Step |
Hyp |
Ref |
Expression |
0 |
|
coch |
|- ocH |
1 |
|
vk |
|- k |
2 |
|
cvv |
|- _V |
3 |
|
vw |
|- w |
4 |
|
clh |
|- LHyp |
5 |
1
|
cv |
|- k |
6 |
5 4
|
cfv |
|- ( LHyp ` k ) |
7 |
|
vx |
|- x |
8 |
|
cbs |
|- Base |
9 |
|
cdvh |
|- DVecH |
10 |
5 9
|
cfv |
|- ( DVecH ` k ) |
11 |
3
|
cv |
|- w |
12 |
11 10
|
cfv |
|- ( ( DVecH ` k ) ` w ) |
13 |
12 8
|
cfv |
|- ( Base ` ( ( DVecH ` k ) ` w ) ) |
14 |
13
|
cpw |
|- ~P ( Base ` ( ( DVecH ` k ) ` w ) ) |
15 |
|
cdih |
|- DIsoH |
16 |
5 15
|
cfv |
|- ( DIsoH ` k ) |
17 |
11 16
|
cfv |
|- ( ( DIsoH ` k ) ` w ) |
18 |
|
coc |
|- oc |
19 |
5 18
|
cfv |
|- ( oc ` k ) |
20 |
|
cglb |
|- glb |
21 |
5 20
|
cfv |
|- ( glb ` k ) |
22 |
|
vy |
|- y |
23 |
5 8
|
cfv |
|- ( Base ` k ) |
24 |
7
|
cv |
|- x |
25 |
22
|
cv |
|- y |
26 |
25 17
|
cfv |
|- ( ( ( DIsoH ` k ) ` w ) ` y ) |
27 |
24 26
|
wss |
|- x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) |
28 |
27 22 23
|
crab |
|- { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } |
29 |
28 21
|
cfv |
|- ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) |
30 |
29 19
|
cfv |
|- ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) |
31 |
30 17
|
cfv |
|- ( ( ( DIsoH ` k ) ` w ) ` ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) ) |
32 |
7 14 31
|
cmpt |
|- ( x e. ~P ( Base ` ( ( DVecH ` k ) ` w ) ) |-> ( ( ( DIsoH ` k ) ` w ) ` ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) ) ) |
33 |
3 6 32
|
cmpt |
|- ( w e. ( LHyp ` k ) |-> ( x e. ~P ( Base ` ( ( DVecH ` k ) ` w ) ) |-> ( ( ( DIsoH ` k ) ` w ) ` ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) ) ) ) |
34 |
1 2 33
|
cmpt |
|- ( k e. _V |-> ( w e. ( LHyp ` k ) |-> ( x e. ~P ( Base ` ( ( DVecH ` k ) ` w ) ) |-> ( ( ( DIsoH ` k ) ` w ) ` ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) ) ) ) ) |
35 |
0 34
|
wceq |
|- ocH = ( k e. _V |-> ( w e. ( LHyp ` k ) |-> ( x e. ~P ( Base ` ( ( DVecH ` k ) ` w ) ) |-> ( ( ( DIsoH ` k ) ` w ) ` ( ( oc ` k ) ` ( ( glb ` k ) ` { y e. ( Base ` k ) | x C_ ( ( ( DIsoH ` k ) ` w ) ` y ) } ) ) ) ) ) ) |