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Mirrors > Home > MPE Home > Th. List > df-cpmat2mat | Structured version Visualization version Unicode version |
Description: Transformation of a constant polynomial matrix (over a ring) into a matrix over the corresponding ring. Since this function is the inverse function of matToPolyMat, see m2cpminv 20565, it is also called "inverse matrix transformation" in the following. (Contributed by AV, 14-Dec-2019.) |
Ref | Expression |
---|---|
df-cpmat2mat | cPolyMatToMat ConstPolyMat coe1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ccpmat2mat 20510 | . 2 cPolyMatToMat | |
2 | vn | . . 3 | |
3 | vr | . . 3 | |
4 | cfn 7955 | . . 3 | |
5 | cvv 3200 | . . 3 | |
6 | vm | . . . 4 | |
7 | 2 | cv 1482 | . . . . 5 |
8 | 3 | cv 1482 | . . . . 5 |
9 | ccpmat 20508 | . . . . 5 ConstPolyMat | |
10 | 7, 8, 9 | co 6650 | . . . 4 ConstPolyMat |
11 | vx | . . . . 5 | |
12 | vy | . . . . 5 | |
13 | cc0 9936 | . . . . . 6 | |
14 | 11 | cv 1482 | . . . . . . . 8 |
15 | 12 | cv 1482 | . . . . . . . 8 |
16 | 6 | cv 1482 | . . . . . . . 8 |
17 | 14, 15, 16 | co 6650 | . . . . . . 7 |
18 | cco1 19548 | . . . . . . 7 coe1 | |
19 | 17, 18 | cfv 5888 | . . . . . 6 coe1 |
20 | 13, 19 | cfv 5888 | . . . . 5 coe1 |
21 | 11, 12, 7, 7, 20 | cmpt2 6652 | . . . 4 coe1 |
22 | 6, 10, 21 | cmpt 4729 | . . 3 ConstPolyMat coe1 |
23 | 2, 3, 4, 5, 22 | cmpt2 6652 | . 2 ConstPolyMat coe1 |
24 | 1, 23 | wceq 1483 | 1 cPolyMatToMat ConstPolyMat coe1 |
Colors of variables: wff setvar class |
This definition is referenced by: cpm2mfval 20554 |
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