0 ") /* (fm + fp)) + (- n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((x0 ") /* (fm + fp)) - n) . h is V22() real ext-real Element of REAL
((x0 ") /* (fm + fp)) . h is V22() real ext-real Element of REAL
(((x0 ") /* (fm + fp)) . h) - (n . h) is V22() real ext-real Element of REAL
(fm + fp) . h is V22() real ext-real Element of REAL
(x0 ") . ((fm + fp) . h) is V22() real ext-real Element of REAL
((x0 ") . ((fm + fp) . h)) - (n . h) is V22() real ext-real Element of REAL
x0 . ((a . h) + (n . h)) is V22() real ext-real Element of REAL
(x0 ") . (x0 . ((a . h) + (n . h))) is V22() real ext-real Element of REAL
((x0 ") . (x0 . ((a . h) + (n . h)))) - (n . h) is V22() real ext-real Element of REAL
((a . h) + (n . h)) - (n . h) is V22() real ext-real Element of REAL
lim n is V22() real ext-real Element of REAL
n . 0 is V22() real ext-real Element of REAL
lim ((x0 ") /* (fm + fp)) is V22() real ext-real Element of REAL
lim (((x0 ") /* (fm + fp)) - n) is V22() real ext-real Element of REAL
((x0 ") . f) - ((x0 ") . f) is V22() real ext-real Element of REAL
lim a is V22() real ext-real Element of REAL
a + n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + n) is V72() V73() V74() Element of K19(REAL)
h is set
h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
h " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng n is V72() V73() V74() Element of K19(REAL)
{((x0 ") . f)} is V72() V73() V74() set
c is set
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n . a is V22() real ext-real Element of REAL
c is set
c is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
fp . c is V22() real ext-real Element of REAL
x0 /* n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(x0 /* n) . c is V22() real ext-real Element of REAL
n . c is V22() real ext-real Element of REAL
x0 . (n . c) is V22() real ext-real Element of REAL
x0 . ((x0 ") . f) is V22() real ext-real Element of REAL
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(fm + fp) . c is V22() real ext-real Element of REAL
n . c is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
(n . c) + (h . c) is V22() real ext-real Element of REAL
x0 . ((n . c) + (h . c)) is V22() real ext-real Element of REAL
fm . c is V22() real ext-real Element of REAL
fp . c is V22() real ext-real Element of REAL
(fm . c) + (fp . c) is V22() real ext-real Element of REAL
(h . c) + (n . c) is V22() real ext-real Element of REAL
x0 . ((h . c) + (n . c)) is V22() real ext-real Element of REAL
(x0 /* n) . c is V22() real ext-real Element of REAL
(x0 . ((h . c) + (n . c))) - ((x0 /* n) . c) is V22() real ext-real Element of REAL
h + n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h + n) . c is V22() real ext-real Element of REAL
x0 . ((h + n) . c) is V22() real ext-real Element of REAL
(x0 . ((h + n) . c)) - ((x0 /* n) . c) is V22() real ext-real Element of REAL
x0 /* (h + n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(x0 /* (h + n)) . c is V22() real ext-real Element of REAL
((x0 /* (h + n)) . c) - ((x0 /* n) . c) is V22() real ext-real Element of REAL
(x0 /* (h + n)) - (x0 /* n) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (x0 /* n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (x0 /* n) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(x0 /* (h + n)) + (- (x0 /* n)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((x0 /* (h + n)) - (x0 /* n)) . c is V22() real ext-real Element of REAL
(h ") (#) ((x0 /* (h + n)) - (x0 /* n)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is set
c is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
n . c is V22() real ext-real Element of REAL
h . c is V22() real ext-real Element of REAL
(n . c) + (h . c) is V22() real ext-real Element of REAL
fp . c is V22() real ext-real Element of REAL
((fm ") (#) (((x0 ") /* (fm + fp)) - ((x0 ") /* fp))) . c is V22() real ext-real Element of REAL
(fm ") . c is V22() real ext-real Element of REAL
(((x0 ") /* (fm + fp)) - ((x0 ") /* fp)) . c is V22() real ext-real Element of REAL
((fm ") . c) * ((((x0 ") /* (fm + fp)) - ((x0 ") /* fp)) . c) is V22() real ext-real Element of REAL
((x0 ") /* (fm + fp)) . c is V22() real ext-real Element of REAL
((x0 ") /* fp) . c is V22() real ext-real Element of REAL
(((x0 ") /* (fm + fp)) . c) - (((x0 ") /* fp) . c) is V22() real ext-real Element of REAL
((fm ") . c) * ((((x0 ") /* (fm + fp)) . c) - (((x0 ") /* fp) . c)) is V22() real ext-real Element of REAL
(fm + fp) . c is V22() real ext-real Element of REAL
(x0 ") . ((fm + fp) . c) is V22() real ext-real Element of REAL
((x0 ") . ((fm + fp) . c)) - (((x0 ") /* fp) . c) is V22() real ext-real Element of REAL
((fm ") . c) * (((x0 ") . ((fm + fp) . c)) - (((x0 ") /* fp) . c)) is V22() real ext-real Element of REAL
x0 . ((n . c) + (h . c)) is V22() real ext-real Element of REAL
(x0 ") . (x0 . ((n . c) + (h . c))) is V22() real ext-real Element of REAL
((x0 ") . (x0 . ((n . c) + (h . c)))) - (((x0 ") /* fp) . c) is V22() real ext-real Element of REAL
((fm ") . c) * (((x0 ") . (x0 . ((n . c) + (h . c)))) - (((x0 ") /* fp) . c)) is V22() real ext-real Element of REAL
((n . c) + (h . c)) - (((x0 ") /* fp) . c) is V22() real ext-real Element of REAL
((fm ") . c) * (((n . c) + (h . c)) - (((x0 ") /* fp) . c)) is V22() real ext-real Element of REAL
(x0 ") . (fp . c) is V22() real ext-real Element of REAL
((n . c) + (h . c)) - ((x0 ") . (fp . c)) is V22() real ext-real Element of REAL
((fm ") . c) * (((n . c) + (h . c)) - ((x0 ") . (fp . c))) is V22() real ext-real Element of REAL
((n . c) + (h . c)) - (n . c) is V22() real ext-real Element of REAL
((fm ") . c) * (((n . c) + (h . c)) - (n . c)) is V22() real ext-real Element of REAL
(h ") " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(fm ") (#) ((h ") ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((fm ") (#) ((h ") ")) . c is V22() real ext-real Element of REAL
((h ") (#) ((x0 /* (h + n)) - (x0 /* n))) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((h ") (#) ((x0 /* (h + n)) - (x0 /* n))) ") . c is V22() real ext-real Element of REAL
lim ((h ") (#) ((x0 /* (h + n)) - (x0 /* n))) is V22() real ext-real Element of REAL
(diff (x0,((x0 ") . f))) " is V22() real ext-real Element of REAL
c is open V72() V73() V74() Neighbourhood of f
f is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
diff ((x0 "),f) is V22() real ext-real Element of REAL
(x0 ") . f is V22() real ext-real Element of REAL
diff (x0,((x0 ") . f)) is V22() real ext-real Element of REAL
