:: FIB_NUM4 semantic presentation

REAL is set
NAT is non empty epsilon-transitive epsilon-connected ordinal Element of bool REAL
bool REAL is set
COMPLEX is set
omega is non empty epsilon-transitive epsilon-connected ordinal set
bool omega is set
bool NAT is set
[:NAT,REAL:] is set
bool [:NAT,REAL:] is set
K99(REAL,REAL,NAT,NAT) is Element of bool [:REAL,REAL:]
[:REAL,REAL:] is set
bool [:REAL,REAL:] is set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
the empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative integer set is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative integer set
Fib 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
sqrt 0 is V11() real ext-real Element of REAL
sqrt 1 is V11() real ext-real Element of REAL
4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
sqrt 4 is V11() real ext-real Element of REAL
tau is non empty V11() real ext-real positive non negative set
5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
sqrt 5 is V11() real ext-real Element of REAL
1 + (sqrt 5) is V11() real ext-real set
(1 + (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
tau_bar is non empty V11() real ext-real non positive negative set
1 - (sqrt 5) is V11() real ext-real set
(1 - (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
Lucas 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
Lucas 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
Lucas 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
Lucas 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
Lucas 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
7 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
- 1 is non empty V11() real ext-real non positive negative integer set
Fib 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib 4 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
- s5 is V11() real ext-real non positive integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
s5 * ((- 1) to_power n) is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
- s5 is V11() real ext-real non positive integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
s5 * ((- 1) to_power n) is V11() real ext-real set
- (s5 * ((- 1) to_power n)) is V11() real ext-real set
s5 is V11() real ext-real set
n is V11() real ext-real set
s5 / n is V11() real ext-real Element of COMPLEX
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(s5 / n) to_power k is V11() real ext-real set
(s5 / n) |^ k is V11() real ext-real set
s5 to_power k is V11() real ext-real set
s5 |^ k is V11() real ext-real set
n to_power k is V11() real ext-real set
n |^ k is V11() real ext-real set
(s5 to_power k) / (n to_power k) is V11() real ext-real Element of COMPLEX
1 / n is V11() real ext-real Element of COMPLEX
s5 * (1 / n) is V11() real ext-real set
(s5 * (1 / n)) |^ k is V11() real ext-real set
(1 / n) |^ k is V11() real ext-real set
(s5 to_power k) * ((1 / n) |^ k) is V11() real ext-real set
1 / (n |^ k) is V11() real ext-real Element of COMPLEX
(s5 to_power k) * (1 / (n |^ k)) is V11() real ext-real set
(s5 to_power k) / (n |^ k) is V11() real ext-real Element of COMPLEX
s5 is V11() real ext-real set
n is V11() real ext-real integer set
k is V11() real ext-real integer set
n + k is V11() real ext-real integer set
s5 to_power (n + k) is V11() real ext-real set
s5 to_power n is V11() real ext-real set
s5 to_power k is V11() real ext-real set
(s5 to_power n) * (s5 to_power k) is V11() real ext-real set
s5 #Z n is V11() real ext-real set
(s5 #Z n) * (s5 to_power k) is V11() real ext-real set
s5 #Z k is V11() real ext-real set
(s5 #Z n) * (s5 #Z k) is V11() real ext-real set
s5 #Z (n + k) is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is V11() real ext-real set
- n is V11() real ext-real set
(- n) to_power s5 is V11() real ext-real set
(- n) |^ s5 is V11() real ext-real set
n to_power s5 is V11() real ext-real set
n |^ s5 is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is V11() real ext-real set
- n is V11() real ext-real set
(- n) to_power s5 is V11() real ext-real set
(- n) |^ s5 is V11() real ext-real set
n to_power s5 is V11() real ext-real set
n |^ s5 is V11() real ext-real set
- (n to_power s5) is V11() real ext-real set
tau * tau_bar is non empty V11() real ext-real non positive negative set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
(1 ^2) - ((sqrt 5) ^2) is V11() real ext-real set
((1 ^2) - ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
1 - 5 is V11() real ext-real integer set
(1 - 5) / 4 is V11() real ext-real Element of COMPLEX
tau_bar / tau is non empty V11() real ext-real non positive negative Element of COMPLEX
(sqrt 5) - 3 is V11() real ext-real set
((sqrt 5) - 3) / 2 is V11() real ext-real Element of COMPLEX
- (sqrt 5) is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
(- (sqrt 5)) + 1 is V11() real ext-real set
(1 - (sqrt 5)) * 2 is V11() real ext-real set
(1 + (sqrt 5)) * 2 is V11() real ext-real set
((1 - (sqrt 5)) * 2) / ((1 + (sqrt 5)) * 2) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) / (1 + (sqrt 5)) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) * (1 - (sqrt 5)) is V11() real ext-real set
(1 + (sqrt 5)) * (1 - (sqrt 5)) is V11() real ext-real set
((1 - (sqrt 5)) * (1 - (sqrt 5))) / ((1 + (sqrt 5)) * (1 - (sqrt 5))) is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 - (2 * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
(1 - (2 * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(1 ^2) - ((sqrt 5) ^2) is V11() real ext-real set
((1 - (2 * (sqrt 5))) + ((sqrt 5) ^2)) / ((1 ^2) - ((sqrt 5) ^2)) is V11() real ext-real Element of COMPLEX
(1 - (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 - (2 * (sqrt 5))) + 5) / ((1 ^2) - ((sqrt 5) ^2)) is V11() real ext-real Element of COMPLEX
6 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
6 - (2 * (sqrt 5)) is V11() real ext-real set
(1 ^2) - 5 is V11() real ext-real integer set
(6 - (2 * (sqrt 5))) / ((1 ^2) - 5) is V11() real ext-real Element of COMPLEX
3 - (sqrt 5) is V11() real ext-real set
2 * (3 - (sqrt 5)) is V11() real ext-real set
- 2 is non empty V11() real ext-real non positive negative integer set
(- 2) * 2 is non empty V11() real ext-real non positive negative integer even set
(2 * (3 - (sqrt 5))) / ((- 2) * 2) is V11() real ext-real Element of COMPLEX
tau / tau_bar is non empty V11() real ext-real non positive negative Element of COMPLEX
- 3 is non empty V11() real ext-real non positive negative integer set
(- 3) - (sqrt 5) is V11() real ext-real set
((- 3) - (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(1 + (sqrt 5)) * 2 is V11() real ext-real set
(1 - (sqrt 5)) * 2 is V11() real ext-real set
((1 + (sqrt 5)) * 2) / ((1 - (sqrt 5)) * 2) is V11() real ext-real Element of COMPLEX
(1 + (sqrt 5)) / (1 - (sqrt 5)) is V11() real ext-real Element of COMPLEX
(1 + (sqrt 5)) * (1 + (sqrt 5)) is V11() real ext-real set
(1 - (sqrt 5)) * (1 + (sqrt 5)) is V11() real ext-real set
((1 + (sqrt 5)) * (1 + (sqrt 5))) / ((1 - (sqrt 5)) * (1 + (sqrt 5))) is V11() real ext-real Element of COMPLEX
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
1 - ((sqrt 5) ^2) is V11() real ext-real set
((1 + (sqrt 5)) * (1 + (sqrt 5))) / (1 - ((sqrt 5) ^2)) is V11() real ext-real Element of COMPLEX
1 - 5 is V11() real ext-real integer set
((1 + (sqrt 5)) * (1 + (sqrt 5))) / (1 - 5) is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 + (2 * (sqrt 5)) is V11() real ext-real set
(1 + (2 * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
- 4 is non empty V11() real ext-real non positive negative integer set
((1 + (2 * (sqrt 5))) + ((sqrt 5) ^2)) / (- 4) is V11() real ext-real Element of COMPLEX
(1 + (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 + (2 * (sqrt 5))) + 5) / (- 4) is V11() real ext-real Element of COMPLEX
tau to_power 2 is V11() real ext-real set
tau |^ 2 is V11() real ext-real set
3 + (sqrt 5) is V11() real ext-real set
(3 + (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) / 2) ^2 is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) / 2) * ((1 + (sqrt 5)) / 2) is V11() real ext-real set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * 1) * (sqrt 5) is V11() real ext-real set
(1 ^2) + ((2 * 1) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
((1 ^2) + ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
(((1 ^2) + ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 + (2 * (sqrt 5)) is V11() real ext-real set
(1 + (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 + (2 * (sqrt 5))) + 5) / 4 is V11() real ext-real Element of COMPLEX
2 * (3 + (sqrt 5)) is V11() real ext-real set
2 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * (3 + (sqrt 5))) / (2 * 2) is V11() real ext-real Element of COMPLEX
tau_bar to_power 2 is V11() real ext-real set
tau_bar |^ 2 is V11() real ext-real set
3 - (sqrt 5) is V11() real ext-real set
(3 - (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / 2) ^2 is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / 2) * ((1 - (sqrt 5)) / 2) is V11() real ext-real set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * 1) * (sqrt 5) is V11() real ext-real set
(1 ^2) - ((2 * 1) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
(((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 - (2 * (sqrt 5)) is V11() real ext-real set
(1 - (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 - (2 * (sqrt 5))) + 5) / 4 is V11() real ext-real Element of COMPLEX
2 * (3 - (sqrt 5)) is V11() real ext-real set
2 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * (3 - (sqrt 5))) / (2 * 2) is V11() real ext-real Element of COMPLEX
tau_bar to_power 3 is V11() real ext-real set
tau_bar |^ 3 is V11() real ext-real set
2 - (sqrt 5) is V11() real ext-real set
(sqrt 5) - (sqrt 5) is V11() real ext-real set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((1 - (sqrt 5)) / 2) to_power (2 + 1) is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ (2 + 1) is V11() real ext-real set
((1 - (sqrt 5)) / 2) to_power 2 is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ 2 is V11() real ext-real set
((1 - (sqrt 5)) / 2) to_power 1 is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ 1 is V11() real ext-real set
(((1 - (sqrt 5)) / 2) to_power 2) * (((1 - (sqrt 5)) / 2) to_power 1) is V11() real ext-real set
(((1 - (sqrt 5)) / 2) to_power 2) * ((1 - (sqrt 5)) / 2) is V11() real ext-real set
((1 - (sqrt 5)) / 2) ^2 is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / 2) * ((1 - (sqrt 5)) / 2) is V11() real ext-real set
(((1 - (sqrt 5)) / 2) ^2) * ((1 - (sqrt 5)) / 2) is V11() real ext-real Element of COMPLEX
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * 1) * (sqrt 5) is V11() real ext-real set
1 - ((2 * 1) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
(1 - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
((1 - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) * (1 - (sqrt 5)) is V11() real ext-real set
8 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
(((1 - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) * (1 - (sqrt 5))) / 8 is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 - (2 * (sqrt 5)) is V11() real ext-real set
(1 - (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 - (2 * (sqrt 5))) + 5) * (1 - (sqrt 5)) is V11() real ext-real set
(((1 - (2 * (sqrt 5))) + 5) * (1 - (sqrt 5))) / 8 is V11() real ext-real Element of COMPLEX
6 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
8 * (sqrt 5) is V11() real ext-real set
6 - (8 * (sqrt 5)) is V11() real ext-real set
2 * ((sqrt 5) ^2) is V11() real ext-real set
(6 - (8 * (sqrt 5))) + (2 * ((sqrt 5) ^2)) is V11() real ext-real set
((6 - (8 * (sqrt 5))) + (2 * ((sqrt 5) ^2))) / 8 is V11() real ext-real Element of COMPLEX
2 * 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(6 - (8 * (sqrt 5))) + (2 * 5) is V11() real ext-real set
((6 - (8 * (sqrt 5))) + (2 * 5)) / 8 is V11() real ext-real Element of COMPLEX
6 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
tau_bar to_power 6 is V11() real ext-real set
tau_bar |^ 6 is V11() real ext-real set
9 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
4 * (sqrt 5) is V11() real ext-real set
9 - (4 * (sqrt 5)) is V11() real ext-real set
3 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
tau_bar to_power (3 * 2) is V11() real ext-real set
tau_bar |^ (3 * 2) is V11() real ext-real set
(2 - (sqrt 5)) to_power 2 is V11() real ext-real set
(2 - (sqrt 5)) |^ 2 is V11() real ext-real set
(2 - (sqrt 5)) ^2 is V11() real ext-real set
(2 - (sqrt 5)) * (2 - (sqrt 5)) is V11() real ext-real set
2 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * 2) * (sqrt 5) is V11() real ext-real set
(2 ^2) - ((2 * 2) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
((2 ^2) - ((2 * 2) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
4 - (4 * (sqrt 5)) is V11() real ext-real set
(4 - (4 * (sqrt 5))) + 5 is V11() real ext-real set
abs tau_bar is non empty V11() real ext-real positive non negative Element of REAL
3 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
3 * 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
sqrt (3 ^2) is V11() real ext-real set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(2 + 1) - 1 is V11() real ext-real integer set
(sqrt 5) - 1 is V11() real ext-real set
- ((sqrt 5) - 1) is V11() real ext-real set
- 2 is non empty V11() real ext-real non positive negative integer set
(- 2) / 2 is non empty V11() real ext-real non positive negative Element of COMPLEX
abs (- 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of REAL
abs 0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative integer Element of REAL
(abs (- 1)) + (abs 0) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
- (- 1) is non empty V11() real ext-real positive non negative integer set
1 + 0 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
1 / (sqrt 5) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(abs tau_bar) to_power s5 is V11() real ext-real set
(abs tau_bar) |^ s5 is V11() real ext-real set
((abs tau_bar) to_power s5) * (1 / (sqrt 5)) is V11() real ext-real set
1 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(abs tau_bar) to_power s5 is V11() real ext-real set
(abs tau_bar) |^ s5 is V11() real ext-real set
((abs tau_bar) to_power s5) * (1 / (sqrt 5)) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
1 to_power s5 is V11() real ext-real set
1 |^ s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(sqrt 5) / 1 is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / ((sqrt 5) / 1) is V11() real ext-real Element of COMPLEX
((abs tau_bar) to_power s5) / ((sqrt 5) / 1) is V11() real ext-real Element of COMPLEX
1 * (sqrt 5) is V11() real ext-real set
2 * (sqrt 5) is V11() real ext-real set
(1 * (sqrt 5)) / (2 * (sqrt 5)) is V11() real ext-real Element of COMPLEX
((abs tau_bar) to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is non empty V11() real ext-real set
n to_power s5 is V11() real ext-real set
n |^ s5 is V11() real ext-real set
- n is non empty V11() real ext-real set
(- n) to_power s5 is V11() real ext-real set
(- n) |^ s5 is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is V11() real ext-real set
n to_power s5 is V11() real ext-real set
n |^ s5 is V11() real ext-real set
- n is V11() real ext-real set
- (- n) is V11() real ext-real set
(- (- n)) to_power s5 is V11() real ext-real set
(- (- n)) |^ s5 is V11() real ext-real set
(- n) to_power s5 is V11() real ext-real set
(- n) |^ s5 is V11() real ext-real set
- ((- n) to_power s5) is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(abs tau_bar) to_power 2 is V11() real ext-real Element of REAL
(abs tau_bar) |^ 2 is V11() real ext-real set
- tau_bar is non empty V11() real ext-real positive non negative set
(- tau_bar) to_power 2 is V11() real ext-real set
(- tau_bar) |^ 2 is V11() real ext-real set
(- tau_bar) ^2 is V11() real ext-real set
(- tau_bar) * (- tau_bar) is non empty V11() real ext-real positive non negative set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * 1) * (sqrt 5) is V11() real ext-real set
(1 ^2) - ((2 * 1) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
(((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
2 * (sqrt 5) is V11() real ext-real set
1 - (2 * (sqrt 5)) is V11() real ext-real set
(1 - (2 * (sqrt 5))) + 5 is V11() real ext-real set
((1 - (2 * (sqrt 5))) + 5) / 4 is V11() real ext-real Element of COMPLEX
- 2 is non empty V11() real ext-real non positive negative integer set
- (sqrt 5) is V11() real ext-real set
(- 2) + 3 is V11() real ext-real integer set
(- (sqrt 5)) + 3 is V11() real ext-real set
(abs tau_bar) to_power 2 is V11() real ext-real set
n is non trivial epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(abs tau_bar) to_power n is V11() real ext-real set
(abs tau_bar) |^ n is V11() real ext-real set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(abs tau_bar) to_power (n + 1) is V11() real ext-real set
(abs tau_bar) |^ (n + 1) is V11() real ext-real set
(1 / 2) * (abs tau_bar) is non empty V11() real ext-real positive non negative set
((abs tau_bar) to_power n) * (abs tau_bar) is V11() real ext-real set
(abs tau_bar) to_power 1 is V11() real ext-real Element of REAL
(abs tau_bar) |^ 1 is V11() real ext-real set
((abs tau_bar) to_power n) * ((abs tau_bar) to_power 1) is V11() real ext-real set
(1 / 2) * 1 is non empty V11() real ext-real positive non negative set
n is non trivial epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(abs tau_bar) to_power n is V11() real ext-real set
(abs tau_bar) |^ n is V11() real ext-real set
abs (tau_bar to_power n) is V11() real ext-real non negative Element of REAL
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k is V11() real ext-real set
k to_power n is V11() real ext-real set
k |^ n is V11() real ext-real set
k to_power s5 is V11() real ext-real set
k |^ s5 is V11() real ext-real set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
s5 - n is V11() real ext-real integer set
(k to_power s5) - (k to_power n) is V11() real ext-real set
tb is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tb + n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k to_power (tb + n) is V11() real ext-real set
k |^ (tb + n) is V11() real ext-real set
(k to_power (tb + n)) - (k to_power n) is V11() real ext-real set
k to_power tb is V11() real ext-real set
k |^ tb is V11() real ext-real set
(k to_power tb) * (k to_power n) is V11() real ext-real set
1 * (k to_power n) is V11() real ext-real set
((k to_power tb) * (k to_power n)) - (1 * (k to_power n)) is V11() real ext-real set
(k to_power tb) - 1 is V11() real ext-real set
((k to_power tb) - 1) * (k to_power n) is V11() real ext-real set
abs k is V11() real ext-real non negative Element of REAL
abs 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of REAL
1 to_power tb is V11() real ext-real set
1 |^ tb is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(abs k) to_power tb is V11() real ext-real set
(abs k) |^ tb is V11() real ext-real set
abs (k to_power tb) is V11() real ext-real non negative Element of REAL
1 - 1 is V11() real ext-real integer set
0 + (k to_power n) is V11() real ext-real set
((k to_power s5) - (k to_power n)) + (k to_power n) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
s5 - n is V11() real ext-real integer set
(tau_bar to_power s5) - (tau_bar to_power n) is V11() real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k + n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + n) is V11() real ext-real set
tau_bar |^ (k + n) is V11() real ext-real set
(tau_bar to_power (k + n)) - (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power k is V11() real ext-real set
tau_bar |^ k is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power n) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power k) * (tau_bar to_power n)) - (1 * (tau_bar to_power n)) is V11() real ext-real set
(tau_bar to_power k) - 1 is V11() real ext-real set
((tau_bar to_power k) - 1) * (tau_bar to_power n) is V11() real ext-real set
1 to_power k is V11() real ext-real set
1 |^ k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(abs tau_bar) to_power k is V11() real ext-real set
(abs tau_bar) |^ k is V11() real ext-real set
abs (tau_bar to_power k) is V11() real ext-real non negative Element of REAL
1 - 1 is V11() real ext-real integer set
0 + (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power s5) - (tau_bar to_power n)) + (tau_bar to_power n) is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
s5 - n is V11() real ext-real integer set
(tau_bar to_power s5) - (tau_bar to_power n) is V11() real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k + n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + n) is V11() real ext-real set
tau_bar |^ (k + n) is V11() real ext-real set
(tau_bar to_power (k + n)) - (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power k is V11() real ext-real set
tau_bar |^ k is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power n) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power k) * (tau_bar to_power n)) - (1 * (tau_bar to_power n)) is V11() real ext-real set
(tau_bar to_power k) - 1 is V11() real ext-real set
((tau_bar to_power k) - 1) * (tau_bar to_power n) is V11() real ext-real set
n - n is V11() real ext-real integer set
1 - 1 is V11() real ext-real integer set
0 + (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power s5) - (tau_bar to_power n)) + (tau_bar to_power n) is V11() real ext-real set
n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
s5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + k is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tb is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas tb is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tb + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (tb + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tb - 0 is V11() real ext-real integer set
tb is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tb + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tk is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas tk is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tk + (tb + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (tk + (tb + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tk + tb is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tn is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas (tk + tb) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(tk + tb) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas ((tk + tb) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tk is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas tk is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tk + (tb + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (tk + (tb + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tk is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas tk is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tb is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tk + tb is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (tk + tb) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau_bar ^2 is V11() real ext-real set
tau_bar * tau_bar is non empty V11() real ext-real positive non negative set
(sqrt 5) + 3 is V11() real ext-real set
- (sqrt 5) is V11() real ext-real set
(- (sqrt 5)) + 3 is V11() real ext-real set
((sqrt 5) + 3) / 2 is V11() real ext-real Element of COMPLEX
((- (sqrt 5)) + 3) / 2 is V11() real ext-real Element of COMPLEX
tau ^2 is V11() real ext-real set
tau * tau is non empty V11() real ext-real positive non negative set
3 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
3 * 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
sqrt (3 ^2) is V11() real ext-real set
3 - 3 is V11() real ext-real integer set
s5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau to_power s5 is V11() real ext-real set
tau |^ s5 is V11() real ext-real set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
s5 - 0 is V11() real ext-real integer set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(tau to_power 2) to_power k is V11() real ext-real set
(tau to_power 2) |^ k is V11() real ext-real set
(tau ^2) to_power k is V11() real ext-real set
(tau ^2) |^ k is V11() real ext-real set
(tau_bar to_power 2) to_power k is V11() real ext-real set
(tau_bar to_power 2) |^ k is V11() real ext-real set
(tau_bar ^2) to_power k is V11() real ext-real set
(tau_bar ^2) |^ k is V11() real ext-real set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * k) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer non even set
tau to_power (2 * k) is V11() real ext-real set
tau |^ (2 * k) is V11() real ext-real set
(tau / tau_bar) to_power (2 * k) is V11() real ext-real set
(tau / tau_bar) |^ (2 * k) is V11() real ext-real set
(tau / tau_bar) to_power 2 is V11() real ext-real set
(tau / tau_bar) |^ 2 is V11() real ext-real set
((tau / tau_bar) to_power 2) to_power k is V11() real ext-real set
((tau / tau_bar) to_power 2) |^ k is V11() real ext-real set
(tau / tau_bar) ^2 is V11() real ext-real Element of COMPLEX
(tau / tau_bar) * (tau / tau_bar) is non empty V11() real ext-real positive non negative set
((tau / tau_bar) ^2) to_power k is V11() real ext-real set
((tau / tau_bar) ^2) |^ k is V11() real ext-real set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
(tau_bar to_power 2) to_power k is V11() real ext-real set
(tau_bar to_power 2) |^ k is V11() real ext-real set
(tau_bar ^2) to_power k is V11() real ext-real set
(tau_bar ^2) |^ k is V11() real ext-real set
(tau_bar / tau) * (((- 3) - (sqrt 5)) / 2) is V11() real ext-real Element of COMPLEX
((tau / tau_bar) to_power (2 * k)) * (((- 3) - (sqrt 5)) / 2) is V11() real ext-real set
((tau / tau_bar) to_power (2 * k)) * (tau / tau_bar) is V11() real ext-real set
(tau to_power (2 * k)) / (tau_bar to_power (2 * k)) is V11() real ext-real Element of COMPLEX
((tau to_power (2 * k)) / (tau_bar to_power (2 * k))) * (tau / tau_bar) is V11() real ext-real Element of COMPLEX
1 / (tau_bar to_power (2 * k)) is V11() real ext-real Element of COMPLEX
(tau to_power (2 * k)) * (1 / (tau_bar to_power (2 * k))) is V11() real ext-real set
((tau to_power (2 * k)) * (1 / (tau_bar to_power (2 * k)))) * (tau / tau_bar) is V11() real ext-real set
1 * (tau_bar to_power (2 * k)) is V11() real ext-real set
(((tau to_power (2 * k)) * (1 / (tau_bar to_power (2 * k)))) * (tau / tau_bar)) * (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau to_power (2 * k)) * (tau / tau_bar) is V11() real ext-real set
(tau_bar to_power (2 * k)) * (1 / (tau_bar to_power (2 * k))) is V11() real ext-real set
((tau to_power (2 * k)) * (tau / tau_bar)) * ((tau_bar to_power (2 * k)) * (1 / (tau_bar to_power (2 * k)))) is V11() real ext-real set
(tau_bar to_power (2 * k)) / (tau_bar to_power (2 * k)) is V11() real ext-real Element of COMPLEX
((tau to_power (2 * k)) * (tau / tau_bar)) * ((tau_bar to_power (2 * k)) / (tau_bar to_power (2 * k))) is V11() real ext-real set
((tau to_power (2 * k)) * (tau / tau_bar)) * 1 is V11() real ext-real set
1 / tau_bar is non empty V11() real ext-real non positive negative Element of COMPLEX
tau * (1 / tau_bar) is non empty V11() real ext-real non positive negative set
(tau to_power (2 * k)) * (tau * (1 / tau_bar)) is V11() real ext-real set
((tau to_power (2 * k)) * (tau * (1 / tau_bar))) * 1 is V11() real ext-real set
