The Beraisa cites the Pasuk there "ve'Lo Sisov Nachalah li'Venei Yisrael mi'Mateh el Mateh", because from the first Pasuk ("ve'Chol Bas Yoreshes Nachalah le'Echad mi'Mishpachas Mateh Avihah Tih'yeh le'Ishah"), we would have learned Hasavas Ben (had the daughter who married into another tribe had a son she would have moved the inheritance away from her tribe, but not Hasavas Ba'al ...

... because a husband does not inherit his wife.

The Tana then cites a third Pasuk "ve'Lo Sisov Nachalah mi'Mateh le'Mateh Acher" to teach us Hasavas ha'Ba'al because, we would otherwise have established the second Pasuk too, by Hasavas ha'Ben, to teach us a Lav (seeing as the first Pasuk is only an Aseh), rendering the transgressor subject to Malkos.

He also needs to add the Pasuk in ...

... Yehoshua (concerning Pinchas' property) that we cited earlier because we would otherwise have thought that we need the previous three Pesukim for an Aseh and two Lavin by Hasavas ha'Ben (see Shitah Mekubetzes).

... Divrei Hayamim (concerning Ya'ir's twenty-three cities) because otherwise, we might have established the case of Pinchas where Pinchas inherited the property from his mother.

We know that there it cannot have been the wife of S'guv, Ya'ir's father who died, and whom he inherited because we would not require two Pesukim to teach us 'Yerushas ha'Eim'.

Rav Papa then tries to refute the proof from Pinchas and Ya'ir by attributing their property, neither to Hasavas Av nor to Hasavas ha'Ba'al (nor to Yerushas ha'Eim) but to their having purchased it; and the Navi would then be coming to teach us how wealthy they were.

Abaye rejects this suggestion because bearing in mind that purchased property is returned to the owner in the Yovel, it would mean that Elazar ha'Tzadik was buried in a temporary grave, to be exhumed and re-buried in the Yovel (a disgrace to which Pinchas would never have subjected his father).

We nevertheless reinstate the Kashya by switching from a field that they purchased to a Sdei ha'Cherem which means either a field which the owner declared Cherem or a field of Hekdesh which someone other than the owner or his son redeemed, and which goes to the Kohanim in Yovel.

This Kashya pertains to the case of Pinchas, who was a Kohen (and who might therefore have received such a field), but not to Ya'ir, who was from the tribe of Menasheh.

This Kashya dispenses with our proof for Hasavas ha'Ba'al, since now, the case of Pinchas need not necessarily be speaking about Hasavas ha'Ba'al.

The truth of the matter is however, that even if Abaye had not refuted Rav Papa's Kashya from Pinchas (as we just explained) the proof for Hasavas ha'Ba'al would have been refuted, since Ya'ir may well have purchased his cities, in which case we would no longer have two Pesukim for Hasavah, one of which we would have inevitably used for Hasavas ha'Ba'al (as we explained earlier).

When Abaye asks (with regard to the Pasuk "ve'Chol Bas Yoreshes Nachalah mi'Matos Bnei Yisrael") 'Sof Sof ha ka Mis'akra Nachalah mi'Shivta de'Eima le'Shivta de'Aba', he is querying whether the Torah is equally worried about the Yerushas ha'Eim as it is about Yerushas ha'Av, in which case, the daughter will be obligated to marry a member of the same tribe as her mother as well as of her father (as will be explained later), or whether "le'Echad mi'Mishpachas Avihah" comes to preclude the family of the mother, about which the Torah is not particular.

When we suggest 've'Dilma Sha'ani Hasam she'Kevar Husvah', we mean to resolve Abaye's She'eilah, on the grounds that it would be pointless to restrict the daughter to marry a member of her mother's tribe, seeing as, the moment her mother dies, her property has already passed from her own tribe to that of her daughter (who belongs to the tribe of her father).

