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Mirrors > Home > MPE Home > Th. List > df-mpl | Structured version Visualization version Unicode version |
Description: Define the subalgebra of the power series algebra generated by the variables; this is the polynomial algebra (the set of power series with finite degree). (Contributed by Mario Carneiro, 7-Jan-2015.) (Revised by AV, 25-Jun-2019.) |
Ref | Expression |
---|---|
df-mpl | mPoly mPwSer ↾s finSupp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmpl 19353 | . 2 mPoly | |
2 | vi | . . 3 | |
3 | vr | . . 3 | |
4 | cvv 3200 | . . 3 | |
5 | vw | . . . 4 | |
6 | 2 | cv 1482 | . . . . 5 |
7 | 3 | cv 1482 | . . . . 5 |
8 | cmps 19351 | . . . . 5 mPwSer | |
9 | 6, 7, 8 | co 6650 | . . . 4 mPwSer |
10 | 5 | cv 1482 | . . . . 5 |
11 | vf | . . . . . . . 8 | |
12 | 11 | cv 1482 | . . . . . . 7 |
13 | c0g 16100 | . . . . . . . 8 | |
14 | 7, 13 | cfv 5888 | . . . . . . 7 |
15 | cfsupp 8275 | . . . . . . 7 finSupp | |
16 | 12, 14, 15 | wbr 4653 | . . . . . 6 finSupp |
17 | cbs 15857 | . . . . . . 7 | |
18 | 10, 17 | cfv 5888 | . . . . . 6 |
19 | 16, 11, 18 | crab 2916 | . . . . 5 finSupp |
20 | cress 15858 | . . . . 5 ↾s | |
21 | 10, 19, 20 | co 6650 | . . . 4 ↾s finSupp |
22 | 5, 9, 21 | csb 3533 | . . 3 mPwSer ↾s finSupp |
23 | 2, 3, 4, 4, 22 | cmpt2 6652 | . 2 mPwSer ↾s finSupp |
24 | 1, 23 | wceq 1483 | 1 mPoly mPwSer ↾s finSupp |
Colors of variables: wff setvar class |
This definition is referenced by: reldmmpl 19427 mplval 19428 |
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