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Mirrors > Home > MPE Home > Th. List > df-toply1 | Structured version Visualization version GIF version |
Description: Define a function which maps a coefficient function for a univariate polynomial to the corresponding polynomial object. (Contributed by Mario Carneiro, 12-Jun-2015.) |
Ref | Expression |
---|---|
df-toply1 | ⊢ toPoly1 = (𝑓 ∈ V ↦ (𝑛 ∈ (ℕ0 ↑m 1o) ↦ (𝑓‘(𝑛‘∅)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ctp1 21348 | . 2 class toPoly1 | |
2 | vf | . . 3 setvar 𝑓 | |
3 | cvv 3431 | . . 3 class V | |
4 | vn | . . . 4 setvar 𝑛 | |
5 | cn0 12233 | . . . . 5 class ℕ0 | |
6 | c1o 8281 | . . . . 5 class 1o | |
7 | cmap 8598 | . . . . 5 class ↑m | |
8 | 5, 6, 7 | co 7271 | . . . 4 class (ℕ0 ↑m 1o) |
9 | c0 4262 | . . . . . 6 class ∅ | |
10 | 4 | cv 1541 | . . . . . 6 class 𝑛 |
11 | 9, 10 | cfv 6432 | . . . . 5 class (𝑛‘∅) |
12 | 2 | cv 1541 | . . . . 5 class 𝑓 |
13 | 11, 12 | cfv 6432 | . . . 4 class (𝑓‘(𝑛‘∅)) |
14 | 4, 8, 13 | cmpt 5162 | . . 3 class (𝑛 ∈ (ℕ0 ↑m 1o) ↦ (𝑓‘(𝑛‘∅))) |
15 | 2, 3, 14 | cmpt 5162 | . 2 class (𝑓 ∈ V ↦ (𝑛 ∈ (ℕ0 ↑m 1o) ↦ (𝑓‘(𝑛‘∅)))) |
16 | 1, 15 | wceq 1542 | 1 wff toPoly1 = (𝑓 ∈ V ↦ (𝑛 ∈ (ℕ0 ↑m 1o) ↦ (𝑓‘(𝑛‘∅)))) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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