Explanation for calculating dilution from TSM

In the context of LBO modeling, working through an old BX case from the 00s.

Say you're purchasing a public company that has 50mm shares trading at $10ea purchased at a 25% premium.

Additionally, for treasury stock, you've got 10mm options with a $5.00 exercise price.

So when you're calculating dilution from TSM, you do 10-(10*50/12.50) to get 6m dilution from TSM, which you then add to 50 for 56 diluted shares.

What I don't understand is the 10-(10*50/12.50) calculation to get 6m diluted shares. Can anyone understand what that means or how that works?

I'm trying to think through it. You have 10m shares at $5 ea for a total value of $50. And then you divide by 12.50 since there's a 25% premium and you're more or less trying to get like for like at the premium price. But why do you subtract that from the original 10m exerciseable options?

Thank you much as always.

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