URM Programs are Countably Infinite
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Theorem
The set $\mathbf P$ of all URM programs is countably infinite.
Proof
We can immediately see that $\mathbf P$ is infinite as the number of URM instructions is infinite.
From Unique Code for URM Program, we see that $\gamma: \mathbf P \to \N$ is also an injection.
The result follows from Domain of Injection to Countable Set is Countable.
$\blacksquare$