1 / (diff (x0,((x0 ") . f))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
left_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(-infty,x0) is set
f is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (left_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f | (left_open_halfline x0)) " is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom ((f | (left_open_halfline x0)) ") is V72() V73() V74() Element of K19(REAL)
rng (f | (left_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
rng ((f | (left_open_halfline x0)) ") is V72() V73() V74() Element of K19(REAL)
dom (f | (left_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
fm is V22() real ext-real Element of REAL
diff (((f | (left_open_halfline x0)) "),fm) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . fm is V22() real ext-real Element of REAL
diff (f,(((f | (left_open_halfline x0)) ") . fm)) is V22() real ext-real Element of REAL
1 / (diff (f,(((f | (left_open_halfline x0)) ") . fm))) is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
(f | (left_open_halfline x0)) . fp is V22() real ext-real Element of REAL
{fm} is V72() V73() V74() set
f .: (left_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
((f | (left_open_halfline x0)) ") | (f .: (left_open_halfline x0)) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((f | (left_open_halfline x0)) ") | (rng (f | (left_open_halfline x0))) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (((f | (left_open_halfline x0)) ") | (rng (f | (left_open_halfline x0)))) is V72() V73() V74() Element of K19(REAL)
NAT --> (((f | (left_open_halfline x0)) ") . fm) is V1() V4( REAL ) V4( NAT ) V5( REAL ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued non-decreasing non-increasing V79() Element of K19(K20(REAL,REAL))
a is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
a " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng h is V72() V73() V74() Element of K19(REAL)
a + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + h) is V72() V73() V74() Element of K19(REAL)
((f | (left_open_halfline x0)) ") /* (a + h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f | (left_open_halfline x0)) ") /* h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((f | (left_open_halfline x0)) ") /* h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((f | (left_open_halfline x0)) ") /* h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f | (left_open_halfline x0)) ") /* (a + h)) + (- (((f | (left_open_halfline x0)) ") /* h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(a ") (#) ((((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((a ") (#) ((((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h))) is V22() real ext-real Element of REAL
lim (a + h) is V22() real ext-real Element of REAL
n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . a is V22() real ext-real Element of REAL
c . a is V22() real ext-real Element of REAL
b is V22() real ext-real Element of REAL
(f | (left_open_halfline x0)) . b is V22() real ext-real Element of REAL
b - fp is V22() real ext-real Element of REAL
b is V22() real ext-real Element of REAL
n is V22() real ext-real set
r1 is V22() real ext-real set
r1 + b is V22() real ext-real set
f . (r1 + b) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
r1 + b is V22() real ext-real Element of REAL
f . (r1 + b) is V22() real ext-real Element of REAL
(dom f) /\ (left_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") /* (a + h)) - c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- c is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) c is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f | (left_open_halfline x0)) ") /* (a + h)) + (- c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f | (left_open_halfline x0)) ") /* (a + h)) - c) . b is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") /* (a + h)) . b is V22() real ext-real Element of REAL
((((f | (left_open_halfline x0)) ") /* (a + h)) . b) - (c . b) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((a + h) . b) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . ((a + h) . b)) - (c . b) is V22() real ext-real Element of REAL
f . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . (f . ((c . b) + (a . b))) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . (f . ((c . b) + (a . b)))) - (c . b) is V22() real ext-real Element of REAL
(f | (left_open_halfline x0)) . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . ((c . b) + (a . b))) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . ((c . b) + (a . b)))) - (c . b) is V22() real ext-real Element of REAL
((c . b) + (a . b)) - (c . b) is V22() real ext-real Element of REAL
lim c is V22() real ext-real Element of REAL
c . 0 is V22() real ext-real Element of REAL
lim (((f | (left_open_halfline x0)) ") /* (a + h)) is V22() real ext-real Element of REAL
lim ((((f | (left_open_halfline x0)) ") /* (a + h)) - c) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . fm) - (((f | (left_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
lim a is V22() real ext-real Element of REAL
a + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + c) is V72() V73() V74() Element of K19(REAL)
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + c) . b is V22() real ext-real Element of REAL
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
(dom f) /\ (left_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h . b is V22() real ext-real Element of REAL
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
f . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
(a + h) . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
(a . b) + (h . b) is V22() real ext-real Element of REAL
(a . b) + ((f | (left_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
b is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
b " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng c is V72() V73() V74() Element of K19(REAL)
{(((f | (left_open_halfline x0)) ") . fm)} is V72() V73() V74() set
b is set
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . n is V22() real ext-real Element of REAL
b is set
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h . b is V22() real ext-real Element of REAL
f /* c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* c) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
f . (c . b) is V22() real ext-real Element of REAL
f . (((f | (left_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
