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.