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Temurah 4b-6 - אי עביד לא מהני - If he did it, it doesn't work

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This is one of the most famous sugyos in Shas, and I'm having a really tough time. I have some specific questions, but first, a couple of comments.
1) I guess it is obvious that if someone did a physical action that is an aveirah, it is "מהני". Abbaye and Rava will not argue about someone who ate pork, or killed someone: there is no way to deny the impact of what he did. They only argue about the subset of aveiros where the impact is purely halachic.

2) The original presentation of their argument has two parts. a) Abbaye: If he did something the Torah doesn't allow, it does work (take halachic effect). And the proof to this is malkus - if it didn't work, how could he get malkus?
b) Rava: No, it doesn't take effect. And as for malkus, the punishment is not for the effect, but because he (tried to) violate Hashem's will.
-They aren't just talking about things with malkus, as many of the examples don't have that. They're speaking in general, anytime the Torah says what should be. Malkus is used to prove the point in those cases where it applies.
-As we will see from the whole sugya, Abbaye doesn't mean it always works, and Rava doesn't mean it never works. Rather, the default is it works/doesn't work. Additional drashos can change that in either direction.
-In (pretty much?) every case we discuss, Abbaye and Rava will find drashos to move away from the default. That being so, I have my first question: How can Abbaye prove his point from malkus? Does he have a example in mind, where he and Rava argue on whether it's מהני, and therefore he can question Rava on why there is malkus? Maybe there isn't! I don't think any of the examples in the gemara will serve.
-It does seem that I can identify a clear נפקא מינה concerning malkus (if you'd find me a case). Abbaye seems to be saying that malkus absolutely requires that the act was effective; Rava disagrees.

Now on to questions on the cases in the sugya.
5b: bechor. The verse says it doesn't have pidyon, and if you try, it doesn't work. [Aside: It's really hard to figure out how Rashi is explaining the sugya. Seems that the long Rashi is on a side point (איטליז), which the Shita makes part of the girsa of the gemara. But the actual question is from the fact that they don't have pidyon at all.]
Now if I understand it right (see 21a), the bechor and ma'aser don't have pidyon - with money - because there is nothing to be done. The animal got a mum, now it can't be a korban. For most korbonos, you buy it back from hekdesh, the animal goes to the owner, the money is used by hekdesh to replace the korbon. Here you can't do that. The replacement animal isn't a bechor, or isn't the tenth. There is no way to replace the korbon, there is no point really, so the cohen/ma'aser owner are just allowed to go ahead and shecht the animal.
So I don't really get what אין להם פדיון means. How would you even try to redeem them; redeem them from what? Give money to the gizbar... Of course it wouldn't work. What's the אי עביד that would be לא מהני?
I really have this question, a little weaker, on the earlier case of חרמים as well. There at least I understand what פדיון would mean; without it, the object remains חרם. But what would you try to do, give money to the gizbar for it? The gizbar trying to accept it? Why isn't it obvious that the gizbar can't do a redemption on an object that isn't redeemable, and can't even try - isn't it just out of his jurisdiction? If you tried to redeem my car (חולין) from the gizbar, would you need a posuk to understand why it is לא מהני? But it must be that the Torah considers the bechor in the gizbar's jurisdiction, at least potentially.

A little bit of this question goes to the first part of the principle כל מילתא דאמר רחמנא לא תעביד - anything the Torah said not to do. Aside from prohibitions (and violating positive commandments, as we see in the sugya), does this also include things that the Rambam calls שלילי in his Sefer Hamitzvos? That is, things where the Torah is just blocking you from thinking that something would happen - "No, it doesn't". His classical example there is לא תצא כצאת העבדים. You would think that an אמה עבריה goes free from a knocked out tooth, like a regular slave - no, she doesn't. It's not a prohibition, it's just a limitation in the guidelines.
Anyhow, that's what I thought לא תפדה amounts to for a bechor. It's not a prohibition (I do not think the Rambam counts it as a mitzvah), it just says that the usual rules of pidyon don't apply. How can that be included in Abbaye and Rava's discussion? The Torah must not be reading it that way?

Update: I see that the Rambam actually does count לא תפדה as a לא תעשה in Sefer Hamitzvos.

Ma'aser (בהמה). Here is posuk is לא יגאל, which is in the passive (I don't know how to do the vowels), It shall not be redeemed. I might well have thought that that fact would make us lean toward Rava here, that even Abbaye would agree that the verse is saying it cannot be redeemed, even בדיעבד.
However, the gemara does not agree with me.

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