(((tau to_power (2 * k)) * (tau * (1 / tau_bar))) * 1) * tau_bar is V11() real ext-real set
(tau_bar to_power (2 * k)) * tau_bar is V11() real ext-real set
(tau to_power (2 * k)) * tau is V11() real ext-real set
(1 / tau_bar) * 1 is non empty V11() real ext-real non positive negative set
((1 / tau_bar) * 1) * tau_bar is non empty V11() real ext-real positive non negative set
((tau to_power (2 * k)) * tau) * (((1 / tau_bar) * 1) * tau_bar) is V11() real ext-real set
tau_bar / tau_bar is non empty V11() real ext-real positive non negative Element of COMPLEX
((tau to_power (2 * k)) * tau) * (tau_bar / tau_bar) is V11() real ext-real set
((tau to_power (2 * k)) * tau) * 1 is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power (2 * k)) * (tau_bar to_power 1) is V11() real ext-real set
tau_bar to_power ((2 * k) + 1) is V11() real ext-real set
tau_bar |^ ((2 * k) + 1) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power (2 * k)) * (tau to_power 1) is V11() real ext-real set
- (1 / 2) is non empty V11() real ext-real non positive negative Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
s5 - 0 is V11() real ext-real integer set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
0 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
0 * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(tau_bar to_power n) to_power 2 is V11() real ext-real set
(tau_bar to_power n) |^ 2 is V11() real ext-real set
(tau_bar to_power n) ^2 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power n) is V11() real ext-real set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
5 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
(5 / 2) ^2 is V11() real ext-real Element of COMPLEX
(5 / 2) * (5 / 2) is non empty V11() real ext-real positive non negative set
sqrt ((5 / 2) ^2) is V11() real ext-real set
2 * (5 / 2) is non empty V11() real ext-real positive non negative set
2 * (sqrt 5) is V11() real ext-real set
- (2 * (sqrt 5)) is V11() real ext-real set
- 5 is non empty V11() real ext-real non positive negative integer set
(- (2 * (sqrt 5))) + 4 is V11() real ext-real set
(- 5) + 4 is V11() real ext-real integer set
2 * (2 - (sqrt 5)) is V11() real ext-real set
(2 * (2 - (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
(- 1) / 2 is non empty V11() real ext-real non positive negative Element of COMPLEX
- (1 / (sqrt 5)) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
2 * (sqrt 5) is V11() real ext-real set
4 - 5 is V11() real ext-real integer set
(2 * (sqrt 5)) - 5 is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
(2 * (sqrt 5)) - ((sqrt 5) ^2) is V11() real ext-real set
(- 1) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(2 - (sqrt 5)) * (sqrt 5) is V11() real ext-real set
((2 - (sqrt 5)) * (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
7 / 3 is non empty V11() real ext-real positive non negative Element of COMPLEX
(7 / 3) ^2 is V11() real ext-real Element of COMPLEX
(7 / 3) * (7 / 3) is non empty V11() real ext-real positive non negative set
sqrt ((7 / 3) ^2) is V11() real ext-real set
3 * (sqrt 5) is V11() real ext-real set
(7 / 3) * 3 is non empty V11() real ext-real positive non negative set
(3 * (sqrt 5)) - 5 is V11() real ext-real set
7 - 5 is V11() real ext-real integer set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
(3 * (sqrt 5)) - ((sqrt 5) ^2) is V11() real ext-real set
(3 * (sqrt 5)) - ((sqrt 5) * (sqrt 5)) is V11() real ext-real set
((3 * (sqrt 5)) - ((sqrt 5) * (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
((3 - (sqrt 5)) / 2) * (sqrt 5) is V11() real ext-real set
(((3 - (sqrt 5)) / 2) * (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
(tau_bar to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau_bar to_power s5) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
abs ((1 - (sqrt 5)) / 2) is V11() real ext-real non negative Element of REAL
- ((1 - (sqrt 5)) / 2) is V11() real ext-real Element of COMPLEX
(abs ((1 - (sqrt 5)) / 2)) to_power s5 is V11() real ext-real set
(abs ((1 - (sqrt 5)) / 2)) |^ s5 is V11() real ext-real set
((abs ((1 - (sqrt 5)) / 2)) to_power s5) * (1 / (sqrt 5)) is V11() real ext-real set
((1 - (sqrt 5)) / 2) to_power s5 is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ s5 is V11() real ext-real set
(((1 - (sqrt 5)) / 2) to_power s5) * (1 / (sqrt 5)) is V11() real ext-real set
((((1 - (sqrt 5)) / 2) to_power s5) * (1 / (sqrt 5))) + (1 / 2) is V11() real ext-real set
(1 / 2) + (1 / 2) is non empty V11() real ext-real positive non negative Element of COMPLEX
- (((1 - (sqrt 5)) / 2) to_power s5) is V11() real ext-real set
(- (((1 - (sqrt 5)) / 2) to_power s5)) * (1 / (sqrt 5)) is V11() real ext-real set
- ((((1 - (sqrt 5)) / 2) to_power s5) * (1 / (sqrt 5))) is V11() real ext-real set
(((1 - (sqrt 5)) / 2) to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- ((((1 - (sqrt 5)) / 2) to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
- (- ((((1 - (sqrt 5)) / 2) to_power s5) / (sqrt 5))) is V11() real ext-real Element of COMPLEX
0 + (1 / 2) is non empty V11() real ext-real positive non negative set
((((1 - (sqrt 5)) / 2) to_power s5) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
(- (1 / 2)) + (1 / 2) is V11() real ext-real Element of COMPLEX
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau to_power s5 is V11() real ext-real set
tau |^ s5 is V11() real ext-real set
(tau to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power s5) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
[\(((tau to_power s5) / (sqrt 5)) + (1 / 2))/] is V11() real ext-real integer set
Fib s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
(tau to_power s5) - (tau_bar to_power s5) is V11() real ext-real set
((tau to_power s5) - (tau_bar to_power s5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power s5) - (tau_bar to_power s5)) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
((((tau to_power s5) - (tau_bar to_power s5)) / (sqrt 5)) + (1 / 2)) - (1 / 2) is V11() real ext-real Element of COMPLEX
(tau_bar to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power s5) / (sqrt 5)) - ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(((tau to_power s5) / (sqrt 5)) - ((tau_bar to_power s5) / (sqrt 5))) + (1 / 2) is V11() real ext-real Element of COMPLEX
((((tau to_power s5) / (sqrt 5)) - ((tau_bar to_power s5) / (sqrt 5))) + (1 / 2)) - (1 / 2) is V11() real ext-real Element of COMPLEX
((tau_bar to_power s5) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
(((tau to_power s5) / (sqrt 5)) + (1 / 2)) - (((tau_bar to_power s5) / (sqrt 5)) + (1 / 2)) is V11() real ext-real Element of COMPLEX
(((tau_bar to_power s5) / (sqrt 5)) + (1 / 2)) + (Fib s5) is V11() real ext-real set
0 + (Fib s5) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
1 - (1 / 2) is V11() real ext-real set
(((tau_bar to_power s5) / (sqrt 5)) + (1 / 2)) - (1 / 2) is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power s5) / (sqrt 5))) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- (1 / 2)) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(((tau to_power s5) / (sqrt 5)) + (1 / 2)) - 1 is V11() real ext-real set
s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau to_power s5 is V11() real ext-real set
tau |^ s5 is V11() real ext-real set
(tau to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power s5) / (sqrt 5)) - (1 / 2) is V11() real ext-real Element of COMPLEX
[/(((tau to_power s5) / (sqrt 5)) - (1 / 2))\] is V11() real ext-real integer set
Fib s5 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau_bar to_power s5 is V11() real ext-real set
tau_bar |^ s5 is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
(tau_bar to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- (1 / 2)) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power s5) / (sqrt 5))) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power s5) / (sqrt 5)) - ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau to_power s5) - (tau_bar to_power s5) is V11() real ext-real set
((tau to_power s5) - (tau_bar to_power s5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power s5) / (sqrt 5)) - (1 / 2)) + 1 is V11() real ext-real set
s5 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau / (sqrt 5)) - (1 / 2) is V11() real ext-real Element of COMPLEX
((tau / (sqrt 5)) - (1 / 2)) + 1 is V11() real ext-real set
((1 + (sqrt 5)) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
1 - (1 / 2) is V11() real ext-real set
(((1 + (sqrt 5)) / 2) / (sqrt 5)) + (1 - (1 / 2)) is V11() real ext-real set
(1 + (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(((1 + (sqrt 5)) / (sqrt 5)) / 2) + (1 / 2) is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) / (sqrt 5)) + 1 is V11() real ext-real set
(((1 + (sqrt 5)) / (sqrt 5)) + 1) / 2 is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(1 / (sqrt 5)) + ((sqrt 5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((1 / (sqrt 5)) + ((sqrt 5) / (sqrt 5))) + 1 is V11() real ext-real set
(((1 / (sqrt 5)) + ((sqrt 5) / (sqrt 5))) + 1) / 2 is V11() real ext-real Element of COMPLEX
(1 / (sqrt 5)) + 1 is V11() real ext-real set
((1 / (sqrt 5)) + 1) + 1 is V11() real ext-real set
(((1 / (sqrt 5)) + 1) + 1) / 2 is V11() real ext-real Element of COMPLEX
(1 / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
((1 / (sqrt 5)) / 2) + (2 / 2) is V11() real ext-real Element of COMPLEX
((1 / (sqrt 5)) / 2) + 1 is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
- ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
(tau_bar to_power s5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
- (((sqrt 5) / (sqrt 5)) / 2) is V11() real ext-real Element of COMPLEX
- (- (1 / 2)) is non empty V11() real ext-real positive non negative Element of COMPLEX
- ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(1 / 2) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power s5) / (sqrt 5))) + ((tau to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power s5) / (sqrt 5)) - ((tau_bar to_power s5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau to_power s5) - (tau_bar to_power s5) is V11() real ext-real set
((tau to_power s5) - (tau_bar to_power s5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) ^2 is V11() real ext-real set
(1 - (sqrt 5)) * (1 - (sqrt 5)) is V11() real ext-real set
(1 - (sqrt 5)) to_power 2 is V11() real ext-real set
(1 - (sqrt 5)) |^ 2 is V11() real ext-real set
2 * (sqrt 5) is V11() real ext-real set
2 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
- 2 is non empty V11() real ext-real non positive negative integer set
- (2 * (sqrt 5)) is V11() real ext-real set
(- 2) + 6 is V11() real ext-real integer set
(- (2 * (sqrt 5))) + 6 is V11() real ext-real set
1 - (2 * (sqrt 5)) is V11() real ext-real set
(1 - (2 * (sqrt 5))) + 5 is V11() real ext-real set
1 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
1 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(2 * 1) * (sqrt 5) is V11() real ext-real set
(1 ^2) - ((2 * 1) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) ^2 is V11() real ext-real Element of REAL
(sqrt 5) * (sqrt 5) is V11() real ext-real set
((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2) is V11() real ext-real set
2 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
2 to_power 2 is V11() real ext-real Element of REAL
2 |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau to_power (2 * n) is V11() real ext-real set
tau |^ (2 * n) is V11() real ext-real set
(tau to_power (2 * n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
[\((tau to_power (2 * n)) / (sqrt 5))/] is V11() real ext-real integer set
Fib (2 * n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
((tau to_power (2 * n)) / (sqrt 5)) - 1 is V11() real ext-real set
2 to_power (2 * n) is V11() real ext-real set
2 |^ (2 * n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 to_power 2) to_power n is V11() real ext-real set
(2 to_power 2) |^ n is V11() real ext-real set
((1 - (sqrt 5)) to_power 2) to_power n is V11() real ext-real set
((1 - (sqrt 5)) to_power 2) |^ n is V11() real ext-real set
(1 - (sqrt 5)) to_power (2 * n) is V11() real ext-real set
(1 - (sqrt 5)) |^ (2 * n) is V11() real ext-real set
(2 to_power (2 * n)) / (2 to_power (2 * n)) is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) to_power (2 * n)) / (2 to_power (2 * n)) is V11() real ext-real Element of COMPLEX
tau_bar to_power (2 * n) is V11() real ext-real set
tau_bar |^ (2 * n) is V11() real ext-real set
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power (2 * n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power (2 * n)) / (sqrt 5))) + ((tau to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- 1) + ((tau to_power (2 * n)) / (sqrt 5)) is V11() real ext-real set
((tau to_power (2 * n)) / (sqrt 5)) - ((tau_bar to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau to_power (2 * n)) - (tau_bar to_power (2 * n)) is V11() real ext-real set
((tau to_power (2 * n)) - (tau_bar to_power (2 * n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau_bar to_power (2 * n) is V11() real ext-real set
tau_bar |^ (2 * n) is V11() real ext-real set
(tau_bar to_power 2) |^ n is V11() real ext-real set
(tau_bar ^2) to_power n is V11() real ext-real set
(tau_bar ^2) |^ n is V11() real ext-real set
0 + ((tau to_power (2 * n)) / (sqrt 5)) is V11() real ext-real set
(tau_bar to_power (2 * n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power (2 * n)) / (sqrt 5))) + ((tau to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power (2 * n)) / (sqrt 5)) - ((tau_bar to_power (2 * n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau to_power (2 * n)) - (tau_bar to_power (2 * n)) is V11() real ext-real set
((tau to_power (2 * n)) - (tau_bar to_power (2 * n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer non even set
tau to_power ((2 * n) + 1) is V11() real ext-real set
tau |^ ((2 * n) + 1) is V11() real ext-real set
(tau to_power ((2 * n) + 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
[/((tau to_power ((2 * n) + 1)) / (sqrt 5))\] is V11() real ext-real integer set
Fib ((2 * n) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau_bar to_power ((2 * n) + 1) is V11() real ext-real set
tau_bar |^ ((2 * n) + 1) is V11() real ext-real set
(tau to_power ((2 * n) + 1)) - (tau_bar to_power ((2 * n) + 1)) is V11() real ext-real set
((tau to_power ((2 * n) + 1)) - (tau_bar to_power ((2 * n) + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power ((2 * n) + 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power ((2 * n) + 1)) / (sqrt 5)) - ((tau_bar to_power ((2 * n) + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
- tau_bar is non empty V11() real ext-real positive non negative set
- (- tau_bar) is non empty V11() real ext-real non positive negative set
(- (- tau_bar)) to_power ((2 * n) + 1) is V11() real ext-real set
(- (- tau_bar)) |^ ((2 * n) + 1) is V11() real ext-real set
(- tau_bar) to_power ((2 * n) + 1) is V11() real ext-real set
(- tau_bar) |^ ((2 * n) + 1) is V11() real ext-real set
- ((- tau_bar) to_power ((2 * n) + 1)) is V11() real ext-real set
((tau_bar to_power ((2 * n) + 1)) / (sqrt 5)) + (1 / 2) is V11() real ext-real Element of COMPLEX
(((tau_bar to_power ((2 * n) + 1)) / (sqrt 5)) + (1 / 2)) - (1 / 2) is V11() real ext-real Element of COMPLEX
0 - (1 / 2) is V11() real ext-real set
- (- 1) is non empty V11() real ext-real positive non negative integer set
- ((tau_bar to_power ((2 * n) + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
1 + ((tau to_power ((2 * n) + 1)) / (sqrt 5)) is V11() real ext-real set
(- ((tau_bar to_power ((2 * n) + 1)) / (sqrt 5))) + ((tau to_power ((2 * n) + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power ((2 * n) + 1)) / (sqrt 5)) + 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau * (Fib n) is V11() real ext-real non negative set
(tau * (Fib n)) + 1 is non empty V11() real ext-real positive non negative set
[\((tau * (Fib n)) + 1)/] is V11() real ext-real integer set
(1 ^2) - ((sqrt 5) ^2) is V11() real ext-real set
((1 ^2) - ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
1 - 5 is V11() real ext-real integer set
(1 - 5) / 4 is V11() real ext-real Element of COMPLEX
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
- tau_bar is non empty V11() real ext-real positive non negative set
(- tau_bar) to_power n is V11() real ext-real set
(- tau_bar) |^ n is V11() real ext-real set
(tau_bar to_power 2) + 1 is V11() real ext-real set
(tau_bar ^2) + 1 is V11() real ext-real set
(((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
((((1 ^2) - ((2 * 1) * (sqrt 5))) + ((sqrt 5) ^2)) / 4) + 1 is V11() real ext-real set
((1 - (2 * (sqrt 5))) + 5) / 4 is V11() real ext-real Element of COMPLEX
(((1 - (2 * (sqrt 5))) + 5) / 4) + 1 is V11() real ext-real set
5 - (sqrt 5) is V11() real ext-real set
(5 - (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
((sqrt 5) ^2) - (sqrt 5) is V11() real ext-real set
(((sqrt 5) ^2) - (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(sqrt 5) * tau_bar is V11() real ext-real set
- ((sqrt 5) * tau_bar) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
tau * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
(tau * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau * (tau to_power n) is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau to_power n)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau * (tau to_power n)) - (tau * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
((tau to_power 1) * (tau to_power n)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power 1) * (tau to_power n)) - (tau * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
n - 1 is V11() real ext-real integer set
(n - 1) + 1 is V11() real ext-real integer set
tau_bar to_power ((n - 1) + 1) is V11() real ext-real set
tau * (tau_bar to_power ((n - 1) + 1)) is V11() real ext-real set
(tau to_power (n + 1)) - (tau * (tau_bar to_power ((n - 1) + 1))) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * (tau_bar to_power ((n - 1) + 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau_bar to_power (n - 1) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power (n - 1)) * (tau_bar to_power 1) is V11() real ext-real set
tau * ((tau_bar to_power (n - 1)) * (tau_bar to_power 1)) is V11() real ext-real set
(tau to_power (n + 1)) - (tau * ((tau_bar to_power (n - 1)) * (tau_bar to_power 1))) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * ((tau_bar to_power (n - 1)) * (tau_bar to_power 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power (n - 1)) * tau_bar is V11() real ext-real set
tau * ((tau_bar to_power (n - 1)) * tau_bar) is V11() real ext-real set
(tau to_power (n + 1)) - (tau * ((tau_bar to_power (n - 1)) * tau_bar)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * ((tau_bar to_power (n - 1)) * tau_bar))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau * tau_bar) * (tau_bar to_power (n - 1)) is V11() real ext-real set
(tau to_power (n + 1)) - ((tau * tau_bar) * (tau_bar to_power (n - 1))) is V11() real ext-real set
((tau to_power (n + 1)) - ((tau * tau_bar) * (tau_bar to_power (n - 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- 1) * (tau_bar to_power (n - 1)) is V11() real ext-real set
(tau to_power (n + 1)) - ((- 1) * (tau_bar to_power (n - 1))) is V11() real ext-real set
((tau to_power (n + 1)) - ((- 1) * (tau_bar to_power (n - 1)))) + (tau_bar to_power (n - 1)) is V11() real ext-real set
(((tau to_power (n + 1)) - ((- 1) * (tau_bar to_power (n - 1)))) + (tau_bar to_power (n - 1))) - (tau_bar to_power (n - 1)) is V11() real ext-real set
((((tau to_power (n + 1)) - ((- 1) * (tau_bar to_power (n - 1)))) + (tau_bar to_power (n - 1))) - (tau_bar to_power (n - 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
(tau_bar to_power (n - 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) + ((tau_bar to_power (n - 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) + ((tau_bar to_power (n - 1)) + (tau_bar to_power (n + 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(n - 1) + 2 is V11() real ext-real integer set
tau_bar to_power ((n - 1) + 2) is V11() real ext-real set
(tau_bar to_power (n - 1)) + (tau_bar to_power ((n - 1) + 2)) is V11() real ext-real set
((tau_bar to_power (n - 1)) + (tau_bar to_power ((n - 1) + 2))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) + (((tau_bar to_power (n - 1)) + (tau_bar to_power ((n - 1) + 2))) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + (((tau_bar to_power (n - 1)) + (tau_bar to_power ((n - 1) + 2))) / (sqrt 5)) is V11() real ext-real set
(tau_bar to_power (n - 1)) * 1 is V11() real ext-real set
(tau_bar to_power (n - 1)) * (tau_bar to_power 2) is V11() real ext-real set
((tau_bar to_power (n - 1)) * 1) + ((tau_bar to_power (n - 1)) * (tau_bar to_power 2)) is V11() real ext-real set
(((tau_bar to_power (n - 1)) * 1) + ((tau_bar to_power (n - 1)) * (tau_bar to_power 2))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + ((((tau_bar to_power (n - 1)) * 1) + ((tau_bar to_power (n - 1)) * (tau_bar to_power 2))) / (sqrt 5)) is V11() real ext-real set
1 + (tau_bar to_power 2) is V11() real ext-real set
(tau_bar to_power (n - 1)) * (1 + (tau_bar to_power 2)) is V11() real ext-real set
((tau_bar to_power (n - 1)) * (1 + (tau_bar to_power 2))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + (((tau_bar to_power (n - 1)) * (1 + (tau_bar to_power 2))) / (sqrt 5)) is V11() real ext-real set
(tau_bar to_power (n - 1)) * (- ((sqrt 5) * tau_bar)) is V11() real ext-real set
((tau_bar to_power (n - 1)) * (- ((sqrt 5) * tau_bar))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + (((tau_bar to_power (n - 1)) * (- ((sqrt 5) * tau_bar))) / (sqrt 5)) is V11() real ext-real set
((- 1) * (tau_bar to_power (n - 1))) * tau_bar is V11() real ext-real set
(((- 1) * (tau_bar to_power (n - 1))) * tau_bar) * (sqrt 5) is V11() real ext-real set
((((- 1) * (tau_bar to_power (n - 1))) * tau_bar) * (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + (((((- 1) * (tau_bar to_power (n - 1))) * tau_bar) * (sqrt 5)) / (sqrt 5)) is V11() real ext-real set
(Fib (n + 1)) + (((- 1) * (tau_bar to_power (n - 1))) * tau_bar) is V11() real ext-real set
(Fib (n + 1)) - ((tau_bar to_power (n - 1)) * tau_bar) is V11() real ext-real set
(Fib (n + 1)) - ((tau_bar to_power (n - 1)) * (tau_bar to_power 1)) is V11() real ext-real set
(Fib (n + 1)) - (tau_bar to_power ((n - 1) + 1)) is V11() real ext-real set
(Fib (n + 1)) - (tau_bar to_power n) is V11() real ext-real set
1 - (tau_bar to_power n) is V11() real ext-real set
((tau * (Fib n)) + 1) - (1 - (tau_bar to_power n)) is V11() real ext-real set
- (tau_bar to_power n) is V11() real ext-real set
(- (tau_bar to_power n)) + 1 is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
(Fib (n + 1)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(tau to_power (n + 1)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power (n + 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau * (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) / (sqrt 5)) - ((tau * (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau_bar to_power (n + 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) / (sqrt 5)) - ((tau_bar to_power (n + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * tau is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau_bar to_power n) * (tau_bar to_power 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power (n + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
- ((tau * (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power (n + 1)) / (sqrt 5))) + ((tau to_power (n + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- ((tau * (tau_bar to_power n)) / (sqrt 5))) + ((tau to_power (n + 1)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((Fib (n + 1)) + 1) - 1 is V11() real ext-real integer set
((tau * (Fib n)) + 1) - 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau * (Fib n) is V11() real ext-real non negative set
(tau * (Fib n)) - 1 is V11() real ext-real set
[/((tau * (Fib n)) - 1)\] is V11() real ext-real integer set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau_bar to_power n)) + (sqrt 5) is V11() real ext-real set
(sqrt 5) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
tau + ((sqrt 5) / (tau_bar to_power n)) is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
(tau_bar to_power n) + 1 is V11() real ext-real set
((tau_bar to_power n) + 1) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
0 / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
1 / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
((tau_bar to_power n) / (tau_bar to_power n)) + (1 / (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
1 + (1 / (tau_bar to_power n)) is V11() real ext-real set
(1 + (1 / (tau_bar to_power n))) * (sqrt 5) is V11() real ext-real set
0 * (sqrt 5) is V11() real ext-real set
1 * (sqrt 5) is V11() real ext-real set
(1 / (tau_bar to_power n)) * (sqrt 5) is V11() real ext-real set
(1 * (sqrt 5)) + ((1 / (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
(sqrt 5) + ((sqrt 5) / (tau_bar to_power n)) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) + ((sqrt 5) / (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
(((sqrt 5) / 2) + ((sqrt 5) / (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
((((sqrt 5) / 2) + ((sqrt 5) / (tau_bar to_power n))) + ((sqrt 5) / 2)) - ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
0 - ((sqrt 5) / 2) is V11() real ext-real set
(((sqrt 5) / 2) + ((sqrt 5) / (tau_bar to_power n))) + (1 / 2) is V11() real ext-real Element of COMPLEX
- ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / 2)) + (1 / 2) is V11() real ext-real Element of COMPLEX
tau_bar * (tau_bar to_power n) is V11() real ext-real set
(tau + ((sqrt 5) / (tau_bar to_power n))) * (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
((sqrt 5) / (tau_bar to_power n)) * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau_bar to_power n)) + (((sqrt 5) / (tau_bar to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
- ((tau * (tau_bar to_power n)) + (sqrt 5)) is V11() real ext-real set
- (tau_bar to_power (n + 1)) is V11() real ext-real set
- (tau * (tau_bar to_power n)) is V11() real ext-real set
(- (tau * (tau_bar to_power n))) - (sqrt 5) is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
((- (tau * (tau_bar to_power n))) - (sqrt 5)) + (tau to_power (n + 1)) is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + (tau to_power (n + 1)) is V11() real ext-real set
(tau to_power (n + 1)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * (tau_bar to_power n))) - (sqrt 5) is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
((tau to_power 1) * (tau to_power n)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power 1) * (tau to_power n)) - (tau * (tau_bar to_power n))) - (sqrt 5) is V11() real ext-real set
tau * (tau to_power n) is V11() real ext-real set
(tau * (tau to_power n)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau * (tau to_power n)) - (tau * (tau_bar to_power n))) - (sqrt 5) is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
tau * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
(tau * ((tau to_power n) - (tau_bar to_power n))) - (sqrt 5) is V11() real ext-real set
((tau * ((tau to_power n) - (tau_bar to_power n))) - (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5)) - ((sqrt 5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
(tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) - ((sqrt 5) / (sqrt 5)) is V11() real ext-real set
(tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) - 1 is V11() real ext-real set
((tau * (Fib n)) - 1) + 1 is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
(- (tau * (tau_bar to_power n))) + (tau to_power (n + 1)) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(sqrt 5) * (Fib n) is V11() real ext-real set
(Fib n) + ((sqrt 5) * (Fib n)) is V11() real ext-real set
((Fib n) + ((sqrt 5) * (Fib n))) + 1 is V11() real ext-real set
(((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2 is V11() real ext-real Element of COMPLEX
[\((((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2)/] is V11() real ext-real integer set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
2 * (tau_bar to_power n) is V11() real ext-real set
2 * (1 / 2) is non empty V11() real ext-real positive non negative set
(2 * (tau_bar to_power n)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
1 / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(1 / (tau_bar to_power n)) * (sqrt 5) is V11() real ext-real set
(sqrt 5) + (sqrt 5) is V11() real ext-real set
1 * (sqrt 5) is V11() real ext-real set
(1 * (sqrt 5)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
((sqrt 5) + (sqrt 5)) - (sqrt 5) is V11() real ext-real set
((1 * (sqrt 5)) / (tau_bar to_power n)) - (sqrt 5) is V11() real ext-real set
(sqrt 5) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (tau_bar to_power n)) - (sqrt 5) is V11() real ext-real set
- (((sqrt 5) / (tau_bar to_power n)) - (sqrt 5)) is V11() real ext-real set
- ((sqrt 5) / (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / (tau_bar to_power n))) + (sqrt 5) is V11() real ext-real set
((- ((sqrt 5) / (tau_bar to_power n))) + (sqrt 5)) + 1 is V11() real ext-real set
(- (sqrt 5)) + 1 is V11() real ext-real set
(sqrt 5) + 1 is V11() real ext-real set
((sqrt 5) + 1) - ((sqrt 5) / (tau_bar to_power n)) is V11() real ext-real set
(((sqrt 5) + 1) - ((sqrt 5) / (tau_bar to_power n))) / 2 is V11() real ext-real Element of COMPLEX
((sqrt 5) / (tau_bar to_power n)) / 2 is V11() real ext-real Element of COMPLEX
tau - (((sqrt 5) / (tau_bar to_power n)) / 2) is V11() real ext-real set
(tau - (((sqrt 5) / (tau_bar to_power n)) / 2)) * (tau_bar to_power n) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
tau - (((sqrt 5) / 2) / (tau_bar to_power n)) is V11() real ext-real set
(tau - (((sqrt 5) / 2) / (tau_bar to_power n))) * (tau_bar to_power n) is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(((sqrt 5) / 2) / (tau_bar to_power n)) * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau_bar to_power n)) - ((((sqrt 5) / 2) / (tau_bar to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
(tau * (tau_bar to_power n)) - ((sqrt 5) / 2) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
- (tau_bar to_power (n + 1)) is V11() real ext-real set
- ((tau * (tau_bar to_power n)) - ((sqrt 5) / 2)) is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + (tau to_power (n + 1)) is V11() real ext-real set
- (tau * (tau_bar to_power n)) is V11() real ext-real set
(- (tau * (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real set
((- (tau * (tau_bar to_power n))) + ((sqrt 5) / 2)) + (tau to_power (n + 1)) is V11() real ext-real set
(tau to_power (n + 1)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau * (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
((tau to_power n) * (tau to_power 1)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) * (tau to_power 1)) - (tau * (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) - (tau * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) * tau) - (tau * (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
tau * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
(tau * ((tau to_power n) - (tau_bar to_power n))) + ((sqrt 5) / 2) is V11() real ext-real set
((tau * ((tau to_power n) - (tau_bar to_power n))) + ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
(tau * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real set
tau * (Fib n) is V11() real ext-real non negative set
(tau * (Fib n)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real set
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(tau * (Fib n)) + (((sqrt 5) / (sqrt 5)) / 2) is V11() real ext-real set
(tau * (Fib n)) + (1 / 2) is non empty V11() real ext-real positive non negative set
((((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2) - 1 is V11() real ext-real set
tau * (Fib n) is V11() real ext-real non negative set
(tau * (Fib n)) + 1 is non empty V11() real ext-real positive non negative set
[\((tau * (Fib n)) + 1)/] is V11() real ext-real integer set
((tau * (Fib n)) + 1) - 1 is V11() real ext-real set
((Fib n) + ((sqrt 5) * (Fib n))) + 2 is V11() real ext-real set
(((Fib n) + ((sqrt 5) * (Fib n))) + 2) / 2 is V11() real ext-real Element of COMPLEX
tau * (Fib n) is V11() real ext-real non negative set
(tau * (Fib n)) - 1 is V11() real ext-real set
[/((tau * (Fib n)) - 1)\] is V11() real ext-real integer set
((tau * (Fib n)) - 1) + 1 is V11() real ext-real set
1 + ((Fib n) + ((sqrt 5) * (Fib n))) is V11() real ext-real set
0 + ((Fib n) + ((sqrt 5) * (Fib n))) is V11() real ext-real set
((Fib n) + ((sqrt 5) * (Fib n))) / 2 is V11() real ext-real Element of COMPLEX
((((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2) - 1 is V11() real ext-real set
(2 * (sqrt 5)) * (tau_bar to_power n) is V11() real ext-real set
(2 * (sqrt 5)) * (- (1 / 2)) is V11() real ext-real set
- ((2 * (sqrt 5)) * (- (1 / 2))) is V11() real ext-real set
- ((2 * (sqrt 5)) * (tau_bar to_power n)) is V11() real ext-real set
2 * tau is non empty V11() real ext-real positive non negative set
(2 * tau) * (tau to_power n) is V11() real ext-real set
(sqrt 5) + ((2 * tau) * (tau to_power n)) is V11() real ext-real set
1 * (tau to_power n) is V11() real ext-real set
(sqrt 5) * (tau to_power n) is V11() real ext-real set
(1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n)) is V11() real ext-real set
((1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n))) - ((2 * tau) * (tau to_power n)) is V11() real ext-real set
2 * tau_bar is non empty V11() real ext-real non positive negative set
(2 * tau_bar) * (tau_bar to_power n) is V11() real ext-real set
(((1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n))) - ((2 * tau) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(sqrt 5) * (tau_bar to_power n) is V11() real ext-real set
((((1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n))) - ((2 * tau) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n)) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
(((((1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n))) - ((2 * tau) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n))) - (1 * (tau_bar to_power n)) is V11() real ext-real set
((((((1 * (tau to_power n)) + ((sqrt 5) * (tau to_power n))) - ((2 * tau) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + ((2 * tau) * (tau to_power n)) is V11() real ext-real set
((sqrt 5) + ((2 * tau) * (tau to_power n))) - ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(tau to_power n) + ((sqrt 5) * (tau to_power n)) is V11() real ext-real set
((tau to_power n) + ((sqrt 5) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) + ((sqrt 5) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n)) is V11() real ext-real set
((((tau to_power n) + ((sqrt 5) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n))) - (tau_bar to_power n) is V11() real ext-real set
(((((tau to_power n) + ((sqrt 5) * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - ((sqrt 5) * (tau_bar to_power n))) - (tau_bar to_power n)) - ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(((sqrt 5) + ((2 * tau) * (tau to_power n))) - ((2 * tau_bar) * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
(1 + (sqrt 5)) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((1 + (sqrt 5)) * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau * (tau to_power n) is V11() real ext-real set
2 * (tau * (tau to_power n)) is V11() real ext-real set
(sqrt 5) + (2 * (tau * (tau to_power n))) is V11() real ext-real set
((sqrt 5) + (2 * (tau * (tau to_power n)))) - ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(((sqrt 5) + (2 * (tau * (tau to_power n)))) - ((2 * tau_bar) * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(1 + (sqrt 5)) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
(1 + (sqrt 5)) * (Fib n) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
2 * ((tau to_power 1) * (tau to_power n)) is V11() real ext-real set
(sqrt 5) + (2 * ((tau to_power 1) * (tau to_power n))) is V11() real ext-real set
((sqrt 5) + (2 * ((tau to_power 1) * (tau to_power n)))) - ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
(((sqrt 5) + (2 * ((tau to_power 1) * (tau to_power n)))) - ((2 * tau_bar) * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
2 * (tau to_power (n + 1)) is V11() real ext-real set
(sqrt 5) + (2 * (tau to_power (n + 1))) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
2 * (tau_bar * (tau_bar to_power n)) is V11() real ext-real set
((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * (tau_bar * (tau_bar to_power n))) is V11() real ext-real set
(((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * (tau_bar * (tau_bar to_power n)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
2 * ((tau_bar to_power 1) * (tau_bar to_power n)) is V11() real ext-real set
((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * ((tau_bar to_power 1) * (tau_bar to_power n))) is V11() real ext-real set
(((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
2 * (tau_bar to_power (n + 1)) is V11() real ext-real set
((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * (tau_bar to_power (n + 1))) is V11() real ext-real set
(((sqrt 5) + (2 * (tau to_power (n + 1)))) - (2 * (tau_bar to_power (n + 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) is V11() real ext-real set
(sqrt 5) + (2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1)))) is V11() real ext-real set
((sqrt 5) + (2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1))))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) + ((2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1)))) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
2 * (((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) is V11() real ext-real set
((sqrt 5) / (sqrt 5)) + (2 * (((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5))) is V11() real ext-real set
2 * (Fib (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
((sqrt 5) / (sqrt 5)) + (2 * (Fib (n + 1))) is V11() real ext-real set
1 + (2 * (Fib (n + 1))) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer non even set
(1 + (2 * (Fib (n + 1)))) / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
((1 + (sqrt 5)) * (Fib n)) / 2 is V11() real ext-real Element of COMPLEX
(1 / 2) + (Fib (n + 1)) is non empty V11() real ext-real positive non negative set
((1 / 2) + (Fib (n + 1))) - (1 / 2) is V11() real ext-real set
(((1 + (sqrt 5)) * (Fib n)) / 2) - (1 / 2) is V11() real ext-real Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(sqrt 5) * (Fib n) is V11() real ext-real set
(Fib n) + ((sqrt 5) * (Fib n)) is V11() real ext-real set
((Fib n) + ((sqrt 5) * (Fib n))) - 1 is V11() real ext-real set
(((Fib n) + ((sqrt 5) * (Fib n))) - 1) / 2 is V11() real ext-real Element of COMPLEX
[/((((Fib n) + ((sqrt 5) * (Fib n))) - 1) / 2)\] is V11() real ext-real integer set
((Fib n) + ((sqrt 5) * (Fib n))) + 1 is V11() real ext-real set
(((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2 is V11() real ext-real Element of COMPLEX
[\((((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2)/] is V11() real ext-real integer set
((((Fib n) + ((sqrt 5) * (Fib n))) + 1) / 2) - 1 is V11() real ext-real set
((((Fib n) + ((sqrt 5) * (Fib n))) - 1) / 2) + 1 is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(Fib n) * (1 + (sqrt 5)) is V11() real ext-real set
((Fib n) * (1 + (sqrt 5))) + 1 is V11() real ext-real set
2 * (Fib (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5)) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5))) + 1 is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5))) + 1) * (sqrt 5) is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
2 * (((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) is V11() real ext-real set
(2 * (((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5))) * (sqrt 5) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5))) * (sqrt 5) is V11() real ext-real set
1 * (sqrt 5) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5))) * (sqrt 5)) + (1 * (sqrt 5)) is V11() real ext-real set
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) * (sqrt 5) is V11() real ext-real set
2 * ((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) * (sqrt 5)) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (1 + (sqrt 5))) * (sqrt 5)) + (sqrt 5) is V11() real ext-real set
2 * ((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * (1 + (sqrt 5)) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (1 + (sqrt 5))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((tau to_power n) - (tau_bar to_power n)) * (1 + (sqrt 5))) / (sqrt 5)) * (sqrt 5) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) * (1 + (sqrt 5))) / (sqrt 5)) * (sqrt 5)) + (sqrt 5) is V11() real ext-real set
2 * (tau to_power (n + 1)) is V11() real ext-real set
2 * (tau_bar to_power (n + 1)) is V11() real ext-real set
(2 * (tau to_power (n + 1))) - (2 * (tau_bar to_power (n + 1))) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (1 + (sqrt 5))) + (sqrt 5) is V11() real ext-real set
(tau to_power n) * (1 + (sqrt 5)) is V11() real ext-real set
(tau_bar to_power n) * (sqrt 5) is V11() real ext-real set
(tau_bar to_power n) + ((tau_bar to_power n) * (sqrt 5)) is V11() real ext-real set
((tau to_power n) * (1 + (sqrt 5))) - ((tau_bar to_power n) + ((tau_bar to_power n) * (sqrt 5))) is V11() real ext-real set
(((tau to_power n) * (1 + (sqrt 5))) - ((tau_bar to_power n) + ((tau_bar to_power n) * (sqrt 5)))) + (sqrt 5) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
2 * ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
(2 * ((tau to_power n) * (tau to_power 1))) - (2 * (tau_bar to_power (n + 1))) is V11() real ext-real set
(tau_bar to_power n) * (1 + (sqrt 5)) is V11() real ext-real set
((tau to_power n) * (1 + (sqrt 5))) - ((tau_bar to_power n) * (1 + (sqrt 5))) is V11() real ext-real set
(((tau to_power n) * (1 + (sqrt 5))) - ((tau_bar to_power n) * (1 + (sqrt 5)))) + (sqrt 5) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
2 * ((tau_bar to_power n) * (tau_bar to_power 1)) is V11() real ext-real set
(2 * ((tau to_power n) * (tau to_power 1))) - (2 * ((tau_bar to_power n) * (tau_bar to_power 1))) is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
2 * ((tau to_power n) * tau) is V11() real ext-real set
(2 * ((tau to_power n) * tau)) - (2 * ((tau_bar to_power n) * (tau_bar to_power 1))) is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
2 * ((tau_bar to_power n) * tau_bar) is V11() real ext-real set
(2 * ((tau to_power n) * tau)) - (2 * ((tau_bar to_power n) * tau_bar)) is V11() real ext-real set
2 * tau is non empty V11() real ext-real positive non negative set
(1 + (sqrt 5)) - (2 * tau) is V11() real ext-real set
(tau to_power n) * ((1 + (sqrt 5)) - (2 * tau)) is V11() real ext-real set
2 * tau_bar is non empty V11() real ext-real non positive negative set
(2 * tau_bar) - (1 + (sqrt 5)) is V11() real ext-real set
(tau_bar to_power n) * ((2 * tau_bar) - (1 + (sqrt 5))) is V11() real ext-real set
((tau to_power n) * ((1 + (sqrt 5)) - (2 * tau))) + ((tau_bar to_power n) * ((2 * tau_bar) - (1 + (sqrt 5)))) is V11() real ext-real set
(((tau to_power n) * ((1 + (sqrt 5)) - (2 * tau))) + ((tau_bar to_power n) * ((2 * tau_bar) - (1 + (sqrt 5))))) + (sqrt 5) is V11() real ext-real set
2 * (tau_bar to_power n) is V11() real ext-real set
- (2 * (tau_bar to_power n)) is V11() real ext-real set
(- (2 * (tau_bar to_power n))) + 1 is V11() real ext-real set
((- (2 * (tau_bar to_power n))) + 1) * (sqrt 5) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
4 * ((- 1) to_power n) is V11() real ext-real set
(5 * ((Fib n) ^2)) + (4 * ((- 1) to_power n)) is V11() real ext-real set
sqrt ((5 * ((Fib n) ^2)) + (4 * ((- 1) to_power n))) is V11() real ext-real set
(Fib n) + (sqrt ((5 * ((Fib n) ^2)) + (4 * ((- 1) to_power n)))) is V11() real ext-real set
((Fib n) + (sqrt ((5 * ((Fib n) ^2)) + (4 * ((- 1) to_power n))))) / 2 is V11() real ext-real Element of COMPLEX
n - 0 is V11() real ext-real integer set
2 * (Fib (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) + (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(Lucas n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) ^2) - (5 * ((Fib n) ^2)) is V11() real ext-real integer set
(Lucas n) to_power 2 is V11() real ext-real set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) to_power 2) - (5 * ((Fib n) ^2)) is V11() real ext-real set
(Fib n) to_power 2 is V11() real ext-real set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) to_power 2) is V11() real ext-real set
((Lucas n) to_power 2) - (5 * ((Fib n) to_power 2)) is V11() real ext-real set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 * ((Fib n) |^ 2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2) is V11() real ext-real integer set
- ((5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2)) is V11() real ext-real integer set
(- 1) to_power (n + 1) is V11() real ext-real set
(- 1) |^ (n + 1) is V11() real ext-real set
4 * ((- 1) to_power (n + 1)) is V11() real ext-real set
- (4 * ((- 1) to_power (n + 1))) is V11() real ext-real set
((- 1) to_power (n + 1)) * 4 is V11() real ext-real set
(- 1) * (((- 1) to_power (n + 1)) * 4) is V11() real ext-real set
(- 1) to_power 1 is V11() real ext-real set
(- 1) |^ 1 is V11() real ext-real set
((- 1) to_power 1) * (((- 1) to_power (n + 1)) * 4) is V11() real ext-real set
((- 1) to_power 1) * ((- 1) to_power (n + 1)) is V11() real ext-real set
(((- 1) to_power 1) * ((- 1) to_power (n + 1))) * 4 is V11() real ext-real set
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- 1) to_power ((n + 1) + 1) is V11() real ext-real set
(- 1) |^ ((n + 1) + 1) is V11() real ext-real set
((- 1) to_power ((n + 1) + 1)) * 4 is V11() real ext-real set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- 1) to_power (n + 2) is V11() real ext-real set
(- 1) |^ (n + 2) is V11() real ext-real set
((- 1) to_power (n + 2)) * 4 is V11() real ext-real set
(- 1) to_power 2 is V11() real ext-real set
(- 1) |^ 2 is V11() real ext-real set
((- 1) to_power n) * ((- 1) to_power 2) is V11() real ext-real set
(((- 1) to_power n) * ((- 1) to_power 2)) * 4 is V11() real ext-real set
((- 1) to_power n) * 1 is V11() real ext-real set
(((- 1) to_power n) * 1) * 4 is V11() real ext-real set
((Fib n) + (Lucas n)) / 2 is V11() real ext-real non negative Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Fib n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(5 * ((Fib n) ^2)) - (2 * (Fib n)) is V11() real ext-real integer set
((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1 is V11() real ext-real integer set
sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1) is V11() real ext-real set
((Fib n) + 1) + (sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1)) is V11() real ext-real set
(((Fib n) + 1) + (sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1))) / 2 is V11() real ext-real Element of COMPLEX
[\((((Fib n) + 1) + (sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1))) / 2)/] is V11() real ext-real integer set
n - 0 is V11() real ext-real integer set
2 - 1 is V11() real ext-real integer set
n - 1 is V11() real ext-real integer set
(n + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
((n + 1) -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(n + 1) - 1 is V11() real ext-real integer set
((n + 1) - 1) + 1 is V11() real ext-real integer set
(n - 1) + 1 is V11() real ext-real integer set
((n - 1) + 1) + 1 is V11() real ext-real integer set
n -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(n -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((n -' 1) + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (((n -' 1) + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib (n -' 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib ((n -' 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n -' 1)) + (Fib ((n -' 1) + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Fib ((n + 1) -' 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n -' 1)) + (Fib ((n + 1) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(Fib (n -' 1)) + (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(n + 2) - 1 is V11() real ext-real integer set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) - (Fib n) is V11() real ext-real integer set
Lucas ((n + 1) -' 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
(Lucas ((n + 1) -' 1)) - (Fib n) is V11() real ext-real integer set
Lucas ((n -' 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas ((n -' 1) + 1)) - (Fib n) is V11() real ext-real integer set
(n -' 1) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib ((n -' 1) + 2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n -' 1)) + (Fib ((n -' 1) + 2)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Fib (n -' 1)) + (Fib ((n -' 1) + 2))) - (Fib n) is V11() real ext-real integer set
(n + 2) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Fib ((n + 2) -' 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n -' 1)) + (Fib ((n + 2) -' 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Fib (n -' 1)) + (Fib ((n + 2) -' 1))) - (Fib n) is V11() real ext-real integer set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Fib k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n -' 1)) + (Fib k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Fib (n -' 1)) + (Fib k)) - (Fib n) is V11() real ext-real integer set
2 * (Fib (n -' 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(Lucas n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) ^2) - (5 * ((Fib n) ^2)) is V11() real ext-real integer set
(Fib n) to_power 2 is V11() real ext-real set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) to_power 2) is V11() real ext-real set
((Lucas n) ^2) - (5 * ((Fib n) to_power 2)) is V11() real ext-real set
(Lucas n) to_power 2 is V11() real ext-real set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 * ((Fib n) |^ 2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) to_power 2) - (5 * ((Fib n) |^ 2)) is V11() real ext-real set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2) is V11() real ext-real integer set
(- 1) * ((5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2)) is V11() real ext-real integer set
(- 1) to_power (n + 1) is V11() real ext-real set
(- 1) |^ (n + 1) is V11() real ext-real set
4 * ((- 1) to_power (n + 1)) is V11() real ext-real set
(- 1) * (4 * ((- 1) to_power (n + 1))) is V11() real ext-real set
(- 1) * ((- 1) to_power (n + 1)) is V11() real ext-real set
4 * ((- 1) * ((- 1) to_power (n + 1))) is V11() real ext-real set
(- 1) to_power 1 is V11() real ext-real set
(- 1) |^ 1 is V11() real ext-real set
((- 1) to_power 1) * ((- 1) to_power (n + 1)) is V11() real ext-real set
4 * (((- 1) to_power 1) * ((- 1) to_power (n + 1))) is V11() real ext-real set
1 + (n + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- 1) to_power (1 + (n + 1)) is V11() real ext-real set
(- 1) |^ (1 + (n + 1)) is V11() real ext-real set
4 * ((- 1) to_power (1 + (n + 1))) is V11() real ext-real set
(- 1) to_power (n + 2) is V11() real ext-real set
(- 1) |^ (n + 2) is V11() real ext-real set
4 * ((- 1) to_power (n + 2)) is V11() real ext-real set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
(- 1) to_power 2 is V11() real ext-real set
(- 1) |^ 2 is V11() real ext-real set
((- 1) to_power n) * ((- 1) to_power 2) is V11() real ext-real set
4 * (((- 1) to_power n) * ((- 1) to_power 2)) is V11() real ext-real set
(- 1) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(- 1) * (- 1) is non empty V11() real ext-real positive non negative integer set
((- 1) to_power n) * ((- 1) ^2) is V11() real ext-real set
4 * (((- 1) to_power n) * ((- 1) ^2)) is V11() real ext-real set
4 * ((- 1) to_power n) is V11() real ext-real set
2 -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(2 * 2) * (Fib (n -' 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
2 * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(((Lucas n) ^2) - (5 * ((Fib n) ^2))) - (2 * (Lucas n)) is V11() real ext-real integer set
(2 * (Lucas n)) - (2 * (Fib n)) is V11() real ext-real integer set
((2 * (Lucas n)) - (2 * (Fib n))) - (2 * (Lucas n)) is V11() real ext-real integer set
((((Lucas n) ^2) - (5 * ((Fib n) ^2))) - (2 * (Lucas n))) + 1 is V11() real ext-real integer set
- (2 * (Fib n)) is V11() real ext-real non positive integer set
(- (2 * (Fib n))) + 1 is V11() real ext-real integer set
(((((Lucas n) ^2) - (5 * ((Fib n) ^2))) - (2 * (Lucas n))) + 1) + (5 * ((Fib n) ^2)) is V11() real ext-real integer set
((- (2 * (Fib n))) + 1) + (5 * ((Fib n) ^2)) is V11() real ext-real integer set
2 * (Fib (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * (Fib (n + 1))) - (Fib n) is V11() real ext-real integer set
2 * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
- (Fib n) is V11() real ext-real non positive integer set
(- (Fib n)) + 1 is V11() real ext-real integer set
(- 1) + 1 is V11() real ext-real integer set
((- (Fib n)) + 1) + (Fib n) is V11() real ext-real integer set
(2 * (Fib (n -' 1))) + (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
1 - 1 is V11() real ext-real integer set
((2 * (Fib (n -' 1))) + (Fib n)) - 1 is V11() real ext-real integer set
((2 * (Fib (n + 1))) - (Fib n)) - 1 is V11() real ext-real integer set
(((2 * (Fib (n + 1))) - (Fib n)) - 1) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(((2 * (Fib (n + 1))) - (Fib n)) - 1) * (((2 * (Fib (n + 1))) - (Fib n)) - 1) is V11() real ext-real integer set
sqrt ((((2 * (Fib (n + 1))) - (Fib n)) - 1) ^2) is V11() real ext-real set
(((2 * (Fib (n + 1))) - (Fib n)) - 1) + (Fib n) is V11() real ext-real integer set
(sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1)) + (Fib n) is V11() real ext-real set
((((2 * (Fib (n + 1))) - (Fib n)) - 1) + (Fib n)) + 1 is V11() real ext-real integer set
((sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1)) + (Fib n)) + 1 is V11() real ext-real set
(2 * (Fib (n + 1))) / 2 is V11() real ext-real non negative Element of COMPLEX
(((sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1)) + (Fib n)) + 1) / 2 is V11() real ext-real Element of COMPLEX
5 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(5 * (Fib n)) - 2 is V11() real ext-real integer set
((5 * (Fib n)) - 2) * (Fib n) is V11() real ext-real integer set
5 * 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
5 - 2 is V11() real ext-real integer set
(Fib (n + 1)) + (Fib (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Fib (n + 1)) + (Fib (n + 1))) - (Fib n) is V11() real ext-real integer set
(((Fib (n + 1)) + (Fib (n + 1))) - (Fib n)) + 1 is V11() real ext-real integer set
