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

Definition df-naryf 45028
 Description: Define the n-ary (endo)functions. (Contributed by AV, 11-May-2024.) (Revised by TA and SN, 7-Jun-2024.)
Assertion
Ref Expression
df-naryf -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
Distinct variable group:   𝑥,𝑛

Detailed syntax breakdown of Definition df-naryf
StepHypRef Expression
1 cnaryf 45027 . 2 class -aryF
2 vn . . 3 setvar 𝑛
3 vx . . 3 setvar 𝑥
4 cn0 11889 . . 3 class 0
5 cvv 3444 . . 3 class V
63cv 1537 . . . 4 class 𝑥
7 cc0 10530 . . . . . 6 class 0
82cv 1537 . . . . . 6 class 𝑛
9 cfzo 13032 . . . . . 6 class ..^
107, 8, 9co 7139 . . . . 5 class (0..^𝑛)
11 cmap 8393 . . . . 5 class m
126, 10, 11co 7139 . . . 4 class (𝑥m (0..^𝑛))
136, 12, 11co 7139 . . 3 class (𝑥m (𝑥m (0..^𝑛)))
142, 3, 4, 5, 13cmpo 7141 . 2 class (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
151, 14wceq 1538 1 wff -aryF = (𝑛 ∈ ℕ0, 𝑥 ∈ V ↦ (𝑥m (𝑥m (0..^𝑛))))
 Colors of variables: wff setvar class This definition is referenced by:  naryfval  45029  naryfvalixp  45030  naryrcl  45032  1aryenef  45046  2aryenef  45057
 Copyright terms: Public domain W3C validator