# Null URM Program Computes Identity Function

## Theorem

The null URM program computes the identity function $I_\N: \N \to \N$, defined as:

$\forall n \in \N: \map {I_\N} n = n$

## Proof

The null URM program by definition has no instructions.

Therefore, the contents of $R_1$ remain unchanged when "running" it.

$\blacksquare$