(f | (left_open_halfline x0)) . (((f | (left_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
b . b is V22() real ext-real Element of REAL
(c . b) + (b . b) is V22() real ext-real Element of REAL
f . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
(a . b) + (h . b) is V22() real ext-real Element of REAL
(b . b) + (c . b) is V22() real ext-real Element of REAL
f . ((b . b) + (c . b)) is V22() real ext-real Element of REAL
(f /* c) . b is V22() real ext-real Element of REAL
(f . ((b . b) + (c . b))) - ((f /* c) . b) is V22() real ext-real Element of REAL
b + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(b + c) . b is V22() real ext-real Element of REAL
f . ((b + c) . b) is V22() real ext-real Element of REAL
(f . ((b + c) . b)) - ((f /* c) . b) is V22() real ext-real Element of REAL
f /* (b + c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (b + c)) . b is V22() real ext-real Element of REAL
((f /* (b + c)) . b) - ((f /* c) . b) is V22() real ext-real Element of REAL
(f /* (b + c)) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (b + c)) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (b + c)) - (f /* c)) . b is V22() real ext-real Element of REAL
(b ") (#) ((f /* (b + c)) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
b . b is V22() real ext-real Element of REAL
(c . b) + (b . b) is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
((a ") (#) ((((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h))) . b is V22() real ext-real Element of REAL
(a ") . b is V22() real ext-real Element of REAL
((((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h)) . b is V22() real ext-real Element of REAL
((a ") . b) * (((((f | (left_open_halfline x0)) ") /* (a + h)) - (((f | (left_open_halfline x0)) ") /* h)) . b) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") /* (a + h)) . b is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") /* h) . b is V22() real ext-real Element of REAL
((((f | (left_open_halfline x0)) ") /* (a + h)) . b) - ((((f | (left_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * (((((f | (left_open_halfline x0)) ") /* (a + h)) . b) - ((((f | (left_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((a + h) . b) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . ((a + h) . b)) - ((((f | (left_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (left_open_halfline x0)) ") . ((a + h) . b)) - ((((f | (left_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
f . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . (f . ((c . b) + (b . b))) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . (f . ((c . b) + (b . b)))) - ((((f | (left_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (left_open_halfline x0)) ") . (f . ((c . b) + (b . b)))) - ((((f | (left_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
(f | (left_open_halfline x0)) . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . ((c . b) + (b . b))) is V22() real ext-real Element of REAL
(((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . ((c . b) + (b . b)))) - ((((f | (left_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (left_open_halfline x0)) ") . ((f | (left_open_halfline x0)) . ((c . b) + (b . b)))) - ((((f | (left_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - ((((f | (left_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - ((((f | (left_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . (h . b) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - (((f | (left_open_halfline x0)) ") . (h . b)) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - (((f | (left_open_halfline x0)) ") . (h . b))) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - (c . b) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - (c . b)) is V22() real ext-real Element of REAL
(b ") " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(a ") (#) ((b ") ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((a ") (#) ((b ") ")) . b is V22() real ext-real Element of REAL
((b ") (#) ((f /* (b + c)) - (f /* c))) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((b ") (#) ((f /* (b + c)) - (f /* c))) ") . b is V22() real ext-real Element of REAL
lim ((b ") (#) ((f /* (b + c)) - (f /* c))) is V22() real ext-real Element of REAL
(diff (f,(((f | (left_open_halfline x0)) ") . fm))) " is V22() real ext-real Element of REAL
n is open V72() V73() V74() Neighbourhood of fm
fm is V22() real ext-real Element of REAL
fm is V22() real ext-real Element of REAL
diff (((f | (left_open_halfline x0)) "),fm) is V22() real ext-real Element of REAL
((f | (left_open_halfline x0)) ") . fm is V22() real ext-real Element of REAL
diff (f,(((f | (left_open_halfline x0)) ") . fm)) is V22() real ext-real Element of REAL
1 / (diff (f,(((f | (left_open_halfline x0)) ") . fm))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
right_open_halfline x0 is open V72() V73() V74() Element of K19(REAL)
K202(x0,+infty) is set
f is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
f | (right_open_halfline x0) is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(f | (right_open_halfline x0)) " is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom ((f | (right_open_halfline x0)) ") is V72() V73() V74() Element of K19(REAL)
rng (f | (right_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
rng ((f | (right_open_halfline x0)) ") is V72() V73() V74() Element of K19(REAL)
dom (f | (right_open_halfline x0)) is V72() V73() V74() Element of K19(REAL)
fm is V22() real ext-real Element of REAL
diff (((f | (right_open_halfline x0)) "),fm) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . fm is V22() real ext-real Element of REAL
diff (f,(((f | (right_open_halfline x0)) ") . fm)) is V22() real ext-real Element of REAL
1 / (diff (f,(((f | (right_open_halfline x0)) ") . fm))) is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
(f | (right_open_halfline x0)) . fp is V22() real ext-real Element of REAL
{fm} is V72() V73() V74() set
f .: (right_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
((f | (right_open_halfline x0)) ") | (f .: (right_open_halfline x0)) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((f | (right_open_halfline x0)) ") | (rng (f | (right_open_halfline x0))) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (((f | (right_open_halfline x0)) ") | (rng (f | (right_open_halfline x0)))) is V72() V73() V74() Element of K19(REAL)
NAT --> (((f | (right_open_halfline x0)) ") . fm) is V1() V4( REAL ) V4( NAT ) V5( REAL ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued non-decreasing non-increasing V79() Element of K19(K20(REAL,REAL))
