Description: A coefficient of a product of polynomials. (Contributed by Mario Carneiro, 24-Jul-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | coefv0.1 | |
|
coeadd.2 | |
||
Assertion | coemul | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | coefv0.1 | |
|
2 | coeadd.2 | |
|
3 | eqid | |
|
4 | eqid | |
|
5 | 1 2 3 4 | coemullem | |
6 | 5 | simpld | |
7 | 6 | fveq1d | |
8 | oveq2 | |
|
9 | fvoveq1 | |
|
10 | 9 | oveq2d | |
11 | 10 | adantr | |
12 | 8 11 | sumeq12dv | |
13 | eqid | |
|
14 | sumex | |
|
15 | 12 13 14 | fvmpt | |
16 | 7 15 | sylan9eq | |
17 | 16 | 3impa | |