Step |
Hyp |
Ref |
Expression |
0 |
|
cmdg |
|- mDeg |
1 |
|
vi |
|- i |
2 |
|
cvv |
|- _V |
3 |
|
vr |
|- r |
4 |
|
vf |
|- f |
5 |
|
cbs |
|- Base |
6 |
1
|
cv |
|- i |
7 |
|
cmpl |
|- mPoly |
8 |
3
|
cv |
|- r |
9 |
6 8 7
|
co |
|- ( i mPoly r ) |
10 |
9 5
|
cfv |
|- ( Base ` ( i mPoly r ) ) |
11 |
|
vh |
|- h |
12 |
4
|
cv |
|- f |
13 |
|
csupp |
|- supp |
14 |
|
c0g |
|- 0g |
15 |
8 14
|
cfv |
|- ( 0g ` r ) |
16 |
12 15 13
|
co |
|- ( f supp ( 0g ` r ) ) |
17 |
|
ccnfld |
|- CCfld |
18 |
|
cgsu |
|- gsum |
19 |
11
|
cv |
|- h |
20 |
17 19 18
|
co |
|- ( CCfld gsum h ) |
21 |
11 16 20
|
cmpt |
|- ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) |
22 |
21
|
crn |
|- ran ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) |
23 |
|
cxr |
|- RR* |
24 |
|
clt |
|- < |
25 |
22 23 24
|
csup |
|- sup ( ran ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) , RR* , < ) |
26 |
4 10 25
|
cmpt |
|- ( f e. ( Base ` ( i mPoly r ) ) |-> sup ( ran ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) , RR* , < ) ) |
27 |
1 3 2 2 26
|
cmpo |
|- ( i e. _V , r e. _V |-> ( f e. ( Base ` ( i mPoly r ) ) |-> sup ( ran ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) , RR* , < ) ) ) |
28 |
0 27
|
wceq |
|- mDeg = ( i e. _V , r e. _V |-> ( f e. ( Base ` ( i mPoly r ) ) |-> sup ( ran ( h e. ( f supp ( 0g ` r ) ) |-> ( CCfld gsum h ) ) , RR* , < ) ) ) |