a is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
a " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
h is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng h is V72() V73() V74() Element of K19(REAL)
a + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + h) is V72() V73() V74() Element of K19(REAL)
((f | (right_open_halfline x0)) ") /* (a + h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f | (right_open_halfline x0)) ") /* h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((f | (right_open_halfline x0)) ") /* h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((f | (right_open_halfline x0)) ") /* h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f | (right_open_halfline x0)) ") /* (a + h)) + (- (((f | (right_open_halfline x0)) ") /* h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(a ") (#) ((((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((a ") (#) ((((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h))) is V22() real ext-real Element of REAL
lim (a + h) is V22() real ext-real Element of REAL
n is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
a is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . a is V22() real ext-real Element of REAL
c . a is V22() real ext-real Element of REAL
b is V22() real ext-real Element of REAL
(f | (right_open_halfline x0)) . b is V22() real ext-real Element of REAL
b - fp is V22() real ext-real Element of REAL
b is V22() real ext-real Element of REAL
n is V22() real ext-real set
r1 is V22() real ext-real set
r1 + b is V22() real ext-real set
f . (r1 + b) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
r1 + b is V22() real ext-real Element of REAL
f . (r1 + b) is V22() real ext-real Element of REAL
(dom f) /\ (right_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") /* (a + h)) - c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- c is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) c is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((f | (right_open_halfline x0)) ") /* (a + h)) + (- c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((f | (right_open_halfline x0)) ") /* (a + h)) - c) . b is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") /* (a + h)) . b is V22() real ext-real Element of REAL
((((f | (right_open_halfline x0)) ") /* (a + h)) . b) - (c . b) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((a + h) . b) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . ((a + h) . b)) - (c . b) is V22() real ext-real Element of REAL
f . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . (f . ((c . b) + (a . b))) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . (f . ((c . b) + (a . b)))) - (c . b) is V22() real ext-real Element of REAL
(f | (right_open_halfline x0)) . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . ((c . b) + (a . b))) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . ((c . b) + (a . b)))) - (c . b) is V22() real ext-real Element of REAL
((c . b) + (a . b)) - (c . b) is V22() real ext-real Element of REAL
lim c is V22() real ext-real Element of REAL
c . 0 is V22() real ext-real Element of REAL
lim (((f | (right_open_halfline x0)) ") /* (a + h)) is V22() real ext-real Element of REAL
lim ((((f | (right_open_halfline x0)) ") /* (a + h)) - c) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . fm) - (((f | (right_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
lim a is V22() real ext-real Element of REAL
a + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (a + c) is V72() V73() V74() Element of K19(REAL)
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + c) . b is V22() real ext-real Element of REAL
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
(dom f) /\ (right_open_halfline x0) is V72() V73() V74() Element of K19(REAL)
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h . b is V22() real ext-real Element of REAL
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
(c . b) + (a . b) is V22() real ext-real Element of REAL
f . ((c . b) + (a . b)) is V22() real ext-real Element of REAL
(a + h) . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
(a . b) + (h . b) is V22() real ext-real Element of REAL
(a . b) + ((f | (right_open_halfline x0)) . fp) is V22() real ext-real Element of REAL
b is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
b " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng c is V72() V73() V74() Element of K19(REAL)
{(((f | (right_open_halfline x0)) ") . fm)} is V72() V73() V74() set
b is set
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . n is V22() real ext-real Element of REAL
b is set
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
h . b is V22() real ext-real Element of REAL
f /* c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* c) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
f . (c . b) is V22() real ext-real Element of REAL
f . (((f | (right_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
(f | (right_open_halfline x0)) . (((f | (right_open_halfline x0)) ") . fm) is V22() real ext-real Element of REAL
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
b . b is V22() real ext-real Element of REAL
(c . b) + (b . b) is V22() real ext-real Element of REAL
f . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
(a . b) + (h . b) is V22() real ext-real Element of REAL
(b . b) + (c . b) is V22() real ext-real Element of REAL
f . ((b . b) + (c . b)) is V22() real ext-real Element of REAL
(f /* c) . b is V22() real ext-real Element of REAL
(f . ((b . b) + (c . b))) - ((f /* c) . b) is V22() real ext-real Element of REAL
b + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(b + c) . b is V22() real ext-real Element of REAL
f . ((b + c) . b) is V22() real ext-real Element of REAL
(f . ((b + c) . b)) - ((f /* c) . b) is V22() real ext-real Element of REAL
f /* (b + c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (b + c)) . b is V22() real ext-real Element of REAL
((f /* (b + c)) . b) - ((f /* c) . b) is V22() real ext-real Element of REAL
(f /* (b + c)) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (b + c)) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (b + c)) - (f /* c)) . b is V22() real ext-real Element of REAL
(b ") (#) ((f /* (b + c)) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is set
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(a + h) . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