(Fib (n + 1)) + (Fib (n -' 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Fib (n + 1)) + (Fib (n -' 1))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Lucas n) + (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * ((Lucas n) + (Fib n)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
- (2 * ((Lucas n) + (Fib n))) is V11() real ext-real non positive integer set
0 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((Lucas n) + (Fib n)) * 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
- 4 is non empty V11() real ext-real non positive negative integer set
- (((Lucas n) + (Fib n)) * 2) is V11() real ext-real non positive integer set
(((Lucas n) ^2) - (5 * ((Fib n) ^2))) + (2 * (Lucas n)) is V11() real ext-real integer set
(- (2 * ((Lucas n) + (Fib n)))) + (2 * (Lucas n)) is V11() real ext-real integer set
((((Lucas n) ^2) - (5 * ((Fib n) ^2))) + (2 * (Lucas n))) + (5 * ((Fib n) ^2)) is V11() real ext-real integer set
(- (2 * (Fib n))) + (5 * ((Fib n) ^2)) is V11() real ext-real integer set
(2 * (Lucas n)) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
((Lucas n) ^2) + ((2 * (Lucas n)) * 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((Lucas n) ^2) + ((2 * (Lucas n)) * 1)) + (1 ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + (1 ^2) is V11() real ext-real integer set
((2 * (Fib (n + 1))) - (Fib n)) + 1 is V11() real ext-real integer set
(((2 * (Fib (n + 1))) - (Fib n)) + 1) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(((2 * (Fib (n + 1))) - (Fib n)) + 1) * (((2 * (Fib (n + 1))) - (Fib n)) + 1) is V11() real ext-real integer set
sqrt ((((2 * (Fib (n + 1))) - (Fib n)) + 1) ^2) is V11() real ext-real set
((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + 1 is V11() real ext-real integer set
sqrt (((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + 1) is V11() real ext-real set
(((2 * (Fib (n + 1))) - (Fib n)) + 1) - 1 is V11() real ext-real integer set
(sqrt (((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + 1)) - 1 is V11() real ext-real set
((2 * (Fib (n + 1))) - (Fib n)) + (Fib n) is V11() real ext-real integer set
((sqrt (((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + 1)) - 1) + (Fib n) is V11() real ext-real set
(((sqrt (((- (2 * (Fib n))) + (5 * ((Fib n) ^2))) + 1)) - 1) + (Fib n)) / 2 is V11() real ext-real Element of COMPLEX
((((Fib n) + 1) + (sqrt (((5 * ((Fib n) ^2)) - (2 * (Fib n))) + 1))) / 2) - 1 is V11() real ext-real set
(sqrt 5) - 5 is V11() real ext-real set
((sqrt 5) - 5) * tau is V11() real ext-real set
(sqrt 5) / (((sqrt 5) - 5) * tau) is V11() real ext-real Element of COMPLEX
(sqrt 5) - ((sqrt 5) ^2) is V11() real ext-real set
((sqrt 5) - ((sqrt 5) ^2)) * tau is V11() real ext-real set
(sqrt 5) / (((sqrt 5) - ((sqrt 5) ^2)) * tau) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) * tau is V11() real ext-real set
(sqrt 5) * ((1 - (sqrt 5)) * tau) is V11() real ext-real set
(sqrt 5) / ((sqrt 5) * ((1 - (sqrt 5)) * tau)) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) / ((1 - (sqrt 5)) * tau) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) * (1 + (sqrt 5)) is V11() real ext-real set
((1 - (sqrt 5)) * (1 + (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
1 / (((1 - (sqrt 5)) * (1 + (sqrt 5))) / 2) is V11() real ext-real Element of COMPLEX
1 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(1 * 2) / ((1 - (sqrt 5)) * (1 + (sqrt 5))) is V11() real ext-real Element of COMPLEX
(1 ^2) - ((sqrt 5) ^2) is V11() real ext-real set
2 / ((1 ^2) - ((sqrt 5) ^2)) is V11() real ext-real Element of COMPLEX
(1 ^2) - 5 is V11() real ext-real integer set
2 / ((1 ^2) - 5) is V11() real ext-real Element of COMPLEX
1 / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Fib (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib (n + 1)) + (1 / 2) is non empty V11() real ext-real positive non negative set
(1 / tau) * ((Fib (n + 1)) + (1 / 2)) is non empty V11() real ext-real positive non negative set
[\((1 / tau) * ((Fib (n + 1)) + (1 / 2)))/] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
5 ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 * 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
sqrt (5 ^2) is V11() real ext-real set
5 - 5 is V11() real ext-real integer set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau_bar to_power (n + 1)) / tau is V11() real ext-real Element of COMPLEX
2 * tau is non empty V11() real ext-real positive non negative set
(sqrt 5) / (2 * tau) is V11() real ext-real Element of COMPLEX
((tau_bar to_power (n + 1)) / tau) - ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * (((sqrt 5) - 5) * tau) is V11() real ext-real set
((sqrt 5) / (((sqrt 5) - 5) * tau)) * (((sqrt 5) - 5) * tau) is V11() real ext-real set
tau * ((sqrt 5) - 5) is V11() real ext-real set
(tau * ((sqrt 5) - 5)) * (tau_bar to_power n) is V11() real ext-real set
((tau * ((sqrt 5) - 5)) * (tau_bar to_power n)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(sqrt 5) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(((sqrt 5) - 5) * tau) / tau is V11() real ext-real Element of COMPLEX
((sqrt 5) / (tau_bar to_power n)) / tau is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * tau is V11() real ext-real set
(sqrt 5) / ((tau_bar to_power n) * tau) is V11() real ext-real Element of COMPLEX
(- (sqrt 5)) + 5 is V11() real ext-real set
((sqrt 5) - 5) + ((- (sqrt 5)) + 5) is V11() real ext-real set
((sqrt 5) / ((tau_bar to_power n) * tau)) + ((- (sqrt 5)) + 5) is V11() real ext-real set
((sqrt 5) / ((tau_bar to_power n) * tau)) - (sqrt 5) is V11() real ext-real set
(((sqrt 5) / ((tau_bar to_power n) * tau)) - (sqrt 5)) + 5 is V11() real ext-real set
- ((((sqrt 5) / ((tau_bar to_power n) * tau)) - (sqrt 5)) + 5) is V11() real ext-real set
- ((sqrt 5) / ((tau_bar to_power n) * tau)) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / ((tau_bar to_power n) * tau))) + (sqrt 5) is V11() real ext-real set
((- ((sqrt 5) / ((tau_bar to_power n) * tau))) + (sqrt 5)) - 5 is V11() real ext-real set
(((- ((sqrt 5) / ((tau_bar to_power n) * tau))) + (sqrt 5)) - 5) + 2 is V11() real ext-real set
0 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- ((sqrt 5) / ((tau_bar to_power n) * tau))) + ((sqrt 5) - 3) is V11() real ext-real set
((- ((sqrt 5) / ((tau_bar to_power n) * tau))) + ((sqrt 5) - 3)) / 2 is V11() real ext-real Element of COMPLEX
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
((sqrt 5) / ((tau_bar to_power n) * tau)) / 2 is V11() real ext-real Element of COMPLEX
- (((sqrt 5) / ((tau_bar to_power n) * tau)) / 2) is V11() real ext-real Element of COMPLEX
(- (((sqrt 5) / ((tau_bar to_power n) * tau)) / 2)) + (tau_bar / tau) is V11() real ext-real Element of COMPLEX
((tau_bar to_power n) * tau) * 2 is V11() real ext-real set
(sqrt 5) / (((tau_bar to_power n) * tau) * 2) is V11() real ext-real Element of COMPLEX
- ((sqrt 5) / (((tau_bar to_power n) * tau) * 2)) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / (((tau_bar to_power n) * tau) * 2))) + (tau_bar / tau) is V11() real ext-real Element of COMPLEX
2 * (tau_bar to_power n) is V11() real ext-real set
(2 * (tau_bar to_power n)) * tau is V11() real ext-real set
(sqrt 5) / ((2 * (tau_bar to_power n)) * tau) is V11() real ext-real Element of COMPLEX
(tau_bar / tau) - ((sqrt 5) / ((2 * (tau_bar to_power n)) * tau)) is V11() real ext-real Element of COMPLEX
((tau_bar / tau) - ((sqrt 5) / ((2 * (tau_bar to_power n)) * tau))) * (tau_bar to_power n) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
(tau_bar / tau) * (tau_bar to_power n) is V11() real ext-real set
((sqrt 5) / ((2 * (tau_bar to_power n)) * tau)) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar / tau) * (tau_bar to_power n)) - (((sqrt 5) / ((2 * (tau_bar to_power n)) * tau)) * (tau_bar to_power n)) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
(tau_bar * (tau_bar to_power n)) / tau is V11() real ext-real Element of COMPLEX
((tau_bar * (tau_bar to_power n)) / tau) - (((sqrt 5) / ((2 * (tau_bar to_power n)) * tau)) * (tau_bar to_power n)) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power 1) * (tau_bar to_power n)) / tau is V11() real ext-real Element of COMPLEX
(((tau_bar to_power 1) * (tau_bar to_power n)) / tau) - (((sqrt 5) / ((2 * (tau_bar to_power n)) * tau)) * (tau_bar to_power n)) is V11() real ext-real set
(2 * tau) * (tau_bar to_power n) is V11() real ext-real set
(sqrt 5) / ((2 * tau) * (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
((sqrt 5) / ((2 * tau) * (tau_bar to_power n))) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power (n + 1)) / tau) - (((sqrt 5) / ((2 * tau) * (tau_bar to_power n))) * (tau_bar to_power n)) is V11() real ext-real set
((sqrt 5) / (2 * tau)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(((sqrt 5) / (2 * tau)) / (tau_bar to_power n)) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power (n + 1)) / tau) - ((((sqrt 5) / (2 * tau)) / (tau_bar to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
tau * ((sqrt 5) - 5) is V11() real ext-real set
(sqrt 5) / (tau * ((sqrt 5) - 5)) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * ((sqrt 5) - 5) is V11() real ext-real set
((sqrt 5) / (tau * ((sqrt 5) - 5))) * ((sqrt 5) - 5) is V11() real ext-real set
(sqrt 5) / tau is V11() real ext-real Element of COMPLEX
((sqrt 5) / tau) / ((sqrt 5) - 5) is V11() real ext-real Element of COMPLEX
(((sqrt 5) / tau) / ((sqrt 5) - 5)) * ((sqrt 5) - 5) is V11() real ext-real set
((sqrt 5) / tau) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
((tau_bar to_power n) * ((sqrt 5) - 5)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
tau * (tau_bar to_power n) is V11() real ext-real set
(sqrt 5) / (tau * (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
- ((sqrt 5) - 5) is V11() real ext-real set
- ((sqrt 5) / (tau * (tau_bar to_power n))) is V11() real ext-real Element of COMPLEX
(- (sqrt 5)) + 5 is V11() real ext-real set
((- (sqrt 5)) + 5) + ((sqrt 5) - 3) is V11() real ext-real set
(- ((sqrt 5) / (tau * (tau_bar to_power n)))) + ((sqrt 5) - 3) is V11() real ext-real set
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
((- ((sqrt 5) / (tau * (tau_bar to_power n)))) + ((sqrt 5) - 3)) / 2 is V11() real ext-real Element of COMPLEX
((sqrt 5) / (tau * (tau_bar to_power n))) / 2 is V11() real ext-real Element of COMPLEX
(tau_bar / tau) - (((sqrt 5) / (tau * (tau_bar to_power n))) / 2) is V11() real ext-real Element of COMPLEX
(tau * (tau_bar to_power n)) * 2 is V11() real ext-real set
(sqrt 5) / ((tau * (tau_bar to_power n)) * 2) is V11() real ext-real Element of COMPLEX
(tau_bar / tau) - ((sqrt 5) / ((tau * (tau_bar to_power n)) * 2)) is V11() real ext-real Element of COMPLEX
((tau_bar / tau) - ((sqrt 5) / ((tau * (tau_bar to_power n)) * 2))) * (tau_bar to_power n) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
(tau_bar / tau) * (tau_bar to_power n) is V11() real ext-real set
tau * 2 is non empty V11() real ext-real positive non negative set
(tau * 2) * (tau_bar to_power n) is V11() real ext-real set
(sqrt 5) / ((tau * 2) * (tau_bar to_power n)) is V11() real ext-real Element of COMPLEX
((sqrt 5) / ((tau * 2) * (tau_bar to_power n))) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar / tau) * (tau_bar to_power n)) - (((sqrt 5) / ((tau * 2) * (tau_bar to_power n))) * (tau_bar to_power n)) is V11() real ext-real set
(sqrt 5) / (tau * 2) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (tau * 2)) / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(((sqrt 5) / (tau * 2)) / (tau_bar to_power n)) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar / tau) * (tau_bar to_power n)) - ((((sqrt 5) / (tau * 2)) / (tau_bar to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
((tau_bar / tau) * (tau_bar to_power n)) - ((sqrt 5) / (tau * 2)) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
(tau_bar * (tau_bar to_power n)) / tau is V11() real ext-real Element of COMPLEX
((tau_bar * (tau_bar to_power n)) / tau) - ((sqrt 5) / (tau * 2)) is V11() real ext-real Element of COMPLEX
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power 1) * (tau_bar to_power n)) / tau is V11() real ext-real Element of COMPLEX
(((tau_bar to_power 1) * (tau_bar to_power n)) / tau) - ((sqrt 5) / (tau * 2)) is V11() real ext-real Element of COMPLEX
- (tau_bar to_power n) is V11() real ext-real set
- (((tau_bar to_power (n + 1)) / tau) - ((sqrt 5) / (2 * tau))) is V11() real ext-real Element of COMPLEX
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
(- (tau_bar to_power n)) + (((tau to_power n) * tau) / tau) is V11() real ext-real set
- ((tau_bar to_power (n + 1)) / tau) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power (n + 1)) / tau)) + ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
((- ((tau_bar to_power (n + 1)) / tau)) + ((sqrt 5) / (2 * tau))) + (((tau to_power n) * tau) / tau) is V11() real ext-real Element of COMPLEX
(((tau to_power n) * tau) / tau) - ((tau_bar to_power (n + 1)) / tau) is V11() real ext-real Element of COMPLEX
((((tau to_power n) * tau) / tau) - ((tau_bar to_power (n + 1)) / tau)) + ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
((tau to_power n) * tau) - (tau_bar to_power (n + 1)) is V11() real ext-real set
(((tau to_power n) * tau) - (tau_bar to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
((((tau to_power n) * tau) - (tau_bar to_power (n + 1))) / tau) + ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
(- (tau_bar to_power n)) + (tau to_power n) is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
((tau to_power n) * (tau to_power 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
(((tau to_power n) * (tau to_power 1)) - (tau_bar to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
((((tau to_power n) * (tau to_power 1)) - (tau_bar to_power (n + 1))) / tau) + ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / tau) + ((sqrt 5) / (2 * tau)) is V11() real ext-real Element of COMPLEX
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / tau) + ((sqrt 5) / (2 * tau))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / tau) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (2 * tau)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / tau) / (sqrt 5)) + (((sqrt 5) / (2 * tau)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) / tau is V11() real ext-real Element of COMPLEX
((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) / tau) + (((sqrt 5) / (2 * tau)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) / tau is V11() real ext-real non negative Element of COMPLEX
((Fib (n + 1)) / tau) + (((sqrt 5) / (2 * tau)) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
1 / (2 * tau) is non empty V11() real ext-real positive non negative Element of COMPLEX
(1 / (2 * tau)) * ((sqrt 5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((Fib (n + 1)) / tau) + ((1 / (2 * tau)) * ((sqrt 5) / (sqrt 5))) is V11() real ext-real Element of COMPLEX
(1 / (2 * tau)) * 1 is non empty V11() real ext-real positive non negative set
((Fib (n + 1)) / tau) + ((1 / (2 * tau)) * 1) is non empty V11() real ext-real positive non negative set
(1 / 2) / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
((Fib (n + 1)) / tau) + ((1 / 2) / tau) is non empty V11() real ext-real positive non negative Element of COMPLEX
((Fib (n + 1)) + (1 / 2)) / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
((1 / tau) * ((Fib (n + 1)) + (1 / 2))) - 1 is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
tau - (1 / 2) is V11() real ext-real set
(tau - (1 / 2)) * (sqrt 5) is V11() real ext-real set
(tau_bar to_power n) * (sqrt 5) is V11() real ext-real set
tau * (sqrt 5) is V11() real ext-real set
1 * (sqrt 5) is V11() real ext-real set
(1 * (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(tau * (sqrt 5)) - ((1 * (sqrt 5)) / 2) is V11() real ext-real set
(tau_bar to_power n) * tau is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
((tau_bar to_power n) * tau) - ((tau_bar to_power n) * tau_bar) is V11() real ext-real set
(tau * (sqrt 5)) - ((sqrt 5) / 2) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau_bar to_power n) * tau) - ((tau_bar to_power n) * (tau_bar to_power 1)) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
((tau_bar to_power n) * tau) - (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau * (sqrt 5)) - ((sqrt 5) / 2)) + ((sqrt 5) / 2) is V11() real ext-real set
(((tau_bar to_power n) * tau) - (tau_bar to_power (n + 1))) + ((sqrt 5) / 2) is V11() real ext-real set
(tau * (sqrt 5)) - ((tau_bar to_power n) * tau) is V11() real ext-real set
((((tau_bar to_power n) * tau) - (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) - ((tau_bar to_power n) * tau) is V11() real ext-real set
((tau * (sqrt 5)) - ((tau_bar to_power n) * tau)) - (tau * (sqrt 5)) is V11() real ext-real set
- (tau_bar to_power (n + 1)) is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2) is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) - (tau * (sqrt 5)) is V11() real ext-real set
- ((tau_bar to_power n) * tau) is V11() real ext-real set
(- ((tau_bar to_power n) * tau)) / tau is V11() real ext-real Element of COMPLEX
(((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) - (tau * (sqrt 5))) / tau is V11() real ext-real Element of COMPLEX
(- (tau_bar to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / tau is V11() real ext-real Element of COMPLEX
((- (tau_bar to_power (n + 1))) / tau) + (((sqrt 5) / 2) / tau) is V11() real ext-real Element of COMPLEX
(tau * (sqrt 5)) / tau is V11() real ext-real Element of COMPLEX
(((- (tau_bar to_power (n + 1))) / tau) + (((sqrt 5) / 2) / tau)) - ((tau * (sqrt 5)) / tau) is V11() real ext-real Element of COMPLEX
- (tau_bar to_power n) is V11() real ext-real set
(- (tau_bar to_power n)) * tau is V11() real ext-real set
((- (tau_bar to_power n)) * tau) / tau is V11() real ext-real Element of COMPLEX
(tau_bar to_power (n + 1)) / tau is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power (n + 1)) / tau) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau) is V11() real ext-real Element of COMPLEX
((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - ((tau * (sqrt 5)) / tau) is V11() real ext-real Element of COMPLEX
((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - (sqrt 5) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(- (tau_bar to_power n)) + (tau to_power n) is V11() real ext-real set
(tau to_power n) * 1 is V11() real ext-real set
(((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - (sqrt 5)) + ((tau to_power n) * 1) is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - (sqrt 5)) + ((tau to_power n) * 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
tau / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
(tau to_power n) * (tau / tau) is V11() real ext-real set
(((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - (sqrt 5)) + ((tau to_power n) * (tau / tau)) is V11() real ext-real set
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) - (sqrt 5)) + ((tau to_power n) * (tau / tau))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + ((tau to_power n) * (tau / tau)) is V11() real ext-real set
(((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + ((tau to_power n) * (tau / tau))) - (sqrt 5) is V11() real ext-real set
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + ((tau to_power n) * (tau / tau))) - (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau) is V11() real ext-real Element of COMPLEX
(((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) - (sqrt 5) is V11() real ext-real set
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) - (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) / (sqrt 5)) - ((sqrt 5) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((((- ((tau_bar to_power (n + 1)) / tau)) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) / (sqrt 5)) - 1 is V11() real ext-real set
(((- (tau_bar to_power (n + 1))) / tau) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) / tau) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) / tau) + (((sqrt 5) / 2) / tau)) + (((tau to_power n) * tau) / tau)) / (sqrt 5)) - 1 is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau) is V11() real ext-real set
(((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / tau is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / tau) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / tau) / (sqrt 5)) - 1 is V11() real ext-real set
(((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / (sqrt 5)) / tau is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + ((sqrt 5) / 2)) + ((tau to_power n) * tau)) / (sqrt 5)) / tau) - 1 is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau) is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) + ((sqrt 5) / 2) is V11() real ext-real set
(((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) + ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) + ((sqrt 5) / 2)) / (sqrt 5)) * (1 / tau) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) + ((sqrt 5) / 2)) / (sqrt 5)) * (1 / tau)) - 1 is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * tau)) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau)) - 1 is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + ((tau to_power n) * (tau to_power 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((- (tau_bar to_power (n + 1))) + ((tau to_power n) * (tau to_power 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * (tau to_power 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + ((tau to_power n) * (tau to_power 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau)) - 1 is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(- (tau_bar to_power (n + 1))) + (tau to_power (n + 1)) is V11() real ext-real set
((- (tau_bar to_power (n + 1))) + (tau to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((- (tau_bar to_power (n + 1))) + (tau to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((((- (tau_bar to_power (n + 1))) + (tau to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau) is V11() real ext-real Element of COMPLEX
(((((- (tau_bar to_power (n + 1))) + (tau to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau)) - 1 is V11() real ext-real set
(tau to_power (n + 1)) - (tau_bar to_power (n + 1)) is V11() real ext-real set
((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau) is V11() real ext-real Element of COMPLEX
(((((tau to_power (n + 1)) - (tau_bar to_power (n + 1))) / (sqrt 5)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau)) - 1 is V11() real ext-real set
(Fib (n + 1)) + (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real set
((Fib (n + 1)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau) is V11() real ext-real set
(((Fib (n + 1)) + (((sqrt 5) / 2) / (sqrt 5))) * (1 / tau)) - 1 is V11() real ext-real set
((sqrt 5) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(Fib (n + 1)) + (((sqrt 5) / (sqrt 5)) / 2) is V11() real ext-real set
((Fib (n + 1)) + (((sqrt 5) / (sqrt 5)) / 2)) * (1 / tau) is V11() real ext-real set
(((Fib (n + 1)) + (((sqrt 5) / (sqrt 5)) / 2)) * (1 / tau)) - 1 is V11() real ext-real set
(sqrt 5) - 1 is V11() real ext-real set
1 - 1 is V11() real ext-real integer set
(- 2) + 5 is V11() real ext-real integer set
(- (sqrt 5)) + 5 is V11() real ext-real set
(- (sqrt 5)) + ((sqrt 5) ^2) is V11() real ext-real set
3 / 5 is non empty V11() real ext-real positive non negative Element of COMPLEX
(sqrt 5) * ((sqrt 5) - 1) is V11() real ext-real set
((sqrt 5) * ((sqrt 5) - 1)) / 5 is V11() real ext-real Element of COMPLEX
10 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
6 / 10 is non empty V11() real ext-real positive non negative Element of COMPLEX
(sqrt 5) / 5 is V11() real ext-real Element of COMPLEX
((sqrt 5) - 1) * ((sqrt 5) / 5) is V11() real ext-real set
(sqrt 5) / ((sqrt 5) ^2) is V11() real ext-real Element of COMPLEX
((sqrt 5) - 1) * ((sqrt 5) / ((sqrt 5) ^2)) is V11() real ext-real set
1 * (sqrt 5) is V11() real ext-real set
(1 * (sqrt 5)) / ((sqrt 5) * (sqrt 5)) is V11() real ext-real Element of COMPLEX
((sqrt 5) - 1) * ((1 * (sqrt 5)) / ((sqrt 5) * (sqrt 5))) is V11() real ext-real set
((sqrt 5) - 1) * (1 / (sqrt 5)) is V11() real ext-real set
((sqrt 5) - 1) / (sqrt 5) is V11() real ext-real Element of COMPLEX
3 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
(3 / 2) ^2 is V11() real ext-real Element of COMPLEX
(3 / 2) * (3 / 2) is non empty V11() real ext-real positive non negative set
sqrt ((3 / 2) ^2) is V11() real ext-real set
(3 / 2) * 2 is non empty V11() real ext-real positive non negative set
(sqrt 5) * 2 is V11() real ext-real set
3 / 4 is non empty V11() real ext-real positive non negative Element of COMPLEX
(2 * (sqrt 5)) / (2 * 2) is V11() real ext-real Element of COMPLEX
0 + (sqrt 5) is V11() real ext-real set
(- 1) + (sqrt 5) is V11() real ext-real set
(- 3) + 3 is V11() real ext-real integer set
(- 1) + 3 is V11() real ext-real integer set
2 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau to_power k is V11() real ext-real set
tau |^ k is V11() real ext-real set
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(tau to_power k) * (Fib n) is V11() real ext-real set
((tau to_power k) * (Fib n)) + (1 / 2) is V11() real ext-real set
[\(((tau to_power k) * (Fib n)) + (1 / 2))/] is V11() real ext-real integer set
n + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Fib (n + k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau_bar to_power k is V11() real ext-real set
tau_bar |^ k is V11() real ext-real set
tau to_power (n + k) is V11() real ext-real set
tau |^ (n + k) is V11() real ext-real set
tau_bar to_power (n + k) is V11() real ext-real set
tau_bar |^ (n + k) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power k) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
(tau to_power k) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power k) * ((tau to_power n) - (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power k) * (tau to_power n) is V11() real ext-real set
((tau to_power k) * (tau to_power n)) - (tau_bar to_power (n + k)) is V11() real ext-real set
(tau to_power k) * (tau_bar to_power n) is V11() real ext-real set
(tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power k) * (tau to_power n)) - (tau_bar to_power (n + k))) + ((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n))) is V11() real ext-real set
((((tau to_power k) * (tau to_power n)) - (tau_bar to_power (n + k))) + ((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau to_power (n + k)) - (tau_bar to_power (n + k)) is V11() real ext-real set
((tau to_power (n + k)) - (tau_bar to_power (n + k))) + ((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n))) is V11() real ext-real set
(((tau to_power (n + k)) - (tau_bar to_power (n + k))) + ((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n)))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau to_power (n + k)) - (tau_bar to_power (n + k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power (n + k)) - (tau_bar to_power (n + k))) / (sqrt 5)) + (((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n))) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(Fib (n + k)) + (((tau_bar to_power (n + k)) - ((tau to_power k) * (tau_bar to_power n))) / (sqrt 5)) is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power k) is V11() real ext-real set
((tau_bar to_power n) * (tau_bar to_power k)) - ((tau to_power k) * (tau_bar to_power n)) is V11() real ext-real set
