Chulin 11b - Relying on Rov for Treifa

The gemara goes through a lengthy discussion to prove that we rely on rov (majority), ultimately trying to prove this from shechita itself where we aren't concerned that there was a hole in the esophagus on the exact spot that the shechting took place. The gemara rejects this proof (and the other proofs) by suggesting that wherever possible we don't rely on rov, but when there is no choice we do rely on it. It then proves this from Rebbi Meir who would be concerned even for a minority, so how was he able to eat any meat - clearly when impossible he relied on rov and wasn't concerned for the minority, we too rely on rov when there is no alternative. According to the simple conclusion of the gemara it should be necessary to examine every animal for all 18 possible treifos, since wherever possible we cannot rely on rov. However, Rashi twists the gemara at the very end to have an opposite conclusion. Since following the sources suggested in the gemara for relying on rov we would not be able to rely on rov when it is possible to check, rashi says that it must be that the source for relying on rov is a הלכה למשה מסיני (or from the simple reading of the pasuk - אחרי רבים להטות without exception), and would apply under all circumstances. Therefore, even when it is possible to check, one would not need to check. Although the simple reading of the gemara doesn't yield this conclusion, it seems that the practice of eating meat without checking for all treifos led rashi to interpret the gemara differently and say that one would never need to check for treifos (except for the lungs where they are very common).

Tosafos holds that Rebbi Meir's opinion of being concerned for the minority is only a stringency of the Rabbonon. On a Torah level even R. Meir would follow majority, just that m'drabonon he is concerned for the minority (there is a Mordechai who argues on this Tosafos). According to this approach, Tosafos explains that we are proving from R. Meir that since following the minority is only d'rabonon, they were only go'zer when possible, therefore the Rabbonon who hold that we don't follow majority when possible to check, would also agree that since it is only a chumra m'drabonon, when checking isn't possible we rely on the Rov. According to this approach, on a Torah level one can rely on the Rov even when possible to check, and the requirement to check would only be rabbinic. Therefore, the gemara cannot conclude as Rashi suggests that we have a halacha l'moshe misinai allowing us to rely on rov even when possible to check, because the entire obligation to check when possible is rabbinic. Therefore, according to Tosafos the conclusion of the gemara should be that m'drabonon one is responsible to check after all 18 treifos and not rely on the majority.