001: One who slaughters a wild animal or bird on Yom Tov [and must therefore cover its blood], Beis Shammai: He may dig with a stick [which was previously stuck into loose earth] and cover the blood. Beis Hillel: He may not slaughter unless he has earth prepared for the purpose of covering. Beis Hillel agrees that if he went ahead and slaughtered the animal or bird, he may go ahead and use the stick as permitted by Beis Shammai.
Question: The beginning of the Mishna “One who slaughters” indicates that they’re discussing a case of dieved: if someone went ahead and slaughtered, then Beis Shammai permits. But when Beis Hillel responds, they say “He may not slaughter” - lekatchilah - so we infer that Beis Shammai holds one may, in fact, slaughter lekatchilah.
Response: This is not a difficulty, Beis Hillel’s intention is “He may not slaughter and cover up - lekatchilah”. Rather, he can slaughter and leave the blood uncovered until after Yom Tov. [So both Beis Hillel and Beis Shammai agree that lekatchilah one should not slaughter on Yom Tov if he did not prepare earth from beforehand.]
Challenge: Later the Mishna states “Beis Hillel agrees that if he went ahead…”, which is clearly talking about dieved, so it seems that the beginning of the Mishna is not discussing dieved [and Beis Shammai’s opinion is lekatchilah]?
Rabbah: When the Mishna says “One who slaughters” it means “One who would like to slaughter”, it is thus discussing a lekatchilah situation. 
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