(((tau_bar to_power n) * (tau_bar to_power k)) - ((tau to_power k) * (tau_bar to_power n))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + k)) + ((((tau_bar to_power n) * (tau_bar to_power k)) - ((tau to_power k) * (tau_bar to_power n))) / (sqrt 5)) is V11() real ext-real set
- (tau_bar to_power n) is V11() real ext-real set
(tau to_power k) - (tau_bar to_power k) is V11() real ext-real set
(- (tau_bar to_power n)) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
((- (tau_bar to_power n)) * ((tau to_power k) - (tau_bar to_power k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(Fib (n + k)) + (((- (tau_bar to_power n)) * ((tau to_power k) - (tau_bar to_power k))) / (sqrt 5)) is V11() real ext-real set
((tau to_power k) - (tau_bar to_power k)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- (tau_bar to_power n)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
(Fib (n + k)) + ((- (tau_bar to_power n)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5))) is V11() real ext-real set
Fib k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(- (tau_bar to_power n)) * (Fib k) is V11() real ext-real set
(Fib (n + k)) + ((- (tau_bar to_power n)) * (Fib k)) is V11() real ext-real set
(tau_bar to_power n) * (Fib k) is V11() real ext-real set
(Fib (n + k)) - ((tau_bar to_power n) * (Fib k)) is V11() real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k + m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power m is V11() real ext-real set
tau_bar |^ m is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
((- 1) to_power k) - (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau_bar to_power m) * (((- 1) to_power k) - (tau_bar to_power (2 * k))) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
- (tau_bar to_power (2 * k)) is V11() real ext-real set
(- (tau_bar to_power (2 * k))) + 1 is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
abs (tau_bar to_power m) is V11() real ext-real non negative Element of REAL
1 - (tau_bar to_power (2 * k)) is V11() real ext-real set
(abs (tau_bar to_power m)) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
((sqrt 5) / 2) * 1 is V11() real ext-real set
(tau_bar to_power m) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
(- 1) - (tau_bar to_power (2 * k)) is V11() real ext-real set
tau_bar * ((- 1) - (tau_bar to_power (2 * k))) is V11() real ext-real set
(1 / 2) + 1 is non empty V11() real ext-real positive non negative set
(tau_bar to_power (2 * k)) + 1 is V11() real ext-real set
(6 / 10) * (3 / 2) is non empty V11() real ext-real positive non negative Element of COMPLEX
1 + (tau_bar to_power (2 * k)) is V11() real ext-real set
(((sqrt 5) - 1) / (sqrt 5)) * (1 + (tau_bar to_power (2 * k))) is V11() real ext-real set
((((sqrt 5) - 1) / (sqrt 5)) * (1 + (tau_bar to_power (2 * k)))) * (sqrt 5) is V11() real ext-real set
(((sqrt 5) - 1) * (1 / (sqrt 5))) * (1 + (tau_bar to_power (2 * k))) is V11() real ext-real set
((((sqrt 5) - 1) * (1 / (sqrt 5))) * (1 + (tau_bar to_power (2 * k)))) * (sqrt 5) is V11() real ext-real set
((sqrt 5) - 1) * (1 + (tau_bar to_power (2 * k))) is V11() real ext-real set
(sqrt 5) * (1 / (sqrt 5)) is V11() real ext-real set
(((sqrt 5) - 1) * (1 + (tau_bar to_power (2 * k)))) * ((sqrt 5) * (1 / (sqrt 5))) is V11() real ext-real set
(((sqrt 5) - 1) * (1 + (tau_bar to_power (2 * k)))) * ((sqrt 5) / (sqrt 5)) is V11() real ext-real set
(((sqrt 5) - 1) * (1 + (tau_bar to_power (2 * k)))) * 1 is V11() real ext-real set
(1 - (sqrt 5)) * ((- 1) - (tau_bar to_power (2 * k))) is V11() real ext-real set
((1 - (sqrt 5)) * ((- 1) - (tau_bar to_power (2 * k)))) / 2 is V11() real ext-real Element of COMPLEX
(tau_bar to_power m) * ((- 1) - (tau_bar to_power (2 * k))) is V11() real ext-real set
(- 1) - (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau_bar to_power m) * ((- 1) - (tau_bar to_power (2 * k))) is V11() real ext-real set
1 + (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau_bar to_power m) * (1 + (tau_bar to_power (2 * k))) is V11() real ext-real set
- ((tau_bar to_power m) * (1 + (tau_bar to_power (2 * k)))) is V11() real ext-real set
(tau_bar to_power (2 * k)) + 1 is V11() real ext-real set
(1 / 2) + 1 is non empty V11() real ext-real positive non negative set
- (- (1 / 2)) is non empty V11() real ext-real positive non negative Element of COMPLEX
- (tau_bar to_power m) is V11() real ext-real set
(- (tau_bar to_power m)) * (1 + (tau_bar to_power (2 * k))) is V11() real ext-real set
(1 / 2) * (3 / 2) is non empty V11() real ext-real positive non negative Element of COMPLEX
(tau to_power k) * (tau_bar to_power k) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + k) is V11() real ext-real set
tau_bar |^ (k + k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - (tau_bar to_power (k + k)) is V11() real ext-real set
(tau_bar to_power m) * (((tau to_power k) * (tau_bar to_power k)) - (tau_bar to_power (k + k))) is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - ((tau_bar to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power m) * (((tau to_power k) * (tau_bar to_power k)) - ((tau_bar to_power k) * (tau_bar to_power k))) is V11() real ext-real set
(tau_bar to_power m) * (tau_bar to_power k) is V11() real ext-real set
((tau_bar to_power m) * (tau_bar to_power k)) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
(((tau_bar to_power m) * (tau_bar to_power k)) * ((tau to_power k) - (tau_bar to_power k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((tau_bar to_power m) * (tau_bar to_power k)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
((tau_bar to_power m) * (tau_bar to_power k)) * (Fib k) is V11() real ext-real set
(1 * (sqrt 5)) / (2 * (sqrt 5)) is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power n) * (Fib k)) is V11() real ext-real set
(- (1 / 2)) + (1 / 2) is V11() real ext-real Element of COMPLEX
(- ((tau_bar to_power n) * (Fib k))) + (1 / 2) is V11() real ext-real set
0 + (Fib (n + k)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((- ((tau_bar to_power n) * (Fib k))) + (1 / 2)) + (Fib (n + k)) is V11() real ext-real set
(((tau to_power k) * (Fib n)) + (1 / 2)) - 1 is V11() real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k + m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power m is V11() real ext-real set
tau_bar |^ m is V11() real ext-real set
1 to_power k is V11() real ext-real set
1 |^ k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((3 - (sqrt 5)) / 2) to_power k is V11() real ext-real set
((3 - (sqrt 5)) / 2) |^ k is V11() real ext-real set
- (((3 - (sqrt 5)) / 2) to_power k) is V11() real ext-real set
(- (((3 - (sqrt 5)) / 2) to_power k)) + 1 is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
1 - (tau_bar to_power (2 * k)) is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
((- 1) to_power k) - (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau to_power k) * (tau_bar to_power k) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + k) is V11() real ext-real set
tau_bar |^ (k + k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - (tau_bar to_power (k + k)) is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - ((tau_bar to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power k) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
1 - (((3 - (sqrt 5)) / 2) to_power k) is V11() real ext-real set
(((sqrt 5) - 1) / (sqrt 5)) * (1 - (((3 - (sqrt 5)) / 2) to_power k)) is V11() real ext-real set
- ((((sqrt 5) - 1) / (sqrt 5)) * (1 - (((3 - (sqrt 5)) / 2) to_power k))) is V11() real ext-real set
- (((sqrt 5) - 1) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- (((sqrt 5) - 1) / (sqrt 5))) * (1 - (((3 - (sqrt 5)) / 2) to_power k)) is V11() real ext-real set
- ((sqrt 5) - 1) is V11() real ext-real set
(- ((sqrt 5) - 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((- ((sqrt 5) - 1)) / (sqrt 5)) * (1 - (((3 - (sqrt 5)) / 2) to_power k)) is V11() real ext-real set
(1 - (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / (sqrt 5)) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
(((1 - (sqrt 5)) / (sqrt 5)) * (1 - (tau_bar to_power (2 * k)))) / 2 is V11() real ext-real Element of COMPLEX
(- 1) / 2 is non empty V11() real ext-real non positive negative Element of COMPLEX
(1 - (tau_bar to_power (2 * k))) / 2 is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / (sqrt 5)) * ((1 - (tau_bar to_power (2 * k))) / 2) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) * (1 / (sqrt 5)) is V11() real ext-real set
(1 - (tau_bar to_power (2 * k))) * (1 / 2) is V11() real ext-real set
((1 - (sqrt 5)) * (1 / (sqrt 5))) * ((1 - (tau_bar to_power (2 * k))) * (1 / 2)) is V11() real ext-real set
tau_bar * (1 / (sqrt 5)) is V11() real ext-real set
(tau_bar * (1 / (sqrt 5))) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
(tau_bar * (1 / (sqrt 5))) * ((tau_bar to_power k) * ((tau to_power k) - (tau_bar to_power k))) is V11() real ext-real set
tau_bar * (tau_bar to_power k) is V11() real ext-real set
((tau to_power k) - (tau_bar to_power k)) * (1 / (sqrt 5)) is V11() real ext-real set
(tau_bar * (tau_bar to_power k)) * (((tau to_power k) - (tau_bar to_power k)) * (1 / (sqrt 5))) is V11() real ext-real set
(tau_bar * (tau_bar to_power k)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power k) is V11() real ext-real set
((tau_bar to_power 1) * (tau_bar to_power k)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
1 + k is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power (1 + k) is V11() real ext-real set
tau_bar |^ (1 + k) is V11() real ext-real set
(tau_bar to_power (1 + k)) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
- (- (1 / 2)) is non empty V11() real ext-real positive non negative Element of COMPLEX
- (tau_bar to_power m) is V11() real ext-real set
(- 1) / 2 is non empty V11() real ext-real non positive negative Element of COMPLEX
(- (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
- (tau_bar to_power (2 * k)) is V11() real ext-real set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- (tau_bar to_power (2 * k))) + 1 is V11() real ext-real set
(- (1 / 2)) + 1 is V11() real ext-real set
(1 / 2) * 1 is non empty V11() real ext-real positive non negative set
1 - (tau_bar to_power (2 * k)) is V11() real ext-real set
(- (tau_bar to_power m)) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
(tau_bar to_power m) * (1 - (tau_bar to_power (2 * k))) is V11() real ext-real set
- ((tau_bar to_power m) * (1 - (tau_bar to_power (2 * k)))) is V11() real ext-real set
- (- ((tau_bar to_power m) * (1 - (tau_bar to_power (2 * k))))) is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
((- 1) to_power k) - (tau_bar to_power (2 * k)) is V11() real ext-real set
(tau_bar to_power m) * (((- 1) to_power k) - (tau_bar to_power (2 * k))) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
- ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
(tau to_power k) * (tau_bar to_power k) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + k) is V11() real ext-real set
tau_bar |^ (k + k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - (tau_bar to_power (k + k)) is V11() real ext-real set
(tau_bar to_power m) * (((tau to_power k) * (tau_bar to_power k)) - (tau_bar to_power (k + k))) is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power k) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power k)) - ((tau_bar to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power m) * (((tau to_power k) * (tau_bar to_power k)) - ((tau_bar to_power k) * (tau_bar to_power k))) is V11() real ext-real set
(tau_bar to_power m) * (tau_bar to_power k) is V11() real ext-real set
((tau_bar to_power m) * (tau_bar to_power k)) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power n) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
((tau_bar to_power n) * ((tau to_power k) - (tau_bar to_power k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
((- (sqrt 5)) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- 1) * (sqrt 5) is V11() real ext-real set
((- 1) * (sqrt 5)) / (2 * (sqrt 5)) is V11() real ext-real Element of COMPLEX
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
k + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
3 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
k * 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (k * 2) is V11() real ext-real set
tau_bar |^ (k * 2) is V11() real ext-real set
tau_bar to_power (3 * 2) is V11() real ext-real set
tau_bar |^ (3 * 2) is V11() real ext-real set
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
(tau_bar to_power (2 * k)) + 1 is V11() real ext-real set
(9 - (4 * (sqrt 5))) + 1 is V11() real ext-real set
20 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
20 / 9 is non empty V11() real ext-real positive non negative Element of COMPLEX
(20 / 9) ^2 is V11() real ext-real Element of COMPLEX
(20 / 9) * (20 / 9) is non empty V11() real ext-real positive non negative set
sqrt ((20 / 9) ^2) is V11() real ext-real set
9 * (sqrt 5) is V11() real ext-real set
(20 / 9) * 9 is non empty V11() real ext-real positive non negative set
8 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
8 * (sqrt 5) is V11() real ext-real set
(sqrt 5) + (8 * (sqrt 5)) is V11() real ext-real set
((sqrt 5) + (8 * (sqrt 5))) - (8 * (sqrt 5)) is V11() real ext-real set
20 - (8 * (sqrt 5)) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
(20 - (8 * (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power (2 * k)) + 1) is V11() real ext-real set
- ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
- (tau_bar to_power (2 * k)) is V11() real ext-real set
(- (tau_bar to_power (2 * k))) + (- 1) is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
(- (tau_bar to_power (2 * k))) + ((- 1) to_power k) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + k) is V11() real ext-real set
tau_bar |^ (k + k) is V11() real ext-real set
- (tau_bar to_power (k + k)) is V11() real ext-real set
(tau to_power k) * (tau_bar to_power k) is V11() real ext-real set
(- (tau_bar to_power (k + k))) + ((tau to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power k) is V11() real ext-real set
- ((tau_bar to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(- ((tau_bar to_power k) * (tau_bar to_power k))) + ((tau to_power k) * (tau_bar to_power k)) is V11() real ext-real set
- (tau_bar to_power k) is V11() real ext-real set
(- (tau_bar to_power k)) + (tau to_power k) is V11() real ext-real set
(tau_bar to_power k) * ((- (tau_bar to_power k)) + (tau to_power k)) is V11() real ext-real set
((tau_bar to_power k) * ((- (tau_bar to_power k)) + (tau to_power k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power k) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
(tau_bar to_power k) * (Fib k) is V11() real ext-real set
((sqrt 5) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
- (((sqrt 5) / 2) / (sqrt 5)) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
- (((sqrt 5) / (sqrt 5)) / 2) is V11() real ext-real Element of COMPLEX
3 / (2 * 2) is non empty V11() real ext-real positive non negative Element of COMPLEX
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
tau_bar to_power (2 * k) is V11() real ext-real set
tau_bar |^ (2 * k) is V11() real ext-real set
(1 / 2) + 1 is non empty V11() real ext-real positive non negative set
(tau_bar to_power (2 * k)) + 1 is V11() real ext-real set
(1 / 2) * ((1 / 2) + 1) is non empty V11() real ext-real positive non negative set
(tau_bar to_power m) * ((tau_bar to_power (2 * k)) + 1) is V11() real ext-real set
(sqrt 5) / 2 is V11() real ext-real Element of COMPLEX
- ((tau_bar to_power m) * ((tau_bar to_power (2 * k)) + 1)) is V11() real ext-real set
- ((sqrt 5) / 2) is V11() real ext-real Element of COMPLEX
- (tau_bar to_power (2 * k)) is V11() real ext-real set
(- (tau_bar to_power (2 * k))) + (- 1) is V11() real ext-real set
(tau_bar to_power m) * ((- (tau_bar to_power (2 * k))) + (- 1)) is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
(- (tau_bar to_power (2 * k))) + ((- 1) to_power k) is V11() real ext-real set
(tau_bar to_power m) * ((- (tau_bar to_power (2 * k))) + ((- 1) to_power k)) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
tau_bar to_power (k + k) is V11() real ext-real set
tau_bar |^ (k + k) is V11() real ext-real set
- (tau_bar to_power (k + k)) is V11() real ext-real set
(tau to_power k) * (tau_bar to_power k) is V11() real ext-real set
(- (tau_bar to_power (k + k))) + ((tau to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power m) * ((- (tau_bar to_power (k + k))) + ((tau to_power k) * (tau_bar to_power k))) is V11() real ext-real set
(tau_bar to_power k) * (tau_bar to_power k) is V11() real ext-real set
- ((tau_bar to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(- ((tau_bar to_power k) * (tau_bar to_power k))) + ((tau to_power k) * (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power m) * ((- ((tau_bar to_power k) * (tau_bar to_power k))) + ((tau to_power k) * (tau_bar to_power k))) is V11() real ext-real set
(tau_bar to_power m) * (tau_bar to_power k) is V11() real ext-real set
((tau_bar to_power m) * (tau_bar to_power k)) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
(tau_bar to_power n) * ((tau to_power k) - (tau_bar to_power k)) is V11() real ext-real set
((tau_bar to_power n) * ((tau to_power k) - (tau_bar to_power k))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- ((sqrt 5) / 2)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * (((tau to_power k) - (tau_bar to_power k)) / (sqrt 5)) is V11() real ext-real set
(- (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
((- (sqrt 5)) / 2) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(- 1) * (sqrt 5) is V11() real ext-real set
((- 1) * (sqrt 5)) / (2 * (sqrt 5)) is V11() real ext-real Element of COMPLEX
(- 1) / 2 is non empty V11() real ext-real non positive negative Element of COMPLEX
- (- (1 / 2)) is non empty V11() real ext-real positive non negative Element of COMPLEX
- ((tau_bar to_power n) * (Fib k)) is V11() real ext-real set
(1 / 2) + (1 / 2) is non empty V11() real ext-real positive non negative Element of COMPLEX
(- ((tau_bar to_power n) * (Fib k))) + (1 / 2) is V11() real ext-real set
((- ((tau_bar to_power n) * (Fib k))) + (1 / 2)) - 1 is V11() real ext-real set
0 + (Fib (n + k)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((- ((tau_bar to_power n) * (Fib k))) + (1 / 2)) - 1) + (Fib (n + k)) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power n) + (1 / 2) is V11() real ext-real set
[\((tau to_power n) + (1 / 2))/] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
(1 / 2) - 1 is V11() real ext-real set
(tau to_power n) + ((1 / 2) - 1) is V11() real ext-real set
((tau to_power n) + (1 / 2)) - 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power n) - (1 / 2) is V11() real ext-real set
[/((tau to_power n) - (1 / 2))\] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(- (1 / 2)) + (tau to_power n) is V11() real ext-real set
(tau_bar to_power n) + (tau to_power n) is V11() real ext-real set
(1 / 2) + (tau to_power n) is V11() real ext-real set
((tau to_power n) - (1 / 2)) + 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
Lucas (2 * n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power (2 * n) is V11() real ext-real set
tau |^ (2 * n) is V11() real ext-real set
[/(tau to_power (2 * n))\] is V11() real ext-real integer set
tau_bar to_power (2 * n) is V11() real ext-real set
tau_bar |^ (2 * n) is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
(tau_bar to_power n) to_power 2 is V11() real ext-real set
(tau_bar to_power n) |^ 2 is V11() real ext-real set
(tau_bar to_power n) ^2 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power n) is V11() real ext-real set
n - 0 is V11() real ext-real integer set
0 + (tau to_power (2 * n)) is V11() real ext-real set
(tau to_power (2 * n)) + (tau_bar to_power (2 * n)) is V11() real ext-real set
1 + (tau to_power (2 * n)) is V11() real ext-real set
(tau_bar to_power (2 * n)) + (tau to_power (2 * n)) is V11() real ext-real set
(tau to_power (2 * n)) + 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer non even set
Lucas ((2 * n) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power ((2 * n) + 1) is V11() real ext-real set
tau |^ ((2 * n) + 1) is V11() real ext-real set
[\(tau to_power ((2 * n) + 1))/] is V11() real ext-real integer set
4 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power ((2 * n) + 1) is V11() real ext-real set
tau_bar |^ ((2 * n) + 1) is V11() real ext-real set
(tau to_power ((2 * n) + 1)) + (tau_bar to_power ((2 * n) + 1)) is V11() real ext-real set
(tau to_power ((2 * n) + 1)) + 0 is V11() real ext-real set
(- 1) + (tau to_power ((2 * n) + 1)) is V11() real ext-real set
(tau to_power ((2 * n) + 1)) - 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau * (Lucas n) is V11() real ext-real non negative set
(tau * (Lucas n)) + 1 is non empty V11() real ext-real positive non negative set
[\((tau * (Lucas n)) + 1)/] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
1 * 3 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(sqrt 5) * 3 is V11() real ext-real set
3 + 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
5 + ((sqrt 5) * 3) is V11() real ext-real set
8 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
8 / 2 is non empty V11() real ext-real positive non negative Element of COMPLEX
(5 + ((sqrt 5) * 3)) / 2 is V11() real ext-real Element of COMPLEX
(- (1 / (sqrt 5))) * (sqrt 5) is V11() real ext-real set
(tau_bar to_power n) * (sqrt 5) is V11() real ext-real set
(- 1) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(sqrt 5) * ((- 1) / (sqrt 5)) is V11() real ext-real set
(sqrt 5) * (- 1) is V11() real ext-real set
((sqrt 5) * (- 1)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
((sqrt 5) / (sqrt 5)) * (- 1) is V11() real ext-real set
1 * (- 1) is non empty V11() real ext-real non positive negative integer set
- ((tau_bar to_power n) * (sqrt 5)) is V11() real ext-real set
- (- 1) is non empty V11() real ext-real positive non negative integer set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
(tau_bar to_power n) * tau is V11() real ext-real set
((tau_bar to_power n) * tau_bar) - ((tau_bar to_power n) * tau) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau_bar to_power n) * (tau_bar to_power 1)) - ((tau_bar to_power n) * tau) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau_bar to_power (n + 1)) - ((tau_bar to_power n) * tau) is V11() real ext-real set
((tau_bar to_power (n + 1)) - ((tau_bar to_power n) * tau)) + ((tau_bar to_power n) * tau) is V11() real ext-real set
1 + ((tau_bar to_power n) * tau) is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(tau_bar to_power (n + 1)) + (tau to_power (n + 1)) is V11() real ext-real set
((tau_bar to_power n) * tau) + 1 is V11() real ext-real set
(((tau_bar to_power n) * tau) + 1) + (tau to_power (n + 1)) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
(((tau_bar to_power n) * tau) + 1) + ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
(((tau_bar to_power n) * tau) + 1) + ((tau to_power n) * tau) is V11() real ext-real set
(tau_bar to_power n) + (tau to_power n) is V11() real ext-real set
((tau_bar to_power n) + (tau to_power n)) * tau is V11() real ext-real set
(((tau_bar to_power n) + (tau to_power n)) * tau) + 1 is V11() real ext-real set
(Lucas n) * tau is V11() real ext-real non negative set
((Lucas n) * tau) + 1 is non empty V11() real ext-real positive non negative set
((tau * (Lucas n)) + 1) - 1 is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
tau * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
tau * (tau to_power n) is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau to_power n)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
((tau to_power 1) * (tau to_power n)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
(tau to_power (n + 1)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau * (Lucas n) is V11() real ext-real non negative set
(tau * (Lucas n)) - 1 is V11() real ext-real set
[/((tau * (Lucas n)) - 1)\] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
tau * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
tau * (tau to_power n) is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(tau * (tau to_power n)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
((tau to_power 1) * (tau to_power n)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
(tau to_power (n + 1)) + (tau * (tau_bar to_power n)) is V11() real ext-real set
(tau * (tau_bar to_power n)) - 1 is V11() real ext-real set
1 / (1 / (sqrt 5)) is V11() real ext-real Element of COMPLEX
1 / (tau_bar to_power n) is V11() real ext-real Element of COMPLEX
(1 / (tau_bar to_power n)) * 2 is V11() real ext-real set
(2 * (sqrt 5)) + 1 is V11() real ext-real set
((1 / (tau_bar to_power n)) * 2) + 1 is V11() real ext-real set
((2 * (sqrt 5)) + 1) - (sqrt 5) is V11() real ext-real set
(((1 / (tau_bar to_power n)) * 2) + 1) - (sqrt 5) is V11() real ext-real set
(sqrt 5) + 1 is V11() real ext-real set
((sqrt 5) + 1) / 2 is V11() real ext-real Element of COMPLEX
((1 / (tau_bar to_power n)) * 2) + (1 - (sqrt 5)) is V11() real ext-real set
(((1 / (tau_bar to_power n)) * 2) + (1 - (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
(1 / (tau_bar to_power n)) + tau_bar is V11() real ext-real set
((1 / (tau_bar to_power n)) + tau_bar) * (tau_bar to_power n) is V11() real ext-real set
(1 / (tau_bar to_power n)) * (tau_bar to_power n) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
((1 / (tau_bar to_power n)) * (tau_bar to_power n)) + (tau_bar * (tau_bar to_power n)) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
((1 / (tau_bar to_power n)) * (tau_bar to_power n)) + ((tau_bar to_power 1) * (tau_bar to_power n)) is V11() real ext-real set
1 + ((tau_bar to_power 1) * (tau_bar to_power n)) is V11() real ext-real set
1 + (tau_bar to_power (n + 1)) is V11() real ext-real set
(1 + (tau_bar to_power (n + 1))) - 1 is V11() real ext-real set
(tau to_power (n + 1)) + ((tau * (tau_bar to_power n)) - 1) is V11() real ext-real set
((tau * (Lucas n)) - 1) + 1 is V11() real ext-real set
- tau_bar is non empty V11() real ext-real positive non negative set
(- tau_bar) to_power n is V11() real ext-real set
(- tau_bar) |^ n is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
4 * ((- 1) to_power n) is V11() real ext-real set
((Lucas n) ^2) - (4 * ((- 1) to_power n)) is V11() real ext-real set
5 * (((Lucas n) ^2) - (4 * ((- 1) to_power n))) is V11() real ext-real set
sqrt (5 * (((Lucas n) ^2) - (4 * ((- 1) to_power n)))) is V11() real ext-real set
(Lucas n) + (sqrt (5 * (((Lucas n) ^2) - (4 * ((- 1) to_power n))))) is V11() real ext-real set
((Lucas n) + (sqrt (5 * (((Lucas n) ^2) - (4 * ((- 1) to_power n)))))) / 2 is V11() real ext-real Element of COMPLEX
((- 1) to_power n) * 4 is V11() real ext-real set
((Lucas n) ^2) - (((- 1) to_power n) * 4) is V11() real ext-real set
1 * 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(2 * 2) - (1 * 4) is V11() real ext-real integer set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
- 4 is non empty V11() real ext-real non positive negative integer set
- (4 * ((- 1) to_power n)) is V11() real ext-real set
(2 * 2) + (- 4) is V11() real ext-real integer set
((Lucas n) ^2) + (- (4 * ((- 1) to_power n))) is V11() real ext-real set
n - 0 is V11() real ext-real integer set
