EXPOUNDING SEMICHUS [line 1]
Answer (to Question #2): It says "Do not wear Sha'atnez...; Make for yourself Gedilim (fringes)";
(R. Elazar): "Semuchim La'ad l'Olam Asuyim be'Emes v'Yashar" - this teaches that we derive laws from Semuchim (the adjacency of verses).
(R. Elazar): "Lo Sachsom Shor b'Disho" is followed by Parashas Yibum, to teach that we do not silence a woman who fell to Yibum to a man covered with boils (she can refuse to do Yibum).
(Rav Yosef): Even R. Yehudah, who normally doesn't expound Semuchim, agrees that we do in Sefer Devarim.
Question: What is the source that normally he doesn't expound Semuchim?
Answer (Beraisa - Ben Azai): "Do not allow a witch to live. One who sleeps with an animal will die". The Semichus teaches that just like bestiality is punished by stoning, also witchcraft;
R. Yehudah: Will we stone a witch just because they are adjacent?! Rather, Ov and Yid'oni (ways of conjuring up the dead) were in the category of witchcraft. They were singled out to teach that they are punishable by stoning, and from them we learn to all witchcraft.
Question: What is the source that R. Yehudah expounds Semuchim in Sefer Devarim?
Answer (Mishnah): A man may marry a woman who was Anusah or Mefutah (raped or enticed) by his father or son;
R. Yehudah forbids Anusas Aviv and Mefutas Aviv.
(Rav Gidal): R. Yehudah learns from "Lo Yikach Ish Es Eshes Aviv v'Lo Yegaleh Kenaf Aviv". He knows that Kenaf Aviv refers to an Anusah, since the previous verse discusses this (and he learns Mefutah from Anusah).
Chachamim argue, because the Isur of Eshes Aviv interrupts in between. They say that "Kenaf Aviv" refers to a woman awaiting Yibum from his father. This is a second Lav forbidding her. (The Lav of Dodaso, his uncle's wife, is even after his uncle died. She is forbidden also due to Yevamah l'Shuk.)
Question: Why does R. Yehudah expound Semuchim in Devarim?
Answer #1: Surely, the verses were written here (and not in their proper place earlier in the Torah) to expound Semichus.
Kenaf Aviv belongs with the Arayos (in Acharei Mos). Surely, it was written here for the Semichus,
Answer #2: He expounds Semuchim in Devarim because (one or both of) the verses are superfluous;
In this case, it would have sufficed to write "Lo Yikach Ish Es Eshes Aviv Lo Yegaleh Kenaf Aviv" is extra. (Note: some say that only "Aviv" is extra.)
THE ISUR OF SHA'ATNEZ [line 1]
These same answers apply to Tzitzis.
"Make Tzitzis" should have been taught in Parashas Tzitzis. Rather, it is taught here so we will expound Semuchim.
It already says, "A garment of Sha'atnez will not come upon you", so "Do not wear Sha'atnez" is extra to teach through Semichus.
Objection: It is not extra. Both verses are needed!
Had it said only "It will not come upon you", one would think that even a clothing salesman may not put on Sha'atnez (to display it);
"Do not wear" teaches that it is forbidden only to wear like clothing, i.e. when he benefits from it.
Had it said only "Do not wear", one might have thought that only wearing is prohibited, since there is great benefit;
"It will not come upon you" forbids putting it on yourself.
Answer: It could have said only "Do not wear Sha'atnez". "Wool and linen" is extra.
(Tana d'Vei R. Yishmael): The Torah discusses Stam (unspecified) garments. In one case (regarding Tzara'as), it specified wool and linen. We learn that all Stam garments are of wool or linen.
Rhetorical question: If so, why does it say "wool and linen" regarding Sha'atnez?
Answer: They are extra (therefore, we expound the Semichus).
Question: They are needed! One might have thought that having Sha'atnez on oneself, which is a small pleasure, applies only to wool and linen; but it is forbidden to wear any two different materials in one garment, for this is a big pleasure;
Therefore, it was needed to write wool and linen!
Answer: "Wool and linen" are extra. We would have known from the Gezeirah Shavah "Sha'atnez-Sha'atnez" that it is the same in both places.
SHA'ATNEZ IS ALLOWED IN TZITZIS [line 25]
Observation: Tana d'Vei R. Yishmael knows that Sha'atnez may be worn to fulfill the Mitzvah of Tzitzis only because of the extra words "wool and linen". Otherwise, it would be forbidden.
Question: It says "They will make Tzitzis on the corners of their garments", and Tana d'Vei R. Yishmael taught that all unspecified garments are wool or linen. And the Torah said to put Techeiles, which is wool, on them!
Question: How do we know that Techeiles is wool?
Answer: Since Shesh is linen, Techeiles must be wool. (We know that Bigdei Kehunah contain both of these - see Rashi.)
Answer: The Torah needed to write "wool and linen" so we would not learn like the Hava Amina of Rava (that we must make wool fringes for a wool garment, and linen fringes for a linen garment):
Question (Rava): "The corner" teaches to make fringes of the same material like the garment;
Contradiction: "Wool and linen...; Gedilim Ta'aseh Lecha" teaches that the fringes are wool or linen!
Answer (Rava): Wool and linen are acceptable Tzitzis for any garment. Tzitzis of any other material are valid only for a garment of that material.
Question: Tana d'Vei R. Yishmael exempts other materials, i.e. he does not expound "The corner" like Rava does. Tana d'Vei R. Yishmael has no source to require fringes of the same material like the garment!
Answer: We would have thought to learn like Rava regarding a garment of wool or linen.
We would make wool Tzitzis for a wool garment, and linen for linen.
When the garment is wool, we would dye a thread Techeiles.
We could not make wool Tzitzis for a linen garment, or vice-versa.
"Wool and linen" teaches that either may be used for Tzitzis for a garment of either material.