How do other commentators understand the answer to this question, i.e. that the belt shows that he had to wash, but there is no proof in the case of someone merely losing something.
Sam Iser, Berwyn, PA
(a) According to Rashi in Moed Katan (who explains that one who has only one shirt will wear a belted overcoat instead of a shirt while he is washing the shirt), the Gemara should have said that his "overcoat" proves that he only has one shirt, and not that his "belt" proves it. Perhaps it is only through the belt over the overcoat (which normally does not require a belt, since it covers the shirt and belt) that it is evident that the washer is not wearing a shirt under his overcoat.
(b) RABEINU CHANANEL and RAV SHLOMO BEN HA'YASOM explain that the person is wearing the belt as a loincloth , and is otherwise naked. According to his explanation it is clear why the Gemara mentions the belt. On the other hand, though, it is hard to understand why the Gemara makes a point of the belt rather than the lack of a shirt. From RABEINU GERSHOM in Chulin 108a it seems that the intention of the Gemara is that even a second person, who owns more than one shirt, can wash the shirt for his single-shirted friend. The reason is because normally a person submits his belt to be washed along with his shirt. When he has but a single shirt he must keep the belt for himself [to wear, like Rabeinu Chananel] at home, and he submits a beltless shirt. The shirt's "beltlessness" proves that it is being washed for a person who has no other shirt. The proof is thus from the lack of a belt and not from the belt itself.
(c) RASHI in Chulin 108a (and in the "Perush Rashi to Moed Katan" -- the Perush printed in the Gemara is probably a Talmid of Rabeinu Gershom) explains that the opposite is true. When a single-shirted person washes his shirt, he leaves the belt with the shirt , and does not take it out. Other people remove the belt before giving a shirt to the cleaner in order to use the belt with the shirt that they are currently wearing. (In one Perush, Rashi on Moed Katan adds that the needy person's single shirt is tailored in such a way to make its belt entirely unremoveable.) The belt on the shirt that is being washed proves that it is the owner's only shirt. (Again, this is a better proof than the clothlessness of the owner since even another person can wash the shirt based on this logic. In addition, the shirtless person might be wearing an overcoat ( without a belt) to cover himself while washing the shirt.
M. Kornfeld
Rabbi, thank you very much. I have just one more question. The gemara uses this case of someone of whom it is obvious that he had to wash his clothing to say that somone who lost something is not subject to marit ain like the man who had to wash. By how do we know that someone who lost something has lost something? Why is this so obvious to us as a poor man wearing a belt or without a shirt on?
Thank you for your time
Sam Iser
The Gemara is not comparing the person who has one garment to the person who lost something on Erev Yom Tov (and was not able to shave because he was busy searching for it). The person with a single garment may wash on Chol ha'Moed, since all know that he has only one garment. The person who was busy Erev Yom Tov is not allowed to shave since others do not know that he was busy Erev Yom Tov. (Rashi DH Yomru).
M. Kornfeld