2 * (Lucas (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(Lucas n) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(5 * (Fib n)) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) * 1) + ((5 * (Fib n)) * 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(5 * (Fib n)) + (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((5 * (Fib n)) + (Lucas n)) / 2 is V11() real ext-real non negative Element of COMPLEX
(Fib n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) ^2) - (5 * ((Fib n) ^2)) is V11() real ext-real integer set
(Lucas n) to_power 2 is V11() real ext-real set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) to_power 2) - (5 * ((Fib n) ^2)) is V11() real ext-real set
(Fib n) to_power 2 is V11() real ext-real set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Fib n) to_power 2) is V11() real ext-real set
((Lucas n) to_power 2) - (5 * ((Fib n) to_power 2)) is V11() real ext-real set
(Fib n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 * ((Fib n) |^ 2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(Lucas n) |^ 2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2) is V11() real ext-real integer set
- ((5 * ((Fib n) |^ 2)) - ((Lucas n) |^ 2)) is V11() real ext-real integer set
(- 1) to_power (n + 1) is V11() real ext-real set
(- 1) |^ (n + 1) is V11() real ext-real set
4 * ((- 1) to_power (n + 1)) is V11() real ext-real set
- (4 * ((- 1) to_power (n + 1))) is V11() real ext-real set
((- 1) to_power (n + 1)) * 4 is V11() real ext-real set
(- 1) * (((- 1) to_power (n + 1)) * 4) is V11() real ext-real set
(- 1) to_power 1 is V11() real ext-real set
(- 1) |^ 1 is V11() real ext-real set
((- 1) to_power 1) * (((- 1) to_power (n + 1)) * 4) is V11() real ext-real set
((- 1) to_power 1) * ((- 1) to_power (n + 1)) is V11() real ext-real set
(((- 1) to_power 1) * ((- 1) to_power (n + 1))) * 4 is V11() real ext-real set
(n + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- 1) to_power ((n + 1) + 1) is V11() real ext-real set
(- 1) |^ ((n + 1) + 1) is V11() real ext-real set
((- 1) to_power ((n + 1) + 1)) * 4 is V11() real ext-real set
n + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(- 1) to_power (n + 2) is V11() real ext-real set
(- 1) |^ (n + 2) is V11() real ext-real set
((- 1) to_power (n + 2)) * 4 is V11() real ext-real set
(- 1) to_power 2 is V11() real ext-real set
(- 1) |^ 2 is V11() real ext-real set
((- 1) to_power n) * ((- 1) to_power 2) is V11() real ext-real set
(((- 1) to_power n) * ((- 1) to_power 2)) * 4 is V11() real ext-real set
((- 1) to_power n) * 1 is V11() real ext-real set
(((- 1) to_power n) * 1) * 4 is V11() real ext-real set
(((Lucas n) ^2) - (((- 1) to_power n) * 4)) / 5 is V11() real ext-real Element of COMPLEX
sqrt ((((Lucas n) ^2) - (((- 1) to_power n) * 4)) / 5) is V11() real ext-real set
sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4)) is V11() real ext-real set
(sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) / (sqrt 5) is V11() real ext-real Element of COMPLEX
5 * ((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) / (sqrt 5)) is V11() real ext-real set
(5 * ((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) / (sqrt 5))) + (Lucas n) is V11() real ext-real set
((5 * ((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) / (sqrt 5))) + (Lucas n)) / 2 is V11() real ext-real Element of COMPLEX
(sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * 5 is V11() real ext-real set
((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * 5) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * 5) / (sqrt 5)) + (Lucas n) is V11() real ext-real set
((((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * 5) / (sqrt 5)) + (Lucas n)) / 2 is V11() real ext-real Element of COMPLEX
5 / (sqrt 5) is V11() real ext-real Element of COMPLEX
(sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (5 / (sqrt 5)) is V11() real ext-real set
((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (5 / (sqrt 5))) + (Lucas n) is V11() real ext-real set
(((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (5 / (sqrt 5))) + (Lucas n)) / 2 is V11() real ext-real Element of COMPLEX
(sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (sqrt 5) is V11() real ext-real set
((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (sqrt 5)) + (Lucas n) is V11() real ext-real set
(((sqrt (((Lucas n) ^2) - (((- 1) to_power n) * 4))) * (sqrt 5)) + (Lucas n)) / 2 is V11() real ext-real Element of COMPLEX
(((Lucas n) ^2) - (((- 1) to_power n) * 4)) * 5 is V11() real ext-real set
sqrt ((((Lucas n) ^2) - (((- 1) to_power n) * 4)) * 5) is V11() real ext-real set
(sqrt ((((Lucas n) ^2) - (((- 1) to_power n) * 4)) * 5)) + (Lucas n) is V11() real ext-real set
((sqrt ((((Lucas n) ^2) - (((- 1) to_power n) * 4)) * 5)) + (Lucas n)) / 2 is V11() real ext-real Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Lucas n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas n) * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
5 * ((Lucas n) ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(5 * ((Lucas n) ^2)) - (2 * (Lucas n)) is V11() real ext-real integer set
((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1 is V11() real ext-real integer set
sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1) is V11() real ext-real set
((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1)) is V11() real ext-real set
(((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) / 2 is V11() real ext-real Element of COMPLEX
[\((((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) / 2)/] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
n - 0 is V11() real ext-real integer set
0 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Lucas (n + 1)) + (Lucas (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((Lucas n) + 1) - (Lucas n) is V11() real ext-real integer set
((Lucas (n + 1)) + (Lucas (n + 1))) - (Lucas n) is V11() real ext-real integer set
2 * (Lucas (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * (Lucas (n + 1))) - (Lucas n) is V11() real ext-real integer set
((2 * (Lucas (n + 1))) - (Lucas n)) - 1 is V11() real ext-real integer set
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
(2 * (Lucas (n + 1))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * (Lucas (n + 1))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
((tau to_power n) * (tau to_power 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
2 * (((tau to_power n) * (tau to_power 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(2 * (((tau to_power n) * (tau to_power 1)) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * (((tau to_power n) * (tau to_power 1)) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) + (tau_bar to_power (n + 1)) is V11() real ext-real set
2 * (((tau to_power n) * tau) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(2 * (((tau to_power n) * tau) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * (((tau to_power n) * tau) + (tau_bar to_power (n + 1)))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau to_power n) * tau) + ((tau_bar to_power n) * (tau_bar to_power 1)) is V11() real ext-real set
2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * (tau_bar to_power 1))) is V11() real ext-real set
(2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * (tau_bar to_power 1)))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * (tau_bar to_power 1)))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
((tau to_power n) * tau) + ((tau_bar to_power n) * tau_bar) is V11() real ext-real set
2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * tau_bar)) is V11() real ext-real set
(2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * tau_bar))) - ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((2 * (((tau to_power n) * tau) + ((tau_bar to_power n) * tau_bar))) - ((tau to_power n) + (tau_bar to_power n))) - 1 is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * (sqrt 5) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) - 1 is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5)) * (sqrt 5) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5)) * (sqrt 5)) - 1 is V11() real ext-real set
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) * (sqrt 5) is V11() real ext-real set
((Fib n) * (sqrt 5)) * (sqrt 5) is V11() real ext-real set
(((Fib n) * (sqrt 5)) * (sqrt 5)) - 1 is V11() real ext-real set
(Fib n) * ((sqrt 5) ^2) is V11() real ext-real set
((Fib n) * ((sqrt 5) ^2)) - 1 is V11() real ext-real set
5 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(5 * (Fib n)) - 1 is V11() real ext-real integer set
(((2 * (Lucas (n + 1))) - (Lucas n)) - 1) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(((2 * (Lucas (n + 1))) - (Lucas n)) - 1) * (((2 * (Lucas (n + 1))) - (Lucas n)) - 1) is V11() real ext-real integer set
(5 * (Fib n)) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(5 * (Fib n)) * (5 * (Fib n)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * (5 * (Fib n)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * (5 * (Fib n))) * 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
((5 * (Fib n)) ^2) - ((2 * (5 * (Fib n))) * 1) is V11() real ext-real integer set
(((5 * (Fib n)) ^2) - ((2 * (5 * (Fib n))) * 1)) + (1 ^2) is V11() real ext-real integer set
25 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
(Fib n) ^2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Fib n) * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
25 * ((Fib n) ^2) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
10 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(25 * ((Fib n) ^2)) - (10 * (Fib n)) is V11() real ext-real integer set
((25 * ((Fib n) ^2)) - (10 * (Fib n))) + 1 is V11() real ext-real integer set
4 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
(5 * ((Lucas n) ^2)) - (2 * ((tau to_power n) + (tau_bar to_power n))) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) ^2 is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
5 * (((tau to_power n) + (tau_bar to_power n)) ^2) is V11() real ext-real set
(5 * (((tau to_power n) + (tau_bar to_power n)) ^2)) - (2 * ((tau to_power n) + (tau_bar to_power n))) is V11() real ext-real set
(tau to_power n) ^2 is V11() real ext-real set
(tau to_power n) * (tau to_power n) is V11() real ext-real set
5 * ((tau to_power n) ^2) is V11() real ext-real set
5 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(5 * 2) * (tau to_power n) is V11() real ext-real set
((5 * 2) * (tau to_power n)) * (tau_bar to_power n) is V11() real ext-real set
(5 * ((tau to_power n) ^2)) + (((5 * 2) * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
(tau_bar to_power n) ^2 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power n) is V11() real ext-real set
5 * ((tau_bar to_power n) ^2) is V11() real ext-real set
((5 * ((tau to_power n) ^2)) + (((5 * 2) * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
2 * (tau to_power n) is V11() real ext-real set
(((5 * ((tau to_power n) ^2)) + (((5 * 2) * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - (2 * (tau to_power n)) is V11() real ext-real set
2 * (tau_bar to_power n) is V11() real ext-real set
((((5 * ((tau to_power n) ^2)) + (((5 * 2) * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
10 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
(25 * ((Fib n) ^2)) - (10 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) ^2 is V11() real ext-real Element of COMPLEX
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
25 * ((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) ^2) is V11() real ext-real set
(25 * ((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) ^2)) - (10 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) ^2 is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) ^2) / ((sqrt 5) ^2) is V11() real ext-real Element of COMPLEX
25 * ((((tau to_power n) - (tau_bar to_power n)) ^2) / ((sqrt 5) ^2)) is V11() real ext-real set
(25 * ((((tau to_power n) - (tau_bar to_power n)) ^2) / ((sqrt 5) ^2))) - (10 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) ^2) / 5 is V11() real ext-real Element of COMPLEX
25 * ((((tau to_power n) - (tau_bar to_power n)) ^2) / 5) is V11() real ext-real set
(25 * ((((tau to_power n) - (tau_bar to_power n)) ^2) / 5)) - (10 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) is V11() real ext-real set
(5 * ((tau to_power n) ^2)) - (((5 * 2) * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
((5 * ((tau to_power n) ^2)) - (((5 * 2) * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / ((sqrt 5) ^2) is V11() real ext-real Element of COMPLEX
10 * ((((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / ((sqrt 5) ^2)) is V11() real ext-real set
(((5 * ((tau to_power n) ^2)) - (((5 * 2) * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - (10 * ((((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / ((sqrt 5) ^2))) is V11() real ext-real set
10 * (tau to_power n) is V11() real ext-real set
(10 * (tau to_power n)) * (tau_bar to_power n) is V11() real ext-real set
(5 * ((tau to_power n) ^2)) - ((10 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
((5 * ((tau to_power n) ^2)) - ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / 5 is V11() real ext-real Element of COMPLEX
10 * ((((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / 5) is V11() real ext-real set
(((5 * ((tau to_power n) ^2)) - ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - (10 * ((((tau to_power n) - (tau_bar to_power n)) * (sqrt 5)) / 5)) is V11() real ext-real set
(2 * (tau to_power n)) * (sqrt 5) is V11() real ext-real set
(((5 * ((tau to_power n) ^2)) - ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - ((2 * (tau to_power n)) * (sqrt 5)) is V11() real ext-real set
(2 * (tau_bar to_power n)) * (sqrt 5) is V11() real ext-real set
((((5 * ((tau to_power n) ^2)) - ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - ((2 * (tau to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
n -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(n -' 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(n + 1) -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
- 10 is non empty V11() real ext-real non positive negative integer set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
10 * ((- 1) to_power n) is V11() real ext-real set
5 -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
5 - 1 is V11() real ext-real integer set
Lucas (n -' 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
(Lucas (n -' 1)) * (- 2) is non empty V11() real ext-real non positive negative integer set
5 * (- 2) is non empty V11() real ext-real non positive negative integer set
Lucas ((n -' 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
2 * (Lucas (n -' 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(2 * (Lucas (n -' 1))) + (Lucas ((n -' 1) + 1)) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Lucas ((n -' 1) + 1)) - ((2 * (Lucas (n -' 1))) + (Lucas ((n -' 1) + 1))) is V11() real ext-real integer set
(Lucas n) - (5 * (Fib n)) is V11() real ext-real integer set
((tau to_power n) + (tau_bar to_power n)) - (5 * (Fib n)) is V11() real ext-real set
5 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - (5 * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5)) is V11() real ext-real set
5 * (((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5))) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - (5 * (((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5)))) is V11() real ext-real set
5 * (1 / (sqrt 5)) is V11() real ext-real set
(5 * (1 / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - ((5 * (1 / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n))) is V11() real ext-real set
((sqrt 5) ^2) * (1 / (sqrt 5)) is V11() real ext-real set
(((sqrt 5) ^2) * (1 / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - ((((sqrt 5) ^2) * (1 / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n))) is V11() real ext-real set
(sqrt 5) * (1 / (sqrt 5)) is V11() real ext-real set
(sqrt 5) * ((sqrt 5) * (1 / (sqrt 5))) is V11() real ext-real set
((sqrt 5) * ((sqrt 5) * (1 / (sqrt 5)))) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - (((sqrt 5) * ((sqrt 5) * (1 / (sqrt 5)))) * ((tau to_power n) - (tau_bar to_power n))) is V11() real ext-real set
(sqrt 5) * ((sqrt 5) / (sqrt 5)) is V11() real ext-real set
((sqrt 5) * ((sqrt 5) / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - (((sqrt 5) * ((sqrt 5) / (sqrt 5))) * ((tau to_power n) - (tau_bar to_power n))) is V11() real ext-real set
(sqrt 5) * 1 is V11() real ext-real set
((sqrt 5) * 1) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - (((sqrt 5) * 1) * ((tau to_power n) - (tau_bar to_power n))) is V11() real ext-real set
(sqrt 5) * (tau to_power n) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) - ((sqrt 5) * (tau to_power n)) is V11() real ext-real set
(sqrt 5) * (tau_bar to_power n) is V11() real ext-real set
(((tau to_power n) + (tau_bar to_power n)) - ((sqrt 5) * (tau to_power n))) + ((sqrt 5) * (tau_bar to_power n)) is V11() real ext-real set
(tau * tau_bar) to_power n is V11() real ext-real set
(tau * tau_bar) |^ n is V11() real ext-real set
10 * ((tau * tau_bar) to_power n) is V11() real ext-real set
((((tau to_power n) + (tau_bar to_power n)) - ((sqrt 5) * (tau to_power n))) + ((sqrt 5) * (tau_bar to_power n))) - (10 * ((tau * tau_bar) to_power n)) is V11() real ext-real set
(10 * ((tau * tau_bar) to_power n)) - (10 * ((tau * tau_bar) to_power n)) is V11() real ext-real set
(((((tau to_power n) + (tau_bar to_power n)) - ((sqrt 5) * (tau to_power n))) + ((sqrt 5) * (tau_bar to_power n))) - (10 * ((tau * tau_bar) to_power n))) + ((sqrt 5) * (tau to_power n)) is V11() real ext-real set
0 + ((sqrt 5) * (tau to_power n)) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) + ((sqrt 5) * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) + (tau_bar to_power n)) + ((sqrt 5) * (tau_bar to_power n))) - (10 * ((tau * tau_bar) to_power n)) is V11() real ext-real set
(tau to_power n) * (tau_bar to_power n) is V11() real ext-real set
10 * ((tau to_power n) * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) + (tau_bar to_power n)) + ((sqrt 5) * (tau_bar to_power n))) - (10 * ((tau to_power n) * (tau_bar to_power n))) is V11() real ext-real set
- ((10 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
(- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (tau to_power n) is V11() real ext-real set
((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (tau to_power n)) + (tau_bar to_power n) is V11() real ext-real set
(tau_bar to_power n) * (sqrt 5) is V11() real ext-real set
(((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (tau to_power n)) + (tau_bar to_power n)) + ((tau_bar to_power n) * (sqrt 5)) is V11() real ext-real set
((((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (tau to_power n)) + (tau_bar to_power n)) + ((tau_bar to_power n) * (sqrt 5))) * 2 is V11() real ext-real set
(tau to_power n) * (sqrt 5) is V11() real ext-real set
((tau to_power n) * (sqrt 5)) * 2 is V11() real ext-real set
- ((2 * (tau to_power n)) * (sqrt 5)) is V11() real ext-real set
20 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
20 * (tau to_power n) is V11() real ext-real set
(20 * (tau to_power n)) * (tau_bar to_power n) is V11() real ext-real set
- ((20 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
(- ((20 * (tau to_power n)) * (tau_bar to_power n))) + (2 * (tau to_power n)) is V11() real ext-real set
((- ((20 * (tau to_power n)) * (tau_bar to_power n))) + (2 * (tau to_power n))) + (2 * (tau_bar to_power n)) is V11() real ext-real set
(((- ((20 * (tau to_power n)) * (tau_bar to_power n))) + (2 * (tau to_power n))) + (2 * (tau_bar to_power n))) + ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
- ((((- ((20 * (tau to_power n)) * (tau_bar to_power n))) + (2 * (tau to_power n))) + (2 * (tau_bar to_power n))) + ((2 * (tau_bar to_power n)) * (sqrt 5))) is V11() real ext-real set
(- ((2 * (tau to_power n)) * (sqrt 5))) - ((10 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n)) is V11() real ext-real set
(((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
((((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) - ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
(((((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) - ((2 * (tau_bar to_power n)) * (sqrt 5))) + ((10 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
((((((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) - ((2 * (tau_bar to_power n)) * (sqrt 5))) + ((10 * (tau to_power n)) * (tau_bar to_power n))) - ((10 * (tau to_power n)) * (tau_bar to_power n)) is V11() real ext-real set
(- ((10 * (tau to_power n)) * (tau_bar to_power n))) - ((2 * (tau to_power n)) * (sqrt 5)) is V11() real ext-real set
((- ((10 * (tau to_power n)) * (tau_bar to_power n))) - ((2 * (tau to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
(((((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) - ((2 * (tau_bar to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
(((- ((10 * (tau to_power n)) * (tau_bar to_power n))) - ((2 * (tau to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
((((10 * (tau to_power n)) * (tau_bar to_power n)) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
(- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - ((2 * (tau to_power n)) * (sqrt 5)) is V11() real ext-real set
(((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - ((2 * (tau to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5)) is V11() real ext-real set
((((- ((10 * (tau to_power n)) * (tau_bar to_power n))) + (5 * ((tau_bar to_power n) ^2))) - ((2 * (tau to_power n)) * (sqrt 5))) + ((2 * (tau_bar to_power n)) * (sqrt 5))) + (5 * ((tau to_power n) ^2)) is V11() real ext-real set
((10 * (tau to_power n)) * (tau_bar to_power n)) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
(((10 * (tau to_power n)) * (tau_bar to_power n)) + (5 * ((tau_bar to_power n) ^2))) - (2 * (tau to_power n)) is V11() real ext-real set
((((10 * (tau to_power n)) * (tau_bar to_power n)) + (5 * ((tau_bar to_power n) ^2))) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
(((((10 * (tau to_power n)) * (tau_bar to_power n)) + (5 * ((tau_bar to_power n) ^2))) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2)) is V11() real ext-real set
sqrt ((((2 * (Lucas (n + 1))) - (Lucas n)) - 1) ^2) is V11() real ext-real set
(((2 * (Lucas (n + 1))) - (Lucas n)) - 1) + ((Lucas n) + 1) is V11() real ext-real integer set
(sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1)) + ((Lucas n) + 1) is V11() real ext-real set
(2 * (Lucas (n + 1))) / 2 is V11() real ext-real non negative Element of COMPLEX
((((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) / 2) - 1 is V11() real ext-real set
4 / 5 is non empty V11() real ext-real positive non negative Element of COMPLEX
(Lucas n) / 5 is V11() real ext-real non negative Element of COMPLEX
Fib n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
3 + (4 / 5) is non empty V11() real ext-real positive non negative set
(Fib n) + ((Lucas n) / 5) is V11() real ext-real non negative set
(- 1) to_power n is V11() real ext-real set
(- 1) |^ n is V11() real ext-real set
2 * ((- 1) to_power n) is V11() real ext-real set
(tau to_power n) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) + ((Lucas n) / 5) is V11() real ext-real Element of COMPLEX
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) / 5 is V11() real ext-real Element of COMPLEX
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) + (((tau to_power n) + (tau_bar to_power n)) / 5) is V11() real ext-real Element of COMPLEX
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) + (((tau to_power n) + (tau_bar to_power n)) / 5)) * 10 is V11() real ext-real set
(2 * ((- 1) to_power n)) * 10 is V11() real ext-real set
2 * 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (2 * 5) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) * 2 is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (2 * 5)) + (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
20 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
20 * ((- 1) to_power n) is V11() real ext-real set
2 * ((sqrt 5) ^2) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (2 * ((sqrt 5) ^2)) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (2 * ((sqrt 5) ^2))) + (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5)) * ((sqrt 5) * 2) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) * (sqrt 5)) * ((sqrt 5) * 2)) + (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5)) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5))) + (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
(tau to_power n) ^2 is V11() real ext-real set
(tau to_power n) * (tau to_power n) is V11() real ext-real set
5 * ((tau to_power n) ^2) is V11() real ext-real set
(tau_bar to_power n) ^2 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power n) is V11() real ext-real set
5 * ((tau_bar to_power n) ^2) is V11() real ext-real set
(5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1 is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5))) + (((tau to_power n) + (tau_bar to_power n)) * 2)) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1) is V11() real ext-real set
(20 * ((- 1) to_power n)) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1) is V11() real ext-real set
(((((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5))) + (((tau to_power n) + (tau_bar to_power n)) * 2)) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1)) - (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
((20 * ((- 1) to_power n)) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1)) - (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
(((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5))) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1) is V11() real ext-real set
10 * ((- 1) to_power n) is V11() real ext-real set
((((tau to_power n) - (tau_bar to_power n)) * (2 * (sqrt 5))) + (((5 * ((tau to_power n) ^2)) + (5 * ((tau_bar to_power n) ^2))) + 1)) - (10 * ((- 1) to_power n)) is V11() real ext-real set
(10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n)) is V11() real ext-real set
((10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n))) + (5 * ((tau to_power n) ^2)) is V11() real ext-real set
(((10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
((((10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) + 1 is V11() real ext-real set
(((((10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) + 1) - (((tau to_power n) + (tau_bar to_power n)) * 2) is V11() real ext-real set
((((((10 * ((- 1) to_power n)) + (10 * ((- 1) to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) + 1) - (((tau to_power n) + (tau_bar to_power n)) * 2)) - (10 * ((- 1) to_power n)) is V11() real ext-real set
(2 * (sqrt 5)) * (tau to_power n) is V11() real ext-real set
(2 * (sqrt 5)) * (tau_bar to_power n) is V11() real ext-real set
((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n)) is V11() real ext-real set
(((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2)) is V11() real ext-real set
((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2)) is V11() real ext-real set
(((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) - (10 * ((- 1) to_power n)) is V11() real ext-real set
((((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) - (10 * ((- 1) to_power n))) + 1 is V11() real ext-real set