b . b is V22() real ext-real Element of REAL
(c . b) + (b . b) is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
((a ") (#) ((((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h))) . b is V22() real ext-real Element of REAL
(a ") . b is V22() real ext-real Element of REAL
((((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h)) . b is V22() real ext-real Element of REAL
((a ") . b) * (((((f | (right_open_halfline x0)) ") /* (a + h)) - (((f | (right_open_halfline x0)) ") /* h)) . b) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") /* (a + h)) . b is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") /* h) . b is V22() real ext-real Element of REAL
((((f | (right_open_halfline x0)) ") /* (a + h)) . b) - ((((f | (right_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * (((((f | (right_open_halfline x0)) ") /* (a + h)) . b) - ((((f | (right_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((a + h) . b) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . ((a + h) . b)) - ((((f | (right_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (right_open_halfline x0)) ") . ((a + h) . b)) - ((((f | (right_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
f . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . (f . ((c . b) + (b . b))) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . (f . ((c . b) + (b . b)))) - ((((f | (right_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (right_open_halfline x0)) ") . (f . ((c . b) + (b . b)))) - ((((f | (right_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
(f | (right_open_halfline x0)) . ((c . b) + (b . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . ((c . b) + (b . b))) is V22() real ext-real Element of REAL
(((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . ((c . b) + (b . b)))) - ((((f | (right_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * ((((f | (right_open_halfline x0)) ") . ((f | (right_open_halfline x0)) . ((c . b) + (b . b)))) - ((((f | (right_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - ((((f | (right_open_halfline x0)) ") /* h) . b) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - ((((f | (right_open_halfline x0)) ") /* h) . b)) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . (h . b) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - (((f | (right_open_halfline x0)) ") . (h . b)) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - (((f | (right_open_halfline x0)) ") . (h . b))) is V22() real ext-real Element of REAL
((c . b) + (b . b)) - (c . b) is V22() real ext-real Element of REAL
((a ") . b) * (((c . b) + (b . b)) - (c . b)) is V22() real ext-real Element of REAL
(b ") " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(a ") (#) ((b ") ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((a ") (#) ((b ") ")) . b is V22() real ext-real Element of REAL
((b ") (#) ((f /* (b + c)) - (f /* c))) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((b ") (#) ((f /* (b + c)) - (f /* c))) ") . b is V22() real ext-real Element of REAL
lim ((b ") (#) ((f /* (b + c)) - (f /* c))) is V22() real ext-real Element of REAL
(diff (f,(((f | (right_open_halfline x0)) ") . fm))) " is V22() real ext-real Element of REAL
n is open V72() V73() V74() Neighbourhood of fm
fm is V22() real ext-real Element of REAL
fm is V22() real ext-real Element of REAL
diff (((f | (right_open_halfline x0)) "),fm) is V22() real ext-real Element of REAL
((f | (right_open_halfline x0)) ") . fm is V22() real ext-real Element of REAL
diff (f,(((f | (right_open_halfline x0)) ") . fm)) is V22() real ext-real Element of REAL
1 / (diff (f,(((f | (right_open_halfline x0)) ") . fm))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
f is V22() real ext-real Element of REAL
].x0,f.[ is open V72() V73() V74() Element of K19(REAL)
h is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom h is V72() V73() V74() Element of K19(REAL)
h | ].x0,f.[ is V1() V4( REAL ) V5( REAL ) Function-like one-to-one complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
(h | ].x0,f.[) " is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom ((h | ].x0,f.[) ") is V72() V73() V74() Element of K19(REAL)
rng (h | ].x0,f.[) is V72() V73() V74() Element of K19(REAL)
rng ((h | ].x0,f.[) ") is V72() V73() V74() Element of K19(REAL)
dom (h | ].x0,f.[) is V72() V73() V74() Element of K19(REAL)
fp is V22() real ext-real Element of REAL
diff (((h | ].x0,f.[) "),fp) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . fp is V22() real ext-real Element of REAL
diff (h,(((h | ].x0,f.[) ") . fp)) is V22() real ext-real Element of REAL
1 / (diff (h,(((h | ].x0,f.[) ") . fp))) is V22() real ext-real Element of REAL
n is V22() real ext-real Element of REAL
(h | ].x0,f.[) . n is V22() real ext-real Element of REAL
{fp} is V72() V73() V74() set
a is V22() real ext-real Element of REAL
diff (h,a) is V22() real ext-real Element of REAL
h is V22() real ext-real Element of REAL
diff (h,h) is V22() real ext-real Element of REAL
h .: ].x0,f.[ is V72() V73() V74() Element of K19(REAL)
((h | ].x0,f.[) ") | (h .: ].x0,f.[) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
((h | ].x0,f.[) ") | (rng (h | ].x0,f.[)) is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom (((h | ].x0,f.[) ") | (rng (h | ].x0,f.[))) is V72() V73() V74() Element of K19(REAL)
NAT --> (((h | ].x0,f.[) ") . fp) is V1() V4( REAL ) V4( NAT ) V5( REAL ) Function-like constant non empty total T-Sequence-like complex-valued ext-real-valued real-valued non-decreasing non-increasing V79() Element of K19(K20(REAL,REAL))
h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
h " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng c is V72() V73() V74() Element of K19(REAL)
h + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (h + c) is V72() V73() V74() Element of K19(REAL)
((h | ].x0,f.[) ") /* (h + c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h | ].x0,f.[) ") /* c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (((h | ].x0,f.[) ") /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (((h | ].x0,f.[) ") /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h | ].x0,f.[) ") /* (h + c)) + (- (((h | ].x0,f.[) ") /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h ") (#) ((((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((h ") (#) ((((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c))) is V22() real ext-real Element of REAL
