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A child born from a union between a Be'ulah and a Kohen Gadol is definitely not a Mamzer, even according to Rebbi Akiva. (1)
Everyone agrees that a man who rapes or seduces a Nidah must pay the fine. (2)
Rebbi Nechunyah ben Hakaneh: If one damages property in the process of doing Melachah on Yom ha'Kipurim, he is exempt. (3)
Everything is from Heaven, with the exception of heat and cold.
Although capital punishment no longer applies, a person who sinned is punished from Heaven with a punishment similar to the one that he deserves.
Abaye: If a non-Kohen eats Terumah, he is exempt from payment according to Rebbi Nechunyah ben Hakaneh. (4)
One who steals the Chelev of his friend and eats it must pay, because the obligation to pay precedes the Chiyuv Kares.
A BIT MORE
1. Even Rebbi Yeshavav -- who says that according to Rebbi Akiva, a child born from any type of forbidden union is a Mamzer, including Isurei Kehunah -- agrees that a Be'ulah married to a Kohen Gadol is an exception because it is an Isur Aseh that applies only to a Kohen Gadol.
2. This is because if one is Mekadesh a woman who is a Nidah, it is a valid Kidushin.
3. Even though doing Melachah on Yom ha'Kipurim is not punished with Misah but with Kares, Rebbi Nechunyah ben Hakaneh maintains that the rule that one receives the stricter punishment (Kim Lei bid'Rabah Minei) applies not only to a Chiyuv Misah but also to a Chiyuv Kares.
4. Even though the punishment for a non-Kohen who eats Terumah is Misah bi'Yedei Shamayim and not Kares, the concept of Kim Lei bid'Rabah Minei applies according to Rebbi Nechunyah ben Hakaneh. According to Rava, the concept of Kim Lei bid'Rabah Minei applies only when there is a Chiyuv Kares.
THE FOUR CAPITAL PUNISHMENTS
The Gemara says that although once the Beis ha'Mikdash was destroyed capital punishment no longer applies, a person who sinned is punished from Heaven with a punishment similar to the one that he is Chayav. If he is Chayav Sekilah, he will fall off a roof or be killed by a wild animal. If he is Chayav Sereifah, he will die in a fire or be bitten by a snake. Tosfos asks that we see many evildoers who die natural deaths (despite the fact that they were Chayav Misah). Tosfos answers that if an evildoer does Teshuvah, his punishment is lightened and sometimes even completely forgiven. Alternatively, the Rasha may have merits that are protecting him from punishment. The Maharsha says that just as an evildoer sometimes is protected from punishment because of the few merits that he accrued, a Tzadik sometimes is punished from Heaven because of the few Aveiros that he did.
EATING TERUMAH B' MEZID
A non-Kohen who eats Terumah deliberately is Chayav Misah b'Yedei Shamayim, regardless of whether the person or the Terumah is Tamei or Tahor. If he receives Hasra'ah, he is punished with Malkus. He does not have to pay the value of the Terumah to the Kohen because a person who is punished with Malkus is exempt from payment. If he ate the Terumah b'Shogeg, he must pay the principal plus an additional Chomesh to the Kohen. (Rambam, Hilchos Terumah 6:6)
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