Metamath Proof Explorer


Definition df-naryf

Description: Define the n-ary (endo)functions. (Contributed by AV, 11-May-2024) (Revised by TA and SN, 7-Jun-2024)

Ref Expression
Assertion df-naryf Could not format assertion : No typesetting found for |- -aryF = ( n e. NN0 , x e. _V |-> ( x ^m ( x ^m ( 0 ..^ n ) ) ) ) with typecode |-

Detailed syntax breakdown

Step Hyp Ref Expression
0 cnaryf Could not format -aryF : No typesetting found for class -aryF with typecode class
1 vn setvar n
2 cn0 class 0
3 vx setvar x
4 cvv class V
5 3 cv setvar x
6 cmap class 𝑚
7 cc0 class 0
8 cfzo class ..^
9 1 cv setvar n
10 7 9 8 co class 0 ..^ n
11 5 10 6 co class x 0 ..^ n
12 5 11 6 co class x x 0 ..^ n
13 1 3 2 4 12 cmpo class n 0 , x V x x 0 ..^ n
14 0 13 wceq Could not format -aryF = ( n e. NN0 , x e. _V |-> ( x ^m ( x ^m ( 0 ..^ n ) ) ) ) : No typesetting found for wff -aryF = ( n e. NN0 , x e. _V |-> ( x ^m ( x ^m ( 0 ..^ n ) ) ) ) with typecode wff