lim (h + c) is V22() real ext-real Element of REAL
a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
a is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h + c) . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
b is V22() real ext-real Element of REAL
(h | ].x0,f.[) . b is V22() real ext-real Element of REAL
b - n is V22() real ext-real Element of REAL
n is V22() real ext-real Element of REAL
r1 is V22() real ext-real set
r2 is V22() real ext-real set
r2 + n is V22() real ext-real set
h . (r2 + n) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h | ].x0,f.[) . n) is V22() real ext-real Element of REAL
r2 + n is V22() real ext-real Element of REAL
h . (r2 + n) is V22() real ext-real Element of REAL
(dom h) /\ ].x0,f.[ is V72() V73() V74() Element of K19(REAL)
b is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h + c) . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
b . b is V22() real ext-real Element of REAL
(a . b) + (b . b) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") /* (h + c)) - a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- a is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) a is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((h | ].x0,f.[) ") /* (h + c)) + (- a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((h | ].x0,f.[) ") /* (h + c)) - a) . b is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") /* (h + c)) . b is V22() real ext-real Element of REAL
((((h | ].x0,f.[) ") /* (h + c)) . b) - (a . b) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h + c) . b) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . ((h + c) . b)) - (a . b) is V22() real ext-real Element of REAL
h . ((a . b) + (b . b)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . (h . ((a . b) + (b . b))) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . (h . ((a . b) + (b . b)))) - (a . b) is V22() real ext-real Element of REAL
(h | ].x0,f.[) . ((a . b) + (b . b)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h | ].x0,f.[) . ((a . b) + (b . b))) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . ((h | ].x0,f.[) . ((a . b) + (b . b)))) - (a . b) is V22() real ext-real Element of REAL
((a . b) + (b . b)) - (a . b) is V22() real ext-real Element of REAL
lim a is V22() real ext-real Element of REAL
a . 0 is V22() real ext-real Element of REAL
lim (((h | ].x0,f.[) ") /* (h + c)) is V22() real ext-real Element of REAL
lim ((((h | ].x0,f.[) ") /* (h + c)) - a) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . fp) - (((h | ].x0,f.[) ") . fp) is V22() real ext-real Element of REAL
lim b is V22() real ext-real Element of REAL
b + a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (b + a) is V72() V73() V74() Element of K19(REAL)
b is set
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(b + a) . n is V22() real ext-real Element of REAL
(h + c) . n is V22() real ext-real Element of REAL
a . n is V22() real ext-real Element of REAL
b . n is V22() real ext-real Element of REAL
(a . n) + (b . n) is V22() real ext-real Element of REAL
(dom h) /\ ].x0,f.[ is V72() V73() V74() Element of K19(REAL)
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . b is V22() real ext-real Element of REAL
b is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
b . b is V22() real ext-real Element of REAL
a . b is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h | ].x0,f.[) . n) is V22() real ext-real Element of REAL
(a . b) + (b . b) is V22() real ext-real Element of REAL
h . ((a . b) + (b . b)) is V22() real ext-real Element of REAL
(h + c) . b is V22() real ext-real Element of REAL
h . b is V22() real ext-real Element of REAL
c . b is V22() real ext-real Element of REAL
(h . b) + (c . b) is V22() real ext-real Element of REAL
(h . b) + ((h | ].x0,f.[) . n) is V22() real ext-real Element of REAL
b is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
b " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng a is V72() V73() V74() Element of K19(REAL)
{(((h | ].x0,f.[) ") . fp)} is V72() V73() V74() set
n is set
r1 is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
a . r1 is V22() real ext-real Element of REAL
n is set
n is set
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
c . n is V22() real ext-real Element of REAL
h /* a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* a) . n is V22() real ext-real Element of REAL
a . n is V22() real ext-real Element of REAL
h . (a . n) is V22() real ext-real Element of REAL
h . (((h | ].x0,f.[) ") . fp) is V22() real ext-real Element of REAL
(h | ].x0,f.[) . (((h | ].x0,f.[) ") . fp) is V22() real ext-real Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h + c) . n is V22() real ext-real Element of REAL
a . n is V22() real ext-real Element of REAL
b . n is V22() real ext-real Element of REAL
(a . n) + (b . n) is V22() real ext-real Element of REAL
h . ((a . n) + (b . n)) is V22() real ext-real Element of REAL
h . n is V22() real ext-real Element of REAL
c . n is V22() real ext-real Element of REAL
(h . n) + (c . n) is V22() real ext-real Element of REAL
(b . n) + (a . n) is V22() real ext-real Element of REAL
h . ((b . n) + (a . n)) is V22() real ext-real Element of REAL
(h /* a) . n is V22() real ext-real Element of REAL
(h . ((b . n) + (a . n))) - ((h /* a) . n) is V22() real ext-real Element of REAL
b + a is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(b + a) . n is V22() real ext-real Element of REAL
h . ((b + a) . n) is V22() real ext-real Element of REAL
(h . ((b + a) . n)) - ((h /* a) . n) is V22() real ext-real Element of REAL
h /* (b + a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h /* (b + a)) . n is V22() real ext-real Element of REAL
((h /* (b + a)) . n) - ((h /* a) . n) is V22() real ext-real Element of REAL
(h /* (b + a)) - (h /* a) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (h /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h /* a) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h /* (b + a)) + (- (h /* a)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((h /* (b + a)) - (h /* a)) . n is V22() real ext-real Element of REAL
(b ") (#) ((h /* (b + a)) - (h /* a)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is set
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(h + c) . n is V22() real ext-real Element of REAL
a . n is V22() real ext-real Element of REAL
b . n is V22() real ext-real Element of REAL
(a . n) + (b . n) is V22() real ext-real Element of REAL
c . n is V22() real ext-real Element of REAL
