| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cstgr |
⊢ StarGr |
| 1 |
|
vn |
⊢ 𝑛 |
| 2 |
|
cn0 |
⊢ ℕ0 |
| 3 |
|
cbs |
⊢ Base |
| 4 |
|
cnx |
⊢ ndx |
| 5 |
4 3
|
cfv |
⊢ ( Base ‘ ndx ) |
| 6 |
|
cc0 |
⊢ 0 |
| 7 |
|
cfz |
⊢ ... |
| 8 |
1
|
cv |
⊢ 𝑛 |
| 9 |
6 8 7
|
co |
⊢ ( 0 ... 𝑛 ) |
| 10 |
5 9
|
cop |
⊢ 〈 ( Base ‘ ndx ) , ( 0 ... 𝑛 ) 〉 |
| 11 |
|
cedgf |
⊢ .ef |
| 12 |
4 11
|
cfv |
⊢ ( .ef ‘ ndx ) |
| 13 |
|
cid |
⊢ I |
| 14 |
|
ve |
⊢ 𝑒 |
| 15 |
9
|
cpw |
⊢ 𝒫 ( 0 ... 𝑛 ) |
| 16 |
|
vx |
⊢ 𝑥 |
| 17 |
|
c1 |
⊢ 1 |
| 18 |
17 8 7
|
co |
⊢ ( 1 ... 𝑛 ) |
| 19 |
14
|
cv |
⊢ 𝑒 |
| 20 |
16
|
cv |
⊢ 𝑥 |
| 21 |
6 20
|
cpr |
⊢ { 0 , 𝑥 } |
| 22 |
19 21
|
wceq |
⊢ 𝑒 = { 0 , 𝑥 } |
| 23 |
22 16 18
|
wrex |
⊢ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } |
| 24 |
23 14 15
|
crab |
⊢ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } |
| 25 |
13 24
|
cres |
⊢ ( I ↾ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } ) |
| 26 |
12 25
|
cop |
⊢ 〈 ( .ef ‘ ndx ) , ( I ↾ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } ) 〉 |
| 27 |
10 26
|
cpr |
⊢ { 〈 ( Base ‘ ndx ) , ( 0 ... 𝑛 ) 〉 , 〈 ( .ef ‘ ndx ) , ( I ↾ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } ) 〉 } |
| 28 |
1 2 27
|
cmpt |
⊢ ( 𝑛 ∈ ℕ0 ↦ { 〈 ( Base ‘ ndx ) , ( 0 ... 𝑛 ) 〉 , 〈 ( .ef ‘ ndx ) , ( I ↾ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } ) 〉 } ) |
| 29 |
0 28
|
wceq |
⊢ StarGr = ( 𝑛 ∈ ℕ0 ↦ { 〈 ( Base ‘ ndx ) , ( 0 ... 𝑛 ) 〉 , 〈 ( .ef ‘ ndx ) , ( I ↾ { 𝑒 ∈ 𝒫 ( 0 ... 𝑛 ) ∣ ∃ 𝑥 ∈ ( 1 ... 𝑛 ) 𝑒 = { 0 , 𝑥 } } ) 〉 } ) |