Null URM Program Computes Identity Function

Theorem
The null URM program computes the identity function $$I_{\N}: \N \to \N$$, defined as:
 * $$\forall n \in \N: I_{\N} \left({n}\right) = n$$.

Proof
The null URM program by definition has no instructions.

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