But Abaye answers that perhaps we do not say she'Kevar Husvah'; since it is not because a woman's property has been partially moved to another tribe, that her daughter is permitted to move it still further.

Rav Yeimar tried to prove to Rav Ashi that we must say 'she'Kevar Husvah' because if we didn't, then since we are concerned about Hasavas ha'Ba'al no less than Hasavas ha'Ben, why does the Torah not worry about the Hasavah of the mother's property (since it only mentions "Mishpachas Avihah", and not 'mi'Mishpachas Imah'). Since, when all's said and done, by marrying someone from her father's tribe, the daughter removes her mother's property still further ...

... to which Rav Ashi replied that Abaye, (who holds Hasavas ha'Ba'al) maintains that it is possible not to say 'she'Kevar Husvah' and still not worry about the daughter removing her mother's property still further when she marries by making her marry a man whose mother is from the same tribe as her own mother was, re-creating exactly the same situation as existed when her mother married her father (before the Isur of Hasavah was declared).

Nevertheless, this will not be considered Hasavah vis-a-vis her father's property, which was one hundred per-cent within his tribe, and now (partially) passed over to another tribe (from the husband's mother's side) since, practically speaking, it is either her husband or his son who will inherit it (and not someone from his mother's side).

Even if in fact, we do not say 'she'Kevar Husvah', forcing the daughter to marry a man from her father's tribe but whose mother was from the same tribe as her mother, the Torah could not have written "le'Echad mi'Mishpachas Mateh Avihah ve'Imah" because we would then have thought that the Torah permits the daughter to marry even someone whose father is from the same tribe as her mother, and his mother from the same tribe as her father (since the property has not been transferred completely from one tribe to another, and a little of the original tribe remains).

Regarding Abaye's initial Kashya, we explained that assuming that we hold of Hasavas ha'Ba'al, but do not say 'she'Kever Husvah', why are we not concerned with the daughter (whose parents were from different tribes) transferring her mother's property to her husband's tribe. Besides the fact that it is impossible to explain it, we reject the text which explains the Kashya to be on Rav Papa (who queries the Tana's proof for Hasavas ha'Ba'al) that even if we did not hold of 'Hasavas ha'Ba'al', what difference would it make, since anyway once the daughter married someone from a different tribe, her sons would transfer her father's property from her father's tribe to that of her husband because Abaye's proof that we may as well concede 'Hasavas ha'Ba'al' is an external one that has nothing to do with the Beraisa that Rav Papa is querying, and even if we assume that he is merely coming to prove that a husband inherits, that is not something that Rav Papa doubted in essence (seeing as our Sugya brings a number of sources for this), only how it can be proved from the Pesukim cited by the Beraisa.

Another Beraisa establishes the Pasuk ...

... "ve'Lo Sisov Nachalah li'Venei Yisrael mi'Mateh el Mateh" by Hasavas ha'Ben.

... "ve'Lo Sisov Nachalah mi'Mateh le'Mateh Acher" by Hasavas ha'Ba'al.

This proves that this Tana holds of both Hasavas ha'Ben and Hasavas ha'Ba'al (even though earlier, we established both Pesukim by Hasavas ha'Ben).

This Tana proves from the fact that the second Pasuk refers to Hasavas ha'Ba'al, the first Pasuk must be referring to Hasavas ha'Ben. A second Tana arrives at exactly the same conclusion, but because since the first Pasuk refers to Hasavas ha'Ben the second one must refer to Hasavas ha'Ba'al.

These Tana'im argue with the Tana earlier in the Sugya, who established the same two Pesukim by Hasavas ha'Ben (to give two sets of Malkos to the transgressor) inasmuch as he holds that we prefer to Darshen an extra Pasuk, rather than to just use it to add an extra Lav.

The Halachic ramifications of the Machlokes are that whether Yerushas ha'Ba'al is d'Oraisa (the current Tana) or not (the earlier Tana)