Our Gemara on 16b and 17a tells us a story about how Rav Yehuda and Rabba visited Rabