| Step |
Hyp |
Ref |
Expression |
| 0 |
|
cstgr |
|- StarGr |
| 1 |
|
vn |
|- n |
| 2 |
|
cn0 |
|- NN0 |
| 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 |
|- E. x e. ( 1 ... n ) e = { 0 , x } |
| 24 |
23 14 15
|
crab |
|- { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } |
| 25 |
13 24
|
cres |
|- ( _I |` { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } ) |
| 26 |
12 25
|
cop |
|- <. ( .ef ` ndx ) , ( _I |` { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } ) >. |
| 27 |
10 26
|
cpr |
|- { <. ( Base ` ndx ) , ( 0 ... n ) >. , <. ( .ef ` ndx ) , ( _I |` { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } ) >. } |
| 28 |
1 2 27
|
cmpt |
|- ( n e. NN0 |-> { <. ( Base ` ndx ) , ( 0 ... n ) >. , <. ( .ef ` ndx ) , ( _I |` { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } ) >. } ) |
| 29 |
0 28
|
wceq |
|- StarGr = ( n e. NN0 |-> { <. ( Base ` ndx ) , ( 0 ... n ) >. , <. ( .ef ` ndx ) , ( _I |` { e e. ~P ( 0 ... n ) | E. x e. ( 1 ... n ) e = { 0 , x } } ) >. } ) |