## A “Side-Swapping” Lemma Regarding Minimum, Using Enriched Indirect Equality

If every solution returned by `D`

is no better than some solution returned by `X`

, any optimal solution by `X`

must be no worse than some optimal solution by `D`

“What? How could this be true?” It turned out that the reasoning can be correct, and the proof uses indirect equality in an unusual way.