((h ") (#) ((((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c))) . n is V22() real ext-real Element of REAL
(h ") . n is V22() real ext-real Element of REAL
((((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c)) . n is V22() real ext-real Element of REAL
((h ") . n) * (((((h | ].x0,f.[) ") /* (h + c)) - (((h | ].x0,f.[) ") /* c)) . n) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") /* (h + c)) . n is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") /* c) . n is V22() real ext-real Element of REAL
((((h | ].x0,f.[) ") /* (h + c)) . n) - ((((h | ].x0,f.[) ") /* c) . n) is V22() real ext-real Element of REAL
((h ") . n) * (((((h | ].x0,f.[) ") /* (h + c)) . n) - ((((h | ].x0,f.[) ") /* c) . n)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h + c) . n) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . ((h + c) . n)) - ((((h | ].x0,f.[) ") /* c) . n) is V22() real ext-real Element of REAL
((h ") . n) * ((((h | ].x0,f.[) ") . ((h + c) . n)) - ((((h | ].x0,f.[) ") /* c) . n)) is V22() real ext-real Element of REAL
h . ((a . n) + (b . n)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . (h . ((a . n) + (b . n))) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . (h . ((a . n) + (b . n)))) - ((((h | ].x0,f.[) ") /* c) . n) is V22() real ext-real Element of REAL
((h ") . n) * ((((h | ].x0,f.[) ") . (h . ((a . n) + (b . n)))) - ((((h | ].x0,f.[) ") /* c) . n)) is V22() real ext-real Element of REAL
(h | ].x0,f.[) . ((a . n) + (b . n)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . ((h | ].x0,f.[) . ((a . n) + (b . n))) is V22() real ext-real Element of REAL
(((h | ].x0,f.[) ") . ((h | ].x0,f.[) . ((a . n) + (b . n)))) - ((((h | ].x0,f.[) ") /* c) . n) is V22() real ext-real Element of REAL
((h ") . n) * ((((h | ].x0,f.[) ") . ((h | ].x0,f.[) . ((a . n) + (b . n)))) - ((((h | ].x0,f.[) ") /* c) . n)) is V22() real ext-real Element of REAL
((a . n) + (b . n)) - ((((h | ].x0,f.[) ") /* c) . n) is V22() real ext-real Element of REAL
((h ") . n) * (((a . n) + (b . n)) - ((((h | ].x0,f.[) ") /* c) . n)) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . (c . n) is V22() real ext-real Element of REAL
((a . n) + (b . n)) - (((h | ].x0,f.[) ") . (c . n)) is V22() real ext-real Element of REAL
((h ") . n) * (((a . n) + (b . n)) - (((h | ].x0,f.[) ") . (c . n))) is V22() real ext-real Element of REAL
((a . n) + (b . n)) - (a . n) is V22() real ext-real Element of REAL
((h ") . n) * (((a . n) + (b . n)) - (a . n)) is V22() real ext-real Element of REAL
(b ") " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h ") (#) ((b ") ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h ") (#) ((b ") ")) . n is V22() real ext-real Element of REAL
((b ") (#) ((h /* (b + a)) - (h /* a))) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(((b ") (#) ((h /* (b + a)) - (h /* a))) ") . n is V22() real ext-real Element of REAL
lim ((b ") (#) ((h /* (b + a)) - (h /* a))) is V22() real ext-real Element of REAL
(diff (h,(((h | ].x0,f.[) ") . fp))) " is V22() real ext-real Element of REAL
a is open V72() V73() V74() Neighbourhood of fp
fp is V22() real ext-real Element of REAL
fp is V22() real ext-real Element of REAL
diff (((h | ].x0,f.[) "),fp) is V22() real ext-real Element of REAL
((h | ].x0,f.[) ") . fp is V22() real ext-real Element of REAL
diff (h,(((h | ].x0,f.[) ") . fp)) is V22() real ext-real Element of REAL
1 / (diff (h,(((h | ].x0,f.[) ") . fp))) is V22() real ext-real Element of REAL
x0 is V22() real ext-real Element of REAL
{x0} is V72() V73() V74() set
f is V1() V4( REAL ) V5( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K19(K20(REAL,REAL))
dom f is V72() V73() V74() Element of K19(REAL)
diff (f,x0) is V22() real ext-real Element of REAL
h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K19(K20(NAT,REAL))
- h is V1() non-empty V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued convergent Element of K19(K20(NAT,REAL))
(- 1) (#) h is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
2 (#) h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 (#) h) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c is V1() V4( NAT ) V5( REAL ) Function-like constant non empty total quasi_total complex-valued ext-real-valued real-valued non-decreasing non-increasing convergent Element of K19(K20(NAT,REAL))
rng c is V72() V73() V74() Element of K19(REAL)
h + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng (h + c) is V72() V73() V74() Element of K19(REAL)
(- h) + c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
rng ((- h) + c) is V72() V73() V74() Element of K19(REAL)
c + h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (c + h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c - h is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- h is V1() non-empty V4( NAT ) Function-like total complex-valued ext-real-valued real-valued convergent set
c + (- h) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
f /* (c - h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + h)) - (f /* (c - h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* (c - h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* (c - h)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + h)) + (- (f /* (c - h))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((2 (#) h) ") (#) ((f /* (c + h)) - (f /* (c - h))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim (((2 (#) h) ") (#) ((f /* (c + h)) - (f /* (c - h)))) is V22() real ext-real Element of REAL
(- h) " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* ((- h) + c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* c is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* ((- h) + c)) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f /* c) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* ((- h) + c)) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((- h) ") (#) ((f /* ((- h) + c)) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim (- h) is V22() real ext-real Element of REAL
lim h is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
- (lim h) is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V22() real ext-real non positive non negative V72() V73() V74() V75() V76() V77() V78() Element of REAL
lim (((- h) ") (#) ((f /* ((- h) + c)) - (f /* c))) is V22() real ext-real Element of REAL
