![]() |
Mathbox for Alexander van der Vekens |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > Mathboxes > df-naryf | Structured version Visualization version GIF version |
Description: Define the n-ary (endo)functions. (Contributed by AV, 11-May-2024.) (Revised by TA and SN, 7-Jun-2024.) |
Ref | Expression |
---|---|
df-naryf | ⊢ -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛)))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cnaryf 47312 | . 2 class -aryF | |
2 | vn | . . 3 setvar 𝑛 | |
3 | vx | . . 3 setvar 𝑥 | |
4 | cn0 12472 | . . 3 class ℕ0 | |
5 | cvv 3475 | . . 3 class V | |
6 | 3 | cv 1541 | . . . 4 class 𝑥 |
7 | cc0 11110 | . . . . . 6 class 0 | |
8 | 2 | cv 1541 | . . . . . 6 class 𝑛 |
9 | cfzo 13627 | . . . . . 6 class ..^ | |
10 | 7, 8, 9 | co 7409 | . . . . 5 class (0..^𝑛) |
11 | cmap 8820 | . . . . 5 class ↑m | |
12 | 6, 10, 11 | co 7409 | . . . 4 class (𝑥 ↑m (0..^𝑛)) |
13 | 6, 12, 11 | co 7409 | . . 3 class (𝑥 ↑m (𝑥 ↑m (0..^𝑛))) |
14 | 2, 3, 4, 5, 13 | cmpo 7411 | . 2 class (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛)))) |
15 | 1, 14 | wceq 1542 | 1 wff -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥 ↑m (𝑥 ↑m (0..^𝑛)))) |
Colors of variables: wff setvar class |
This definition is referenced by: naryfval 47314 naryfvalixp 47315 naryrcl 47317 1aryenef 47331 2aryenef 47342 |
Copyright terms: Public domain | W3C validator |