is identical to the opinion of the Rabbis, as the end of the period that begins with the midpoint of the afternoon is sunset.

The Gemara immediately rejects this proof: Rather, what is the alternative? That until means until and not including? It remains problematic. Say the latter clause of the mishna: The additional prayer may be recited all day. Rabbi Yehuda says: It may be recited until the seven hours. And it was taught in a baraita: If the obligation to recite two prayers was before him, one the additional prayer and one the afternoon prayer, he prays the afternoon prayer first and the additional prayer thereafter, because this, the afternoon prayer, is recited on a frequent basis, and that, the additional prayer, is recited on a relatively infrequent basis as it is only recited on Shabbat, the New Moon, and Festivals. The principle states: When a frequent practice and an infrequent practice clash, the frequent practice takes precedence over the infrequent practice. Rabbi Yehuda says: He recites the additional prayer first and the afternoon prayer thereafter, because the time to recite this, the additional prayer, will soon elapse, and this, the time to recite the afternoon prayer, will not soon elapse, as one may recite it until the midpoint of the afternoon.

The relevant point is: Granted, if you say that until means until and including, that is how you can find a situation where the times to recite two prayers, the afternoon prayer and the additional prayer, overlap. But if you say that until means until and not including, and that until seven hours means until the beginning of the seventh hour, noon, then how can you find a situation where the times to recite two prayers overlap? Once the time to recite the afternoon prayer, a half hour past noon, has arrived, the time to recite the additional prayer is already gone?

Rather, what is the alternative? That until means until and including? Then the first clause of the mishna is difficult, as explained above with regard to the midpoint of the afternoon: What is the halakhic difference between the opinion of Rabbi Yehuda and the opinion of the Rabbis? The Gemara answers: Do you think that when this midpoint of the afternoon was mentioned it was speaking of the period following the midpoint, the last part of the afternoon, from an hour-and-a-quarter before sunset until sunset? This was not the intention. Rather, it was speaking of the period prior to the midpoint, the first part of the afternoon, which, as explained above, is from nine-and-a-half hours after sunrise until an hour-and-a-quarter before sunset. Consequently, until the midpoint of the afternoon means until the end of the first half of that afternoon period. And this is what he is saying: When does the first half leave and the second half enter? From when eleven hours minus a quarter have passed since sunrise. Rabbi Yehuda’s use of the term until always means until and including.

Practically speaking, this means that, according to Rabbi Yehuda, it is permissible to recite the morning prayer until the end of the fourth hour. In support of this Rav Naḥman said: We, too, learned this in a mishna:

Rabbi Yehuda ben Bava testified about five matters of halakha:
When an orphan girl, who was married off by her mother or brother before reaching the age of majority, reaches the age of majority, she may refuse to continue living with her husband and thereby retroactively annul their marriage. Normally, marriage refusals are discouraged. However, in specific instances where it is clear that if the marriage were to remain in effect it would engender problems related to levirate marriage and ḥalitza, Rabbi Yehuda ben Bava testified that one may persuade the minor girl to refuse to continue living with her husband, thereby resolving the complications involved in this case.
And he testified that one may allow a woman who, after hearing of her husband’s death, seeks to remarry, to marry based on the testimony of one witness, as opposed to the two witnesses required for other testimonies of the Torah.
And he testified about a rooster that was stoned to death in Jerusalem for killing a person, in order to teach that the Torah law (Exodus 21:28) which requires the stoning of an ox that killed a person, applies to other animals as well.
And he testified about forty-day-old wine that was used for libation on the altar.
And he testified about the daily morning offering that was sacrificed at four hours of the day.

Learn from this final testimony, which is in accordance with the opinion of Rabbi Yehuda, that until means until and including. The Gemara concludes: Indeed, learn from this.

Based on this mishna, Rav Kahana said: The halakha is in accordance with the opinion of Rabbi Yehuda since we learned in a mishna in the preferred tractate, Eduyyot, in accordance with his opinion. Since the halakha is ruled in accordance with all of the mishnayot in Eduyyot, the opinion of a tanna who rules in accordance with the opinion of Rabbi Yehuda in that mishna means that the halakha is in accordance with that opinion.

And about the daily morning offering that was sacrificed at four hours. Based on this, the Gemara attempts to identify the tanna who taught that which we learned in the mishna about the manna that fell for the children of Israel in the desert: “And they gathered it morning by morning, each according to what he eats, and when the sun grew hot it melted” (Exodus 16:21); that took place four hours into the day.

