Description: The star division ring for the final constructed Hilbert space is a division ring. (Contributed by NM, 20-Jun-2015) (Revised by Mario Carneiro, 28-Jun-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | hlhillvec.h | |
|
hlhillvec.u | |
||
hlhillvec.k | |
||
hlhildrng.r | |
||
Assertion | hlhildrng | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlhillvec.h | |
|
2 | hlhillvec.u | |
|
3 | hlhillvec.k | |
|
4 | hlhildrng.r | |
|
5 | eqid | |
|
6 | 1 5 | erngdv | |
7 | 3 6 | syl | |
8 | eqidd | |
|
9 | eqid | |
|
10 | 1 5 2 4 3 9 | hlhilsbase | |
11 | eqid | |
|
12 | 1 5 2 4 3 11 | hlhilsplus | |
13 | 12 | oveqdr | |
14 | eqid | |
|
15 | 1 5 2 4 3 14 | hlhilsmul | |
16 | 15 | oveqdr | |
17 | 8 10 13 16 | drngpropd | |
18 | 7 17 | mpbid | |