(tau * tau_bar) to_power n is V11() real ext-real set
(tau * tau_bar) |^ n is V11() real ext-real set
2 * ((tau * tau_bar) to_power n) is V11() real ext-real set
(2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2) is V11() real ext-real set
((2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2) is V11() real ext-real set
5 * (((2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2)) is V11() real ext-real set
(5 * (((2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1 is V11() real ext-real set
2 * (tau to_power n) is V11() real ext-real set
((5 * (((2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1) - (2 * (tau to_power n)) is V11() real ext-real set
2 * (tau_bar to_power n) is V11() real ext-real set
(((5 * (((2 * ((tau * tau_bar) to_power n)) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
5 * 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(5 * 2) * ((- 1) to_power n) is V11() real ext-real set
(((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) - ((5 * 2) * ((- 1) to_power n)) is V11() real ext-real set
((((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((tau to_power n) ^2))) + (5 * ((tau_bar to_power n) ^2))) - ((5 * 2) * ((- 1) to_power n))) + 1 is V11() real ext-real set
(tau to_power n) * (tau_bar to_power n) is V11() real ext-real set
2 * ((tau to_power n) * (tau_bar to_power n)) is V11() real ext-real set
(2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2) is V11() real ext-real set
((2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2) is V11() real ext-real set
5 * (((2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2)) is V11() real ext-real set
(5 * (((2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1 is V11() real ext-real set
((5 * (((2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1) - (2 * (tau to_power n)) is V11() real ext-real set
(((5 * (((2 * ((tau to_power n) * (tau_bar to_power n))) + ((tau to_power n) ^2)) + ((tau_bar to_power n) ^2))) + 1) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
((tau to_power n) ^2) + ((tau_bar to_power n) ^2) is V11() real ext-real set
(((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau * tau_bar) to_power n)) is V11() real ext-real set
5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau * tau_bar) to_power n))) is V11() real ext-real set
(((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau * tau_bar) to_power n)))) is V11() real ext-real set
((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau * tau_bar) to_power n))))) + 1 is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) ^2 is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
5 * (((tau to_power n) + (tau_bar to_power n)) ^2) is V11() real ext-real set
(5 * (((tau to_power n) + (tau_bar to_power n)) ^2)) + 1 is V11() real ext-real set
((5 * (((tau to_power n) + (tau_bar to_power n)) ^2)) + 1) - (2 * (tau to_power n)) is V11() real ext-real set
(((5 * (((tau to_power n) + (tau_bar to_power n)) ^2)) + 1) - (2 * (tau to_power n))) - (2 * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau to_power n) * (tau_bar to_power n))) is V11() real ext-real set
5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau to_power n) * (tau_bar to_power n)))) is V11() real ext-real set
(((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau to_power n) * (tau_bar to_power n))))) is V11() real ext-real set
((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * ((((tau to_power n) ^2) + ((tau_bar to_power n) ^2)) - (2 * ((tau to_power n) * (tau_bar to_power n)))))) + 1 is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) ^2 is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
5 * (((tau to_power n) - (tau_bar to_power n)) ^2) is V11() real ext-real set
(((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * (((tau to_power n) - (tau_bar to_power n)) ^2)) is V11() real ext-real set
((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (5 * (((tau to_power n) - (tau_bar to_power n)) ^2))) + 1 is V11() real ext-real set
2 * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((5 * (((tau to_power n) + (tau_bar to_power n)) ^2)) + 1) - (2 * ((tau to_power n) + (tau_bar to_power n))) is V11() real ext-real set
(5 * ((Lucas n) ^2)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((5 * ((Lucas n) ^2)) + 1) - (2 * (Lucas n)) is V11() real ext-real integer set
5 * 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
5 * (Lucas n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
20 - 2 is V11() real ext-real integer set
(5 * (Lucas n)) - 2 is V11() real ext-real integer set
18 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
4 * 18 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(Lucas n) * ((5 * (Lucas n)) - 2) is V11() real ext-real integer set
(4 * 18) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((Lucas n) * ((5 * (Lucas n)) - 2)) + 1 is V11() real ext-real integer set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
2 * (tau to_power (n + 1)) is V11() real ext-real set
(2 * (tau to_power (n + 1))) - (tau to_power n) is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
2 * (tau_bar to_power (n + 1)) is V11() real ext-real set
((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1))) is V11() real ext-real set
(((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n) is V11() real ext-real set
((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
2 * ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
(2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n) is V11() real ext-real set
((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1))) is V11() real ext-real set
(((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n) is V11() real ext-real set
((((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
2 * ((tau_bar to_power n) * (tau_bar to_power 1)) is V11() real ext-real set
((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1))) is V11() real ext-real set
(((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1)))) - (tau_bar to_power n) is V11() real ext-real set
((((2 * ((tau to_power n) * (tau to_power 1))) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1)))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
2 * ((tau to_power n) * tau) is V11() real ext-real set
(2 * ((tau to_power n) * tau)) - (tau to_power n) is V11() real ext-real set
((2 * ((tau to_power n) * tau)) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1))) is V11() real ext-real set
(((2 * ((tau to_power n) * tau)) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1)))) - (tau_bar to_power n) is V11() real ext-real set
((((2 * ((tau to_power n) * tau)) - (tau to_power n)) + (2 * ((tau_bar to_power n) * (tau_bar to_power 1)))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
(tau to_power n) * (sqrt 5) is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
2 * ((tau_bar to_power n) * tau_bar) is V11() real ext-real set
((tau to_power n) * (sqrt 5)) + (2 * ((tau_bar to_power n) * tau_bar)) is V11() real ext-real set
(((tau to_power n) * (sqrt 5)) + (2 * ((tau_bar to_power n) * tau_bar))) - (tau_bar to_power n) is V11() real ext-real set
((((tau to_power n) * (sqrt 5)) + (2 * ((tau_bar to_power n) * tau_bar))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
(sqrt 5) * ((tau to_power n) - (tau_bar to_power n)) is V11() real ext-real set
((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * 1 is V11() real ext-real set
(((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * 1) + 1 is V11() real ext-real set
((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * ((sqrt 5) / (sqrt 5)) is V11() real ext-real set
(((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * ((sqrt 5) / (sqrt 5))) + 1 is V11() real ext-real set
(sqrt 5) * (1 / (sqrt 5)) is V11() real ext-real set
((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * ((sqrt 5) * (1 / (sqrt 5))) is V11() real ext-real set
(((sqrt 5) * ((tau to_power n) - (tau_bar to_power n))) * ((sqrt 5) * (1 / (sqrt 5)))) + 1 is V11() real ext-real set
((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5)) is V11() real ext-real set
(sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5))) is V11() real ext-real set
((sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5)))) * (sqrt 5) is V11() real ext-real set
(((sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) * (1 / (sqrt 5)))) * (sqrt 5)) + 1 is V11() real ext-real set
(sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5)) is V11() real ext-real set
((sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) * (sqrt 5) is V11() real ext-real set
(((sqrt 5) * (((tau to_power n) - (tau_bar to_power n)) / (sqrt 5))) * (sqrt 5)) + 1 is V11() real ext-real set
(sqrt 5) * (Fib n) is V11() real ext-real set
((sqrt 5) * (Fib n)) * (sqrt 5) is V11() real ext-real set
(((sqrt 5) * (Fib n)) * (sqrt 5)) + 1 is V11() real ext-real set
((sqrt 5) ^2) * (Fib n) is V11() real ext-real set
(((sqrt 5) ^2) * (Fib n)) + 1 is V11() real ext-real set
5 * (Fib n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(5 * (Fib n)) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((sqrt 5) ^2) * (((tau to_power n) - (tau_bar to_power n)) ^2) is V11() real ext-real set
(((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (((sqrt 5) ^2) * (((tau to_power n) - (tau_bar to_power n)) ^2)) is V11() real ext-real set
((((2 * (sqrt 5)) * (tau to_power n)) - ((2 * (sqrt 5)) * (tau_bar to_power n))) + (((sqrt 5) ^2) * (((tau to_power n) - (tau_bar to_power n)) ^2))) + 1 is V11() real ext-real set
2 * tau is non empty V11() real ext-real positive non negative set
(2 * tau) * (tau to_power n) is V11() real ext-real set
1 * (tau to_power n) is V11() real ext-real set
((2 * tau) * (tau to_power n)) - (1 * (tau to_power n)) is V11() real ext-real set
2 * tau_bar is non empty V11() real ext-real non positive negative set
(2 * tau_bar) * (tau_bar to_power n) is V11() real ext-real set
(((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
1 * (tau_bar to_power n) is V11() real ext-real set
((((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n)) is V11() real ext-real set
(((((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1 is V11() real ext-real set
((((((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) ^2 is V11() real ext-real set
((((((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) * ((((((2 * tau) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
2 * (tau to_power 1) is V11() real ext-real set
(2 * (tau to_power 1)) * (tau to_power n) is V11() real ext-real set
((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n)) is V11() real ext-real set
(((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n)) is V11() real ext-real set
((((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n)) is V11() real ext-real set
(((((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1 is V11() real ext-real set
((((((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) ^2 is V11() real ext-real set
((((((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) * ((((((2 * (tau to_power 1)) * (tau to_power n)) - (1 * (tau to_power n))) + ((2 * tau_bar) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) is V11() real ext-real set
(tau to_power 1) * (tau to_power n) is V11() real ext-real set
2 * ((tau to_power 1) * (tau to_power n)) is V11() real ext-real set
(2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n)) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
2 * (tau_bar to_power 1) is V11() real ext-real set
(2 * (tau_bar to_power 1)) * (tau_bar to_power n) is V11() real ext-real set
((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n)) is V11() real ext-real set
(((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n))) - (1 * (tau_bar to_power n)) is V11() real ext-real set
((((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1 is V11() real ext-real set
(((((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) ^2 is V11() real ext-real set
(((((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) * (((((2 * ((tau to_power 1) * (tau to_power n))) - (1 * (tau to_power n))) + ((2 * (tau_bar to_power 1)) * (tau_bar to_power n))) - (1 * (tau_bar to_power n))) + 1) is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
2 * ((tau_bar to_power 1) * (tau_bar to_power n)) is V11() real ext-real set
((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n))) is V11() real ext-real set
(((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) - (tau_bar to_power n) is V11() real ext-real set
((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) - (tau_bar to_power n)) + 1 is V11() real ext-real set
(((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) - (tau_bar to_power n)) + 1) ^2 is V11() real ext-real set
(((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) - (tau_bar to_power n)) + 1) * (((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * ((tau_bar to_power 1) * (tau_bar to_power n)))) - (tau_bar to_power n)) + 1) is V11() real ext-real set
(((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1) ^2 is V11() real ext-real set
(((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1) * (((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1) is V11() real ext-real set
((5 * ((Lucas n) ^2)) + 1) - (2 * ((tau to_power n) + (tau_bar to_power n))) is V11() real ext-real set
sqrt ((((((2 * (tau to_power (n + 1))) - (tau to_power n)) + (2 * (tau_bar to_power (n + 1)))) - (tau_bar to_power n)) + 1) ^2) is V11() real ext-real set
sqrt (((5 * ((Lucas n) ^2)) + 1) - (2 * (Lucas n))) is V11() real ext-real set
(tau to_power (n + 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1)))) - (tau to_power n) is V11() real ext-real set
((2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1)))) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
(((2 * ((tau to_power (n + 1)) + (tau_bar to_power (n + 1)))) - (tau to_power n)) - (tau_bar to_power n)) + 1 is V11() real ext-real set
2 * (Lucas (n + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * (Lucas (n + 1))) - (tau to_power n) is V11() real ext-real set
((2 * (Lucas (n + 1))) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
(((2 * (Lucas (n + 1))) - (tau to_power n)) - (tau_bar to_power n)) + 1 is V11() real ext-real set
(2 * (Lucas (n + 1))) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer non even set
((2 * (Lucas (n + 1))) + 1) - (tau to_power n) is V11() real ext-real set
(((2 * (Lucas (n + 1))) + 1) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
((((2 * (Lucas (n + 1))) + 1) - (tau to_power n)) - (tau_bar to_power n)) + 1 is V11() real ext-real set
1 + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1)) is V11() real ext-real set
(2 * (Lucas (n + 1))) + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
((2 * (Lucas (n + 1))) + 2) - (tau to_power n) is V11() real ext-real set
(((2 * (Lucas (n + 1))) + 2) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
((tau to_power n) + (tau_bar to_power n)) + 1 is V11() real ext-real set
(((tau to_power n) + (tau_bar to_power n)) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1)) is V11() real ext-real set
((((tau to_power n) + (tau_bar to_power n)) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - (tau to_power n) is V11() real ext-real set
(((((tau to_power n) + (tau_bar to_power n)) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
(((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - (tau to_power n) is V11() real ext-real set
((((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - (tau to_power n)) - (tau_bar to_power n) is V11() real ext-real set
(((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - 2 is V11() real ext-real set
((((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - 2) + 2 is V11() real ext-real set
(2 * (Lucas (n + 1))) / 2 is V11() real ext-real non negative Element of COMPLEX
((((Lucas n) + 1) + (sqrt (((5 * ((Lucas n) ^2)) - (2 * (Lucas n))) + 1))) - 2) / 2 is V11() real ext-real Element of COMPLEX
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(Lucas (n + 1)) + (1 / 2) is non empty V11() real ext-real positive non negative set
(1 / tau) * ((Lucas (n + 1)) + (1 / 2)) is non empty V11() real ext-real positive non negative set
[\((1 / tau) * ((Lucas (n + 1)) + (1 / 2)))/] is V11() real ext-real integer set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
1 / (2 * (sqrt 5)) is V11() real ext-real Element of COMPLEX
2 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
3 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power 4 is V11() real ext-real set
tau_bar |^ 4 is V11() real ext-real set
tau_bar to_power (3 + 1) is V11() real ext-real set
tau_bar |^ (3 + 1) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 3) * (tau_bar to_power 1) is V11() real ext-real set
(2 - (sqrt 5)) * tau_bar is V11() real ext-real set
2 - (2 * (sqrt 5)) is V11() real ext-real set
(2 - (2 * (sqrt 5))) - (sqrt 5) is V11() real ext-real set
((2 - (2 * (sqrt 5))) - (sqrt 5)) + ((sqrt 5) ^2) is V11() real ext-real set
(((2 - (2 * (sqrt 5))) - (sqrt 5)) + ((sqrt 5) ^2)) / 2 is V11() real ext-real Element of COMPLEX
3 * (sqrt 5) is V11() real ext-real set
2 - (3 * (sqrt 5)) is V11() real ext-real set
(2 - (3 * (sqrt 5))) + 5 is V11() real ext-real set
((2 - (3 * (sqrt 5))) + 5) / 2 is V11() real ext-real Element of COMPLEX
7 - (3 * (sqrt 5)) is V11() real ext-real set
(7 - (3 * (sqrt 5))) / 2 is V11() real ext-real Element of COMPLEX
16 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer Element of NAT
16 / 7 is non empty V11() real ext-real positive non negative Element of COMPLEX
(16 / 7) ^2 is V11() real ext-real Element of COMPLEX
(16 / 7) * (16 / 7) is non empty V11() real ext-real positive non negative set
sqrt ((16 / 7) ^2) is V11() real ext-real set
7 * (sqrt 5) is V11() real ext-real set
(16 / 7) * 7 is non empty V11() real ext-real positive non negative set
3 * 5 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(7 * (sqrt 5)) - (3 * 5) is V11() real ext-real set
16 - (3 * 5) is V11() real ext-real integer set
3 * ((sqrt 5) ^2) is V11() real ext-real set
(7 * (sqrt 5)) - (3 * ((sqrt 5) ^2)) is V11() real ext-real set
(7 - (3 * (sqrt 5))) * (sqrt 5) is V11() real ext-real set
((7 - (3 * (sqrt 5))) * (sqrt 5)) / (sqrt 5) is V11() real ext-real Element of COMPLEX
(1 / (sqrt 5)) / 2 is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) * (sqrt 5) is V11() real ext-real set
(1 / (2 * (sqrt 5))) * (sqrt 5) is V11() real ext-real set
- ((tau_bar to_power n) * (sqrt 5)) is V11() real ext-real set
tau * (tau_bar to_power n) is V11() real ext-real set
(1 / 2) + (tau * (tau_bar to_power n)) is V11() real ext-real set
(- (1 / 2)) + ((1 / 2) + (tau * (tau_bar to_power n))) is V11() real ext-real set
tau_bar * (tau_bar to_power n) is V11() real ext-real set
(tau_bar * (tau_bar to_power n)) - (tau * (tau_bar to_power n)) is V11() real ext-real set
((tau_bar * (tau_bar to_power n)) - (tau * (tau_bar to_power n))) + ((1 / 2) + (tau * (tau_bar to_power n))) is V11() real ext-real set
(tau_bar to_power n) * tau is V11() real ext-real set
((tau_bar to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
(tau_bar * (tau_bar to_power n)) + (1 / 2) is V11() real ext-real set
((tau_bar * (tau_bar to_power n)) + (1 / 2)) / tau is V11() real ext-real Element of COMPLEX
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) / tau is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) + ((tau to_power (n + 1)) / tau) is V11() real ext-real set
(((tau_bar * (tau_bar to_power n)) + (1 / 2)) / tau) + ((tau to_power (n + 1)) / tau) is V11() real ext-real Element of COMPLEX
((tau_bar * (tau_bar to_power n)) + (1 / 2)) + (tau to_power (n + 1)) is V11() real ext-real set
(((tau_bar * (tau_bar to_power n)) + (1 / 2)) + (tau to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power 1) * (tau_bar to_power n) is V11() real ext-real set
((tau_bar to_power 1) * (tau_bar to_power n)) + (1 / 2) is V11() real ext-real set
(((tau_bar to_power 1) * (tau_bar to_power n)) + (1 / 2)) + (tau to_power (n + 1)) is V11() real ext-real set
((((tau_bar to_power 1) * (tau_bar to_power n)) + (1 / 2)) + (tau to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
((tau to_power n) * (tau to_power 1)) / tau is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) + (((tau to_power n) * (tau to_power 1)) / tau) is V11() real ext-real set
((tau_bar to_power 1) * (tau_bar to_power n)) + (tau to_power (n + 1)) is V11() real ext-real set
(((tau_bar to_power 1) * (tau_bar to_power n)) + (tau to_power (n + 1))) + (1 / 2) is V11() real ext-real set
((((tau_bar to_power 1) * (tau_bar to_power n)) + (tau to_power (n + 1))) + (1 / 2)) / tau is V11() real ext-real Element of COMPLEX
1 + n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power (1 + n) is V11() real ext-real set
tau_bar |^ (1 + n) is V11() real ext-real set
(tau_bar to_power (1 + n)) + (tau to_power (n + 1)) is V11() real ext-real set
((tau_bar to_power (1 + n)) + (tau to_power (n + 1))) + (1 / 2) is V11() real ext-real set
(((tau_bar to_power (1 + n)) + (tau to_power (n + 1))) + (1 / 2)) / tau is V11() real ext-real Element of COMPLEX
((Lucas (n + 1)) + (1 / 2)) / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
(tau_bar to_power n) + (((tau to_power n) * tau) / tau) is V11() real ext-real set
(tau_bar to_power n) + (tau to_power n) is V11() real ext-real set
((1 / tau) * ((Lucas (n + 1)) + (1 / 2))) - 1 is V11() real ext-real set
- (- (1 / 2)) is non empty V11() real ext-real positive non negative Element of COMPLEX
- (tau_bar to_power n) is V11() real ext-real set
(1 / 2) * (sqrt 5) is V11() real ext-real set
(- (tau_bar to_power n)) * (sqrt 5) is V11() real ext-real set
tau - (1 / 2) is V11() real ext-real set
(tau_bar to_power n) * tau is V11() real ext-real set
((tau_bar to_power n) * tau) + (1 / 2) is V11() real ext-real set
(tau - (1 / 2)) + (((tau_bar to_power n) * tau) + (1 / 2)) is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
((tau_bar to_power n) * tau_bar) - ((tau_bar to_power n) * tau) is V11() real ext-real set
(((tau_bar to_power n) * tau_bar) - ((tau_bar to_power n) * tau)) + (((tau_bar to_power n) * tau) + (1 / 2)) is V11() real ext-real set
(tau - (1 / 2)) + ((tau_bar to_power n) * tau) is V11() real ext-real set
((tau - (1 / 2)) + ((tau_bar to_power n) * tau)) + (1 / 2) is V11() real ext-real set
(((tau - (1 / 2)) + ((tau_bar to_power n) * tau)) + (1 / 2)) - tau is V11() real ext-real set
((tau_bar to_power n) * tau_bar) + (1 / 2) is V11() real ext-real set
(((tau_bar to_power n) * tau_bar) + (1 / 2)) - tau is V11() real ext-real set
((tau_bar to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
((((tau_bar to_power n) * tau_bar) + (1 / 2)) - tau) / tau is V11() real ext-real Element of COMPLEX
((tau_bar to_power n) * tau_bar) / tau is V11() real ext-real Element of COMPLEX
(1 / 2) / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
(((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau) is V11() real ext-real Element of COMPLEX
tau / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) - (tau / tau) is V11() real ext-real Element of COMPLEX
((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) - 1 is V11() real ext-real set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
(tau_bar to_power n) + (tau to_power n) is V11() real ext-real set
(((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) - 1) + (tau to_power n) is V11() real ext-real set
(tau to_power n) * 1 is V11() real ext-real set
((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + ((tau to_power n) * 1) is V11() real ext-real set
(((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + ((tau to_power n) * 1)) - 1 is V11() real ext-real set
(tau to_power n) * (tau / tau) is V11() real ext-real set
((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + ((tau to_power n) * (tau / tau)) is V11() real ext-real set
(((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + ((tau to_power n) * (tau / tau))) - 1 is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
((tau to_power n) * tau) / tau is V11() real ext-real Element of COMPLEX
((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + (((tau to_power n) * tau) / tau) is V11() real ext-real Element of COMPLEX
(((((tau_bar to_power n) * tau_bar) / tau) + ((1 / 2) / tau)) + (((tau to_power n) * tau) / tau)) - 1 is V11() real ext-real set
(((tau_bar to_power n) * tau_bar) + (1 / 2)) + ((tau to_power n) * tau) is V11() real ext-real set
((((tau_bar to_power n) * tau_bar) + (1 / 2)) + ((tau to_power n) * tau)) / tau is V11() real ext-real Element of COMPLEX
(((((tau_bar to_power n) * tau_bar) + (1 / 2)) + ((tau to_power n) * tau)) / tau) - 1 is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2) is V11() real ext-real set
(((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * tau) is V11() real ext-real set
((((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * tau)) / tau is V11() real ext-real Element of COMPLEX
(((((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * tau)) / tau) - 1 is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
(((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
((((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1))) / tau is V11() real ext-real Element of COMPLEX
(((((tau_bar to_power n) * (tau_bar to_power 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1))) / tau) - 1 is V11() real ext-real set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
(tau_bar to_power (n + 1)) + (1 / 2) is V11() real ext-real set
((tau_bar to_power (n + 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
(((tau_bar to_power (n + 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1))) / tau is V11() real ext-real Element of COMPLEX
((((tau_bar to_power (n + 1)) + (1 / 2)) + ((tau to_power n) * (tau to_power 1))) / tau) - 1 is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
((tau_bar to_power (n + 1)) + (1 / 2)) + (tau to_power (n + 1)) is V11() real ext-real set
(((tau_bar to_power (n + 1)) + (1 / 2)) + (tau to_power (n + 1))) / tau is V11() real ext-real Element of COMPLEX
((((tau_bar to_power (n + 1)) + (1 / 2)) + (tau to_power (n + 1))) / tau) - 1 is V11() real ext-real set
(tau_bar to_power (n + 1)) + (tau to_power (n + 1)) is V11() real ext-real set
((tau_bar to_power (n + 1)) + (tau to_power (n + 1))) + (1 / 2) is V11() real ext-real set
(((tau_bar to_power (n + 1)) + (tau to_power (n + 1))) + (1 / 2)) / tau is V11() real ext-real Element of COMPLEX
((((tau_bar to_power (n + 1)) + (tau to_power (n + 1))) + (1 / 2)) / tau) - 1 is V11() real ext-real set
((Lucas (n + 1)) + (1 / 2)) / tau is non empty V11() real ext-real positive non negative Element of COMPLEX
(((Lucas (n + 1)) + (1 / 2)) / tau) - 1 is V11() real ext-real set
n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
n + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
Lucas (n + k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power k is V11() real ext-real set
tau |^ k is V11() real ext-real set
Lucas n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(tau to_power k) * (Lucas n) is V11() real ext-real set
((tau to_power k) * (Lucas n)) + 1 is V11() real ext-real set
[\(((tau to_power k) * (Lucas n)) + 1)/] is V11() real ext-real integer set
tau to_power n is V11() real ext-real set
tau |^ n is V11() real ext-real set
tau_bar to_power n is V11() real ext-real set
tau_bar |^ n is V11() real ext-real set
