Description: Right multiplication by a lifted scalar is the same as the scalar operation. (Contributed by Mario Carneiro, 9-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | asclmul1.a | |
|
asclmul1.f | |
||
asclmul1.k | |
||
asclmul1.v | |
||
asclmul1.t | |
||
asclmul1.s | |
||
Assertion | asclmul2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | asclmul1.a | |
|
2 | asclmul1.f | |
|
3 | asclmul1.k | |
|
4 | asclmul1.v | |
|
5 | asclmul1.t | |
|
6 | asclmul1.s | |
|
7 | eqid | |
|
8 | 1 2 3 6 7 | asclval | |
9 | 8 | 3ad2ant2 | |
10 | 9 | oveq2d | |
11 | simp1 | |
|
12 | simp2 | |
|
13 | simp3 | |
|
14 | assaring | |
|
15 | 14 | 3ad2ant1 | |
16 | 4 7 | ringidcl | |
17 | 15 16 | syl | |
18 | 4 2 3 6 5 | assaassr | |
19 | 11 12 13 17 18 | syl13anc | |
20 | 4 5 7 | ringridm | |
21 | 15 13 20 | syl2anc | |
22 | 21 | oveq2d | |
23 | 10 19 22 | 3eqtrd | |