h " is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (h + c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h + c)) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (h + c)) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h ") (#) ((f /* (h + c)) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h ") (#) ((f /* (h + c)) - (f /* c))) + (((- h) ") (#) ((f /* ((- h) + c)) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* c) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* c) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((f /* (c + h)) - (f /* (c - h))) + ((f /* c) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
n is epsilon-transitive epsilon-connected ordinal natural V22() real ext-real non negative V72() V73() V74() V75() V76() V77() V94() V95() Element of NAT
(((f /* (c + h)) - (f /* (c - h))) + ((f /* c) - (f /* c))) . n is V22() real ext-real Element of REAL
((f /* (c + h)) - (f /* (c - h))) . n is V22() real ext-real Element of REAL
((f /* c) - (f /* c)) . n is V22() real ext-real Element of REAL
(((f /* (c + h)) - (f /* (c - h))) . n) + (((f /* c) - (f /* c)) . n) is V22() real ext-real Element of REAL
(f /* c) . n is V22() real ext-real Element of REAL
((f /* c) . n) - ((f /* c) . n) is V22() real ext-real Element of REAL
(((f /* (c + h)) - (f /* (c - h))) . n) + (((f /* c) . n) - ((f /* c) . n)) is V22() real ext-real Element of REAL
2 " is non empty V22() real ext-real positive non negative Element of REAL
(2 ") (#) (((h ") (#) ((f /* (h + c)) - (f /* c))) + (((- h) ") (#) ((f /* ((- h) + c)) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + h)) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + h)) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(h ") (#) ((f /* (c + h)) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(- 1) (#) (h ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
c + (- h) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
f /* (c + (- h)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + (- h))) - (f /* c) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + (- h))) + (- (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((- 1) (#) (h ")) (#) ((f /* (c + (- h))) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h ") (#) ((f /* (c + h)) - (f /* c))) + (((- 1) (#) (h ")) (#) ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 ") (#) (((h ") (#) ((f /* (c + h)) - (f /* c))) + (((- 1) (#) (h ")) (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h ") (#) ((f /* (c + (- h))) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(- 1) (#) ((h ") (#) ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h ") (#) ((f /* (c + h)) - (f /* c))) + ((- 1) (#) ((h ") (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 ") (#) (((h ") (#) ((f /* (c + h)) - (f /* c))) + ((- 1) (#) ((h ") (#) ((f /* (c + (- h))) - (f /* c))))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(- 1) (#) ((f /* (c + (- h))) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h ") (#) ((- 1) (#) ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((h ") (#) ((f /* (c + h)) - (f /* c))) + ((h ") (#) ((- 1) (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 ") (#) (((h ") (#) ((f /* (c + h)) - (f /* c))) + ((h ") (#) ((- 1) (#) ((f /* (c + (- h))) - (f /* c))))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((f /* (c + h)) - (f /* c)) + ((- 1) (#) ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(h ") (#) (((f /* (c + h)) - (f /* c)) + ((- 1) (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 ") (#) ((h ") (#) (((f /* (c + h)) - (f /* c)) + ((- 1) (#) ((f /* (c + (- h))) - (f /* c))))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(2 ") (#) (h ") is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((2 ") (#) (h ")) (#) (((f /* (c + h)) - (f /* c)) + ((- 1) (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((2 (#) h) ") (#) (((f /* (c + h)) - (f /* c)) + ((- 1) (#) ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* (c + (- h))) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(- 1) (#) ((f /* (c + (- h))) - (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* c) - (- ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- (- ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (- ((f /* (c + (- h))) - (f /* c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* c) + (- (- ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + h)) - ((f /* c) - (- ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* c) - (- ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* c) - (- ((f /* (c + (- h))) - (f /* c)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + h)) + (- ((f /* c) - (- ((f /* (c + (- h))) - (f /* c))))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((2 (#) h) ") (#) ((f /* (c + h)) - ((f /* c) - (- ((f /* (c + (- h))) - (f /* c))))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
(f /* (c + (- h))) - ((f /* c) - (f /* c)) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* c) - (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* c) - (f /* c)) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + (- h))) + (- ((f /* c) - (f /* c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + h)) - ((f /* (c + (- h))) - ((f /* c) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
- ((f /* (c + (- h))) - ((f /* c) - (f /* c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) ((f /* (c + (- h))) - ((f /* c) - (f /* c))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f /* (c + h)) + (- ((f /* (c + (- h))) - ((f /* c) - (f /* c)))) is V1() V4( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((2 (#) h) ") (#) ((f /* (c + h)) - ((f /* (c + (- h))) - ((f /* c) - (f /* c)))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
((2 (#) h) ") (#) (((f /* (c + h)) - (f /* (c - h))) + ((f /* c) - (f /* c))) is V1() V4( NAT ) V5( REAL ) Function-like non empty total quasi_total complex-valued ext-real-valued real-valued Element of K19(K20(NAT,REAL))
lim ((h ") (#) ((f /* (h + c)) - (f /* c))) is V22() real ext-real Element of REAL
lim (((h ") (#) ((f /* (h + c)) - (f /* c))) + (((- h) ") (#) ((f /* ((- h) + c)) - (f /* c)))) is V22() real ext-real Element of REAL
1 * (diff (f,x0)) is V22() real ext-real Element of REAL
(1 * (diff (f,x0))) + (diff (f,x0)) is V22() real ext-real Element of REAL
2 * (diff (f,x0)) is V22() real ext-real Element of REAL
lim ((2 ") (#) (((h ") (#) ((f /* (h + c)) - (f /* c))) + (((- h) ") (#) ((f /* ((- h) + c)) - (f /* c))))) is V22() real ext-real Element of REAL
(2 ") * (2 * (diff (f,x0))) is V22() real ext-real Element of REAL