Draw the Diagram

Here is paragraph 24 of State v. Silva, 2019 UT 36:

We begin by emphasizing the substantial overlap between the defenses of imperfect and perfect self-defense.  Imperfect self.defense is strict subset of perfect self-defense.  So if a theory of imperfect self-defense is rejected by a jury -- as was the case here -- it may logically follow that  theory of perfect self-defense would likewise be rejected.

The next paragraph provides the definitions of perfect and imperfect self-defense.  The difference is that in perfect self-defense the defendant's belief in the legality of use of force is correct while in imperfect self-defense, the defendant's belief is mistaken. Assume a strict subset is a proper subset.

That means that imperfect is not a struct subset of perfect and cannot be a subset at all.  The key definitional element of one excludes instances of the other.  Correct beliefs exclude mistaken beliefs, so under normal rules of sets, the two sets have no overlap.  So, no struct subset, which I take to mean the same as proper subset.  Which also means that inference proposed in the last sentence is not a logical inference.  I am not sure if it even a reasonable practical inference, but could be.

So what did Justice Lee mean?  What am I misunderstanding?  If I am not, why did no one catch this before publication -- there are four other justices and all of them have three clerks.