[ImPostingOnHN]

it would help for you to define your variables (A, P, L) and notation (=, ->, "lose")

Or, if you could, would you mind rewriting it in english, please?

[nonrandomstring]

Fair enough, you asked, and my attempts to think out loud in logic isn't helping I admit. So the nub is that clearly, to me, when Levitz uses the word "lose" above, s/he cannot be talking about the same "lose" in both parts of the assertion.