Step |
Hyp |
Ref |
Expression |
0 |
|
ctus |
|- toUnifSp |
1 |
|
vu |
|- u |
2 |
|
cust |
|- UnifOn |
3 |
2
|
crn |
|- ran UnifOn |
4 |
3
|
cuni |
|- U. ran UnifOn |
5 |
|
cbs |
|- Base |
6 |
|
cnx |
|- ndx |
7 |
6 5
|
cfv |
|- ( Base ` ndx ) |
8 |
1
|
cv |
|- u |
9 |
8
|
cuni |
|- U. u |
10 |
9
|
cdm |
|- dom U. u |
11 |
7 10
|
cop |
|- <. ( Base ` ndx ) , dom U. u >. |
12 |
|
cunif |
|- UnifSet |
13 |
6 12
|
cfv |
|- ( UnifSet ` ndx ) |
14 |
13 8
|
cop |
|- <. ( UnifSet ` ndx ) , u >. |
15 |
11 14
|
cpr |
|- { <. ( Base ` ndx ) , dom U. u >. , <. ( UnifSet ` ndx ) , u >. } |
16 |
|
csts |
|- sSet |
17 |
|
cts |
|- TopSet |
18 |
6 17
|
cfv |
|- ( TopSet ` ndx ) |
19 |
|
cutop |
|- unifTop |
20 |
8 19
|
cfv |
|- ( unifTop ` u ) |
21 |
18 20
|
cop |
|- <. ( TopSet ` ndx ) , ( unifTop ` u ) >. |
22 |
15 21 16
|
co |
|- ( { <. ( Base ` ndx ) , dom U. u >. , <. ( UnifSet ` ndx ) , u >. } sSet <. ( TopSet ` ndx ) , ( unifTop ` u ) >. ) |
23 |
1 4 22
|
cmpt |
|- ( u e. U. ran UnifOn |-> ( { <. ( Base ` ndx ) , dom U. u >. , <. ( UnifSet ` ndx ) , u >. } sSet <. ( TopSet ` ndx ) , ( unifTop ` u ) >. ) ) |
24 |
0 23
|
wceq |
|- toUnifSp = ( u e. U. ran UnifOn |-> ( { <. ( Base ` ndx ) , dom U. u >. , <. ( UnifSet ` ndx ) , u >. } sSet <. ( TopSet ` ndx ) , ( unifTop ` u ) >. ) ) |