tau_bar to_power (n + k) is V11() real ext-real set
tau_bar |^ (n + k) is V11() real ext-real set
(tau to_power k) * (tau_bar to_power n) is V11() real ext-real set
((tau to_power k) * (tau_bar to_power n)) + 1 is V11() real ext-real set
m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
k + m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 * k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer even set
(2 * k) + m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(1 - (sqrt 5)) to_power ((2 * k) + m) is V11() real ext-real set
(1 - (sqrt 5)) |^ ((2 * k) + m) is V11() real ext-real set
2 to_power ((2 * k) + m) is V11() real ext-real set
2 |^ ((2 * k) + m) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((1 - (sqrt 5)) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(1 - (sqrt 5)) to_power m is V11() real ext-real set
(1 - (sqrt 5)) |^ m is V11() real ext-real set
(- 1) to_power k is V11() real ext-real set
(- 1) |^ k is V11() real ext-real set
((1 - (sqrt 5)) to_power m) * ((- 1) to_power k) is V11() real ext-real set
2 to_power m is V11() real ext-real set
2 |^ m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((1 - (sqrt 5)) to_power m) * ((- 1) to_power k)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * ((- 1) to_power k)) / (2 to_power m)) + 1 is V11() real ext-real set
((1 - (sqrt 5)) to_power m) * 1 is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * 1) / (2 to_power m) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * 1) / (2 to_power m)) + 1 is V11() real ext-real set
- ((- 1) + (sqrt 5)) is V11() real ext-real set
(- ((- 1) + (sqrt 5))) to_power m is V11() real ext-real set
(- ((- 1) + (sqrt 5))) |^ m is V11() real ext-real set
((- ((- 1) + (sqrt 5))) to_power m) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(2 to_power m) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(((- ((- 1) + (sqrt 5))) to_power m) / (2 to_power m)) + ((2 to_power m) / (2 to_power m)) is V11() real ext-real Element of COMPLEX
(- 1) * ((sqrt 5) - 1) is V11() real ext-real set
((- 1) * ((sqrt 5) - 1)) to_power m is V11() real ext-real set
((- 1) * ((sqrt 5) - 1)) |^ m is V11() real ext-real set
(((- 1) * ((sqrt 5) - 1)) to_power m) + (2 to_power m) is V11() real ext-real set
((((- 1) * ((sqrt 5) - 1)) to_power m) + (2 to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(- 1) to_power m is V11() real ext-real set
(- 1) |^ m is V11() real ext-real set
((sqrt 5) - 1) to_power m is V11() real ext-real set
((sqrt 5) - 1) |^ m is V11() real ext-real set
((- 1) to_power m) * (((sqrt 5) - 1) to_power m) is V11() real ext-real set
(((- 1) to_power m) * (((sqrt 5) - 1) to_power m)) + (2 to_power m) is V11() real ext-real set
((((- 1) to_power m) * (((sqrt 5) - 1) to_power m)) + (2 to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(- 1) * (((sqrt 5) - 1) to_power m) is V11() real ext-real set
(2 to_power m) + ((- 1) * (((sqrt 5) - 1) to_power m)) is V11() real ext-real set
((2 to_power m) + ((- 1) * (((sqrt 5) - 1) to_power m))) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(2 to_power m) - (((sqrt 5) - 1) to_power m) is V11() real ext-real set
((2 to_power m) - (((sqrt 5) - 1) to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
3 - 1 is V11() real ext-real integer set
(((sqrt 5) - 1) to_power m) - (((sqrt 5) - 1) to_power m) is V11() real ext-real set
(- 1) * ((- 1) + (sqrt 5)) is V11() real ext-real set
((- 1) * ((- 1) + (sqrt 5))) to_power ((2 * k) + m) is V11() real ext-real set
((- 1) * ((- 1) + (sqrt 5))) |^ ((2 * k) + m) is V11() real ext-real set
(((- 1) * ((- 1) + (sqrt 5))) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(- 1) to_power ((2 * k) + m) is V11() real ext-real set
(- 1) |^ ((2 * k) + m) is V11() real ext-real set
((- 1) + (sqrt 5)) to_power ((2 * k) + m) is V11() real ext-real set
((- 1) + (sqrt 5)) |^ ((2 * k) + m) is V11() real ext-real set
((- 1) to_power ((2 * k) + m)) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m)) is V11() real ext-real set
(((- 1) to_power ((2 * k) + m)) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m))) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(- 1) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m)) is V11() real ext-real set
((- 1) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m))) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(((- 1) + (sqrt 5)) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(- 1) * ((((- 1) + (sqrt 5)) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m))) is V11() real ext-real set
2 to_power (2 * k) is V11() real ext-real set
2 |^ (2 * k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
m - 1 is V11() real ext-real integer set
((1 - (sqrt 5)) to_power m) * (- 1) is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * (- 1)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (- 1)) / (2 to_power m)) + 1 is V11() real ext-real set
(2 to_power m) / (2 to_power m) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (- 1)) / (2 to_power m)) + ((2 to_power m) / (2 to_power m)) is V11() real ext-real Element of COMPLEX
(- 1) * ((- 1) + (sqrt 5)) is V11() real ext-real set
((- 1) * ((- 1) + (sqrt 5))) to_power m is V11() real ext-real set
((- 1) * ((- 1) + (sqrt 5))) |^ m is V11() real ext-real set
(((- 1) * ((- 1) + (sqrt 5))) to_power m) * (- 1) is V11() real ext-real set
((((- 1) * ((- 1) + (sqrt 5))) to_power m) * (- 1)) + (2 to_power m) is V11() real ext-real set
(((((- 1) * ((- 1) + (sqrt 5))) to_power m) * (- 1)) + (2 to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(- 1) to_power m is V11() real ext-real set
(- 1) |^ m is V11() real ext-real set
((- 1) + (sqrt 5)) to_power m is V11() real ext-real set
((- 1) + (sqrt 5)) |^ m is V11() real ext-real set
((- 1) to_power m) * (((- 1) + (sqrt 5)) to_power m) is V11() real ext-real set
(((- 1) to_power m) * (((- 1) + (sqrt 5)) to_power m)) * (- 1) is V11() real ext-real set
((((- 1) to_power m) * (((- 1) + (sqrt 5)) to_power m)) * (- 1)) + (2 to_power m) is V11() real ext-real set
(((((- 1) to_power m) * (((- 1) + (sqrt 5)) to_power m)) * (- 1)) + (2 to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
1 * (((- 1) + (sqrt 5)) to_power m) is V11() real ext-real set
(1 * (((- 1) + (sqrt 5)) to_power m)) * (- 1) is V11() real ext-real set
((1 * (((- 1) + (sqrt 5)) to_power m)) * (- 1)) + (2 to_power m) is V11() real ext-real set
(((1 * (((- 1) + (sqrt 5)) to_power m)) * (- 1)) + (2 to_power m)) / (2 to_power m) is V11() real ext-real Element of COMPLEX
- (((- 1) + (sqrt 5)) to_power m) is V11() real ext-real set
(- (((- 1) + (sqrt 5)) to_power m)) + (2 to_power m) is V11() real ext-real set
((- (((- 1) + (sqrt 5)) to_power m)) + (2 to_power m)) * (2 to_power (2 * k)) is V11() real ext-real set
(2 to_power m) * (2 to_power (2 * k)) is V11() real ext-real set
(((- (((- 1) + (sqrt 5)) to_power m)) + (2 to_power m)) * (2 to_power (2 * k))) / ((2 to_power m) * (2 to_power (2 * k))) is V11() real ext-real Element of COMPLEX
(((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)) is V11() real ext-real set
- ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k))) is V11() real ext-real set
(- ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)))) + ((2 to_power m) * (2 to_power (2 * k))) is V11() real ext-real set
m + (2 * k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 to_power (m + (2 * k)) is V11() real ext-real set
2 |^ (m + (2 * k)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((- ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)))) + ((2 to_power m) * (2 to_power (2 * k)))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
(- ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)))) + (2 to_power (m + (2 * k))) is V11() real ext-real set
((- ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)))) + (2 to_power (m + (2 * k)))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
(2 to_power (m + (2 * k))) - ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k))) is V11() real ext-real set
((2 to_power (m + (2 * k))) - ((((- 1) + (sqrt 5)) to_power m) * (2 to_power (2 * k)))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
((- 1) * ((- 1) + (sqrt 5))) to_power ((2 * k) + m) is V11() real ext-real set
((- 1) * ((- 1) + (sqrt 5))) |^ ((2 * k) + m) is V11() real ext-real set
(((- 1) * ((- 1) + (sqrt 5))) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(- 1) to_power ((2 * k) + m) is V11() real ext-real set
(- 1) |^ ((2 * k) + m) is V11() real ext-real set
((- 1) + (sqrt 5)) to_power ((2 * k) + m) is V11() real ext-real set
((- 1) + (sqrt 5)) |^ ((2 * k) + m) is V11() real ext-real set
((- 1) to_power ((2 * k) + m)) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m)) is V11() real ext-real set
(((- 1) to_power ((2 * k) + m)) * (((- 1) + (sqrt 5)) to_power ((2 * k) + m))) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
1 * (((- 1) + (sqrt 5)) to_power ((2 * k) + m)) is V11() real ext-real set
(1 * (((- 1) + (sqrt 5)) to_power ((2 * k) + m))) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
((sqrt 5) - 1) to_power ((2 * k) + m) is V11() real ext-real set
((sqrt 5) - 1) |^ ((2 * k) + m) is V11() real ext-real set
(((sqrt 5) - 1) to_power ((2 * k) + m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
((sqrt 5) - 1) to_power m is V11() real ext-real set
((sqrt 5) - 1) |^ m is V11() real ext-real set
(2 to_power m) - (((sqrt 5) - 1) to_power m) is V11() real ext-real set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 to_power (1 + 1) is V11() real ext-real set
2 |^ (1 + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((sqrt 5) - 1) to_power (1 + 1) is V11() real ext-real set
((sqrt 5) - 1) |^ (1 + 1) is V11() real ext-real set
(2 to_power (1 + 1)) - (((sqrt 5) - 1) to_power (1 + 1)) is V11() real ext-real set
((sqrt 5) - 1) to_power 2 is V11() real ext-real set
((sqrt 5) - 1) |^ 2 is V11() real ext-real set
(2 ^2) - (((sqrt 5) - 1) to_power 2) is V11() real ext-real set
((sqrt 5) - 1) ^2 is V11() real ext-real set
((sqrt 5) - 1) * ((sqrt 5) - 1) is V11() real ext-real set
4 - (((sqrt 5) - 1) ^2) is V11() real ext-real set
(2 * (sqrt 5)) * 1 is V11() real ext-real set
((sqrt 5) ^2) - ((2 * (sqrt 5)) * 1) is V11() real ext-real set
(((sqrt 5) ^2) - ((2 * (sqrt 5)) * 1)) + (1 ^2) is V11() real ext-real set
4 - ((((sqrt 5) ^2) - ((2 * (sqrt 5)) * 1)) + (1 ^2)) is V11() real ext-real set
5 - (2 * (sqrt 5)) is V11() real ext-real set
(5 - (2 * (sqrt 5))) + 1 is V11() real ext-real set
4 - ((5 - (2 * (sqrt 5))) + 1) is V11() real ext-real set
(2 * (sqrt 5)) - 2 is V11() real ext-real set
6 - (2 * (sqrt 5)) is V11() real ext-real set
sqrt (2 ^2) is V11() real ext-real set
2 * 4 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer even set
(sqrt 5) * 4 is V11() real ext-real set
6 + 2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(6 + 2) - 2 is V11() real ext-real integer set
((sqrt 5) * 2) + ((sqrt 5) * 2) is V11() real ext-real set
(((sqrt 5) * 2) + ((sqrt 5) * 2)) - 2 is V11() real ext-real set
((((sqrt 5) * 2) + ((sqrt 5) * 2)) - 2) - (2 * (sqrt 5)) is V11() real ext-real set
s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
s + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((sqrt 5) - 1) to_power (s + 1) is V11() real ext-real set
((sqrt 5) - 1) |^ (s + 1) is V11() real ext-real set
2 to_power (s + 1) is V11() real ext-real set
2 |^ (s + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 to_power (s + 1)) - (((sqrt 5) - 1) to_power (s + 1)) is V11() real ext-real set
(s + 1) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
((sqrt 5) - 1) to_power ((s + 1) + 1) is V11() real ext-real set
((sqrt 5) - 1) |^ ((s + 1) + 1) is V11() real ext-real set
2 to_power ((s + 1) + 1) is V11() real ext-real set
2 |^ ((s + 1) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 to_power ((s + 1) + 1)) - (((sqrt 5) - 1) to_power ((s + 1) + 1)) is V11() real ext-real set
(((sqrt 5) - 1) to_power (s + 1)) + (((sqrt 5) - 1) to_power (s + 1)) is V11() real ext-real set
((2 to_power (s + 1)) - (((sqrt 5) - 1) to_power (s + 1))) + (((sqrt 5) - 1) to_power (s + 1)) is V11() real ext-real set
2 * (((sqrt 5) - 1) to_power (s + 1)) is V11() real ext-real set
(2 * (((sqrt 5) - 1) to_power (s + 1))) * ((sqrt 5) - 1) is V11() real ext-real set
(2 to_power (s + 1)) * ((sqrt 5) - 1) is V11() real ext-real set
(((sqrt 5) - 1) to_power (s + 1)) * ((sqrt 5) - 1) is V11() real ext-real set
2 * ((((sqrt 5) - 1) to_power (s + 1)) * ((sqrt 5) - 1)) is V11() real ext-real set
((sqrt 5) - 1) to_power 1 is V11() real ext-real set
((sqrt 5) - 1) |^ 1 is V11() real ext-real set
(((sqrt 5) - 1) to_power (s + 1)) * (((sqrt 5) - 1) to_power 1) is V11() real ext-real set
2 * ((((sqrt 5) - 1) to_power (s + 1)) * (((sqrt 5) - 1) to_power 1)) is V11() real ext-real set
2 * (((sqrt 5) - 1) to_power ((s + 1) + 1)) is V11() real ext-real set
3 - 1 is V11() real ext-real integer set
((sqrt 5) - 1) * (2 to_power (s + 1)) is V11() real ext-real set
2 * (2 to_power (s + 1)) is V11() real ext-real set
2 to_power 1 is V11() real ext-real Element of REAL
2 |^ 1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 to_power 1) * (2 to_power (s + 1)) is V11() real ext-real set
1 + s is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
(1 + s) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
2 to_power ((1 + s) + 1) is V11() real ext-real set
2 |^ ((1 + s) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 * (((sqrt 5) - 1) to_power ((s + 1) + 1))) - (((sqrt 5) - 1) to_power ((s + 1) + 1)) is V11() real ext-real set
(2 to_power ((1 + s) + 1)) - (((sqrt 5) - 1) to_power ((s + 1) + 1)) is V11() real ext-real set
(m - 1) + 1 is V11() real ext-real integer set
((sqrt 5) - 1) to_power ((m - 1) + 1) is V11() real ext-real set
2 to_power ((m - 1) + 1) is V11() real ext-real set
(2 to_power ((m - 1) + 1)) - (((sqrt 5) - 1) to_power ((m - 1) + 1)) is V11() real ext-real set
(((sqrt 5) - 1) to_power m) * (2 to_power (2 * k)) is V11() real ext-real set
((2 to_power m) - (((sqrt 5) - 1) to_power m)) * (2 to_power (2 * k)) is V11() real ext-real set
((2 to_power m) * (2 to_power (2 * k))) - ((((sqrt 5) - 1) to_power m) * (2 to_power (2 * k))) is V11() real ext-real set
(2 to_power (m + (2 * k))) - ((((sqrt 5) - 1) to_power m) * (2 to_power (2 * k))) is V11() real ext-real set
((((sqrt 5) - 1) to_power m) * (2 to_power (2 * k))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
((2 to_power (m + (2 * k))) - ((((sqrt 5) - 1) to_power m) * (2 to_power (2 * k)))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
(((2 to_power m) * (2 to_power (2 * k))) - ((((sqrt 5) - 1) to_power m) * (2 to_power (2 * k)))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
3 - 1 is V11() real ext-real integer set
((sqrt 5) - 1) to_power (2 * k) is V11() real ext-real set
((sqrt 5) - 1) |^ (2 * k) is V11() real ext-real set
(((sqrt 5) - 1) to_power (2 * k)) * (((sqrt 5) - 1) to_power m) is V11() real ext-real set
(2 to_power (2 * k)) * (((sqrt 5) - 1) to_power m) is V11() real ext-real set
((((sqrt 5) - 1) to_power (2 * k)) * (((sqrt 5) - 1) to_power m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
((2 to_power (2 * k)) * (((sqrt 5) - 1) to_power m)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(((2 to_power m) - (((sqrt 5) - 1) to_power m)) * (2 to_power (2 * k))) / (2 to_power (m + (2 * k))) is V11() real ext-real Element of COMPLEX
- ((sqrt 5) - 1) is V11() real ext-real set
(1 + (sqrt 5)) * (1 - (sqrt 5)) is V11() real ext-real set
((1 + (sqrt 5)) * (1 - (sqrt 5))) / (2 to_power 2) is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) * (1 - (sqrt 5))) / (2 ^2) is V11() real ext-real Element of COMPLEX
((1 ^2) - ((sqrt 5) ^2)) / 4 is V11() real ext-real Element of COMPLEX
1 - 5 is V11() real ext-real integer set
(1 - 5) / 4 is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k is V11() real ext-real set
((1 + (sqrt 5)) * (1 - (sqrt 5))) |^ k is V11() real ext-real set
(2 to_power 2) to_power k is V11() real ext-real set
(2 to_power 2) |^ k is V11() real ext-real set
(((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k) / ((2 to_power 2) to_power k) is V11() real ext-real Element of COMPLEX
2 to_power (2 * k) is V11() real ext-real set
2 |^ (2 * k) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k) / (2 to_power (2 * k)) is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k) is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / (2 to_power (2 * k)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / (2 to_power (2 * k))) / (2 to_power m) is V11() real ext-real Element of COMPLEX
(((((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / (2 to_power (2 * k))) / (2 to_power m)) + 1 is V11() real ext-real set
(2 to_power (2 * k)) * (2 to_power m) is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / ((2 to_power (2 * k)) * (2 to_power m)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / ((2 to_power (2 * k)) * (2 to_power m))) + 1 is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) * (1 - (sqrt 5))) to_power k)) / (2 to_power ((2 * k) + m))) + 1 is V11() real ext-real set
(1 + (sqrt 5)) to_power k is V11() real ext-real set
(1 + (sqrt 5)) |^ k is V11() real ext-real set
(1 - (sqrt 5)) to_power k is V11() real ext-real set
(1 - (sqrt 5)) |^ k is V11() real ext-real set
((1 + (sqrt 5)) to_power k) * ((1 - (sqrt 5)) to_power k) is V11() real ext-real set
((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) to_power k) * ((1 - (sqrt 5)) to_power k)) is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) to_power k) * ((1 - (sqrt 5)) to_power k))) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power m) * (((1 + (sqrt 5)) to_power k) * ((1 - (sqrt 5)) to_power k))) / (2 to_power ((2 * k) + m))) + 1 is V11() real ext-real set
((1 - (sqrt 5)) to_power m) * ((1 - (sqrt 5)) to_power k) is V11() real ext-real set
(((1 - (sqrt 5)) to_power m) * ((1 - (sqrt 5)) to_power k)) * ((1 + (sqrt 5)) to_power k) is V11() real ext-real set
((((1 - (sqrt 5)) to_power m) * ((1 - (sqrt 5)) to_power k)) * ((1 + (sqrt 5)) to_power k)) / (2 to_power ((2 * k) + m)) is V11() real ext-real Element of COMPLEX
(((((1 - (sqrt 5)) to_power m) * ((1 - (sqrt 5)) to_power k)) * ((1 + (sqrt 5)) to_power k)) / (2 to_power ((2 * k) + m))) + 1 is V11() real ext-real set
m + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(1 - (sqrt 5)) to_power (m + k) is V11() real ext-real set
(1 - (sqrt 5)) |^ (m + k) is V11() real ext-real set
((1 - (sqrt 5)) to_power (m + k)) * ((1 + (sqrt 5)) to_power k) is V11() real ext-real set
k + k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(k + k) + m is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 to_power ((k + k) + m) is V11() real ext-real set
2 |^ ((k + k) + m) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((1 - (sqrt 5)) to_power (m + k)) * ((1 + (sqrt 5)) to_power k)) / (2 to_power ((k + k) + m)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power (m + k)) * ((1 + (sqrt 5)) to_power k)) / (2 to_power ((k + k) + m))) + 1 is V11() real ext-real set
((1 - (sqrt 5)) / 2) to_power ((k + k) + m) is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ ((k + k) + m) is V11() real ext-real set
(1 - (sqrt 5)) to_power n is V11() real ext-real set
(1 - (sqrt 5)) |^ n is V11() real ext-real set
((1 - (sqrt 5)) to_power n) * ((1 + (sqrt 5)) to_power k) is V11() real ext-real set
k + n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 to_power (k + n) is V11() real ext-real set
2 |^ (k + n) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(((1 - (sqrt 5)) to_power n) * ((1 + (sqrt 5)) to_power k)) / (2 to_power (k + n)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power n) * ((1 + (sqrt 5)) to_power k)) / (2 to_power (k + n))) + 1 is V11() real ext-real set
tau_bar to_power (k + n) is V11() real ext-real set
tau_bar |^ (k + n) is V11() real ext-real set
2 to_power n is V11() real ext-real set
2 |^ n is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
2 to_power k is V11() real ext-real set
2 |^ k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
(2 to_power n) * (2 to_power k) is V11() real ext-real set
(((1 - (sqrt 5)) to_power n) * ((1 + (sqrt 5)) to_power k)) / ((2 to_power n) * (2 to_power k)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power n) * ((1 + (sqrt 5)) to_power k)) / ((2 to_power n) * (2 to_power k))) + 1 is V11() real ext-real set
((1 - (sqrt 5)) to_power n) / (2 to_power n) is V11() real ext-real Element of COMPLEX
((1 + (sqrt 5)) to_power k) / (2 to_power k) is V11() real ext-real Element of COMPLEX
(((1 - (sqrt 5)) to_power n) / (2 to_power n)) * (((1 + (sqrt 5)) to_power k) / (2 to_power k)) is V11() real ext-real Element of COMPLEX
((((1 - (sqrt 5)) to_power n) / (2 to_power n)) * (((1 + (sqrt 5)) to_power k) / (2 to_power k))) + 1 is V11() real ext-real set
((1 - (sqrt 5)) / 2) to_power n is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ n is V11() real ext-real set
(((1 - (sqrt 5)) / 2) to_power n) * (((1 + (sqrt 5)) to_power k) / (2 to_power k)) is V11() real ext-real set
((((1 - (sqrt 5)) / 2) to_power n) * (((1 + (sqrt 5)) to_power k) / (2 to_power k))) + 1 is V11() real ext-real set
tau to_power (n + k) is V11() real ext-real set
tau |^ (n + k) is V11() real ext-real set
(tau_bar to_power (n + k)) + (tau to_power (n + k)) is V11() real ext-real set
(((tau to_power k) * (tau_bar to_power n)) + 1) + (tau to_power (n + k)) is V11() real ext-real set
(tau to_power (n + k)) + (tau_bar to_power (n + k)) is V11() real ext-real set
(tau to_power (n + k)) + ((tau to_power k) * (tau_bar to_power n)) is V11() real ext-real set
((tau to_power (n + k)) + ((tau to_power k) * (tau_bar to_power n))) + 1 is V11() real ext-real set
(tau to_power k) * (tau to_power n) is V11() real ext-real set
((tau to_power k) * (tau to_power n)) + ((tau to_power k) * (tau_bar to_power n)) is V11() real ext-real set
(((tau to_power k) * (tau to_power n)) + ((tau to_power k) * (tau_bar to_power n))) + 1 is V11() real ext-real set
(tau to_power n) + (tau_bar to_power n) is V11() real ext-real set
(tau to_power k) * ((tau to_power n) + (tau_bar to_power n)) is V11() real ext-real set
((tau to_power k) * ((tau to_power n) + (tau_bar to_power n))) + 1 is V11() real ext-real set
(((tau to_power k) * (Lucas n)) + 1) - 1 is V11() real ext-real set
(tau_bar to_power n) * tau is V11() real ext-real set
(tau_bar to_power n) * tau_bar is V11() real ext-real set
((tau_bar to_power n) * tau) - ((tau_bar to_power n) * tau_bar) is V11() real ext-real set
tau_bar to_power 1 is V11() real ext-real set
tau_bar |^ 1 is V11() real ext-real set
(tau_bar to_power n) * (tau_bar to_power 1) is V11() real ext-real set
((tau_bar to_power n) * tau) - ((tau_bar to_power n) * (tau_bar to_power 1)) is V11() real ext-real set
n + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power (n + 1) is V11() real ext-real set
tau_bar |^ (n + 1) is V11() real ext-real set
((tau_bar to_power n) * tau) - (tau_bar to_power (n + 1)) is V11() real ext-real set
tau to_power (n + 1) is V11() real ext-real set
tau |^ (n + 1) is V11() real ext-real set
(tau to_power (n + 1)) + (tau_bar to_power (n + 1)) is V11() real ext-real set
0 + ((tau to_power (n + 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
(((tau_bar to_power n) * tau) - (tau_bar to_power (n + 1))) + ((tau to_power (n + 1)) + (tau_bar to_power (n + 1))) is V11() real ext-real set
Lucas (n + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
((tau_bar to_power n) * tau) + (tau to_power (n + 1)) is V11() real ext-real set
tau to_power 1 is V11() real ext-real set
tau |^ 1 is V11() real ext-real set
(tau to_power n) * (tau to_power 1) is V11() real ext-real set
((tau_bar to_power n) * tau) + ((tau to_power n) * (tau to_power 1)) is V11() real ext-real set
(tau to_power n) * tau is V11() real ext-real set
((tau_bar to_power n) * tau) + ((tau to_power n) * tau) is V11() real ext-real set
(tau_bar to_power n) + (tau to_power n) is V11() real ext-real set
((tau_bar to_power n) + (tau to_power n)) * tau is V11() real ext-real set
(Lucas n) * tau is V11() real ext-real non negative set
(tau to_power 1) * (Lucas n) is V11() real ext-real set
m is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + m is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + m) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power m is V11() real ext-real set
tau |^ m is V11() real ext-real set
(tau to_power m) * (Lucas n) is V11() real ext-real set
m + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
n + (m + 1) is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
Lucas (n + (m + 1)) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
tau to_power (m + 1) is V11() real ext-real set
tau |^ (m + 1) is V11() real ext-real set
(tau to_power (m + 1)) * (Lucas n) is V11() real ext-real set
(1 + (sqrt 5)) to_power (m + 1) is V11() real ext-real set
(1 + (sqrt 5)) |^ (m + 1) is V11() real ext-real set
(1 - (sqrt 5)) to_power (m + 1) is V11() real ext-real set
(1 - (sqrt 5)) |^ (m + 1) is V11() real ext-real set
s is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(1 - (sqrt 5)) to_power s is V11() real ext-real set
(1 - (sqrt 5)) |^ s is V11() real ext-real set
abs ((1 - (sqrt 5)) to_power s) is V11() real ext-real non negative Element of REAL
abs (1 - (sqrt 5)) is V11() real ext-real non negative Element of REAL
(abs (1 - (sqrt 5))) to_power s is V11() real ext-real set
(abs (1 - (sqrt 5))) |^ s is V11() real ext-real set
(- 1) + 1 is V11() real ext-real integer set
(- (sqrt 5)) + 1 is V11() real ext-real set
- (1 - (sqrt 5)) is V11() real ext-real set
(1 + (sqrt 5)) to_power s is V11() real ext-real set
(1 + (sqrt 5)) |^ s is V11() real ext-real set
2 to_power (m + 1) is V11() real ext-real set
2 |^ (m + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer set
((1 + (sqrt 5)) to_power (m + 1)) / (2 to_power (m + 1)) is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) to_power (m + 1)) / (2 to_power (m + 1)) is V11() real ext-real Element of COMPLEX
((1 - (sqrt 5)) / 2) to_power (m + 1) is V11() real ext-real set
((1 - (sqrt 5)) / 2) |^ (m + 1) is V11() real ext-real set
tau_bar to_power (m + 1) is V11() real ext-real set
tau_bar |^ (m + 1) is V11() real ext-real set
(tau_bar to_power (m + 1)) * (tau_bar to_power n) is V11() real ext-real set
(tau to_power (m + 1)) * (tau_bar to_power n) is V11() real ext-real set
(n + m) + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau to_power ((n + m) + 1) is V11() real ext-real set
tau |^ ((n + m) + 1) is V11() real ext-real set
((tau_bar to_power (m + 1)) * (tau_bar to_power n)) + (tau to_power ((n + m) + 1)) is V11() real ext-real set
((tau to_power (m + 1)) * (tau_bar to_power n)) + (tau to_power ((n + m) + 1)) is V11() real ext-real set
(m + 1) + n is non empty epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative integer set
tau_bar to_power ((m + 1) + n) is V11() real ext-real set
tau_bar |^ ((m + 1) + n) is V11() real ext-real set
(tau_bar to_power ((m + 1) + n)) + (tau to_power ((n + m) + 1)) is V11() real ext-real set
(tau to_power n) * (tau to_power (m + 1)) is V11() real ext-real set
((tau to_power (m + 1)) * (tau_bar to_power n)) + ((tau to_power n) * (tau to_power (m + 1))) is V11() real ext-real set
Lucas ((n + m) + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative integer Element of NAT
(tau to_power (m + 1)) * ((tau_bar to_power n) + (tau to_power n)) is V11() real ext-real set