The baraita continues: Do you say that the time when the sun grew hot was at four hours, or perhaps it was only at six hours of the day? When the verse says: “In the heat of the day” (Genesis 18:1), six hours is already mentioned in the Torah as the heat of the day. How, then, do I establish the verse: “And when the sun grew hot it melted”? This must refer to an earlier time, at four hours. The Gemara asks: Who is the tanna of this mishna? It is neither Rabbi Yehuda nor the Sages. If it was in accordance with the opinion of Rabbi Yehuda, until four hours is also considered morning, as he holds that the daily morning offering may still be sacrificed then, while here it says that in the morning the manna was gathered and it melted after the morning. If it was in accordance with the opinion of the Rabbis, until noon is also considered morning, since, according to the Sages, the daily morning offering could be sacrificed until noon. Apparently, this is an entirely new position.

The Gemara responds: If you wish, say that the mishna is in accordance with the opinion of Rabbi Yehuda, and if you wish, say instead that the mishna is in accordance with the opinion of the Rabbis. The Gemara explains: If you wish, say in accordance with the opinion of the Rabbis. The verse states: Morning by morning, divide it into two mornings. Morning, according to the Rabbis, lasts until noon. The repetition of the term morning in the Torah indicates that the period when the manna was gathered ended at the conclusion of the first half of the morning, i.e., the end of the third hour. And if you wish, say instead in accordance with the opinion of Rabbi Yehuda, who would say that: This extra morning in the phrase morning by morning comes to make the end of the period when the manna was gathered an hour earlier. In any event, everyone agrees that the verse, And when the sun grew hot it melted, refers to four hours of the day.

The Gemara asks: From where is the inference drawn that this is the meaning of the verse? Rabbi Aḥa bar Ya’akov said: The verse states: “When the sun grew hot it melted.” Which is the hour that the sun is hot but the shade remains cool, before the heat of the day, when even the shade is hot? You must say at four hours.

We learned in the mishna: The Rabbis hold that the afternoon prayer may be recited until the evening. Rabbi Yehuda says: It may be recited only until the midpoint of the afternoon. Rav Ḥisda said to Rav Yitzḥak: There, with regard to the morning prayer, Rav Kahana said: The halakha is in accordance with the opinion of Rabbi Yehuda, since we learned in a mishna in the preferred tractate, Eduyyot, in accordance with his opinion. Here, what is the ruling? He was silent and said nothing to him, as he was familiar with no established ruling in this matter. Rav Ḥisda said: Let us see and try to resolve this ourselves from the fact that Rav prayed the Shabbat prayers on the eve of Shabbat while it was still day. Learn from this that the halakha is in accordance with the opinion of Rabbi Yehuda, and the time for the afternoon prayer ends at the midpoint of the afternoon, after which time one may recite the evening prayer.

The Gemara immediately rejects the proof based on Rav’s practice: On the contrary, from the fact that Rav Huna and the Sages, students of Rav, would not pray until evening, learn from that that the halakha is not in accordance with the opinion of Rabbi Yehuda. The Gemara concludes: Now that the halakha was stated neither in accordance with the opinion of this Sage nor in accordance with the opinion of that Sage, one who acted in accordance with the opinion of this Sage has acted legitimately, and one who acted in accordance with the opinion of that Sage has acted legitimately, as this halakha is left to the decision of each individual.

The Gemara relates: Rav happened by the house of the Sage, Geniva, and he prayed the Shabbat prayer on the eve of Shabbat before nightfall. Rabbi Yirmeya bar Abba was praying behind Rav, and Rav finished his prayer but did not take three steps back and interrupt the prayer of Rabbi Yirmeya. Derive from this incident three halakhot: Derive from this that one may pray the Shabbat prayer on the eve of Shabbat before nightfall. And derive from this that a student may pray behind his rabbi. And derive from this that it is prohibited to pass before those who are praying.

The Gemara responds: This supports the opinion of Rabbi Yehoshua ben Levi, as Rabbi Yehoshua ben Levi said: It is prohibited to pass before those who are praying. The Gemara asks: Is that so? Didn’t Rabbi Ami and Rabbi Asi pass before those who were praying? The Gemara responds: Rabbi Ami and Rabbi Asi were beyond four cubits from those who were praying when they passed.

One particular detail was surprising: How did Rabbi Yirmeya act that way and pray behind Rav? Didn’t Rav Yehuda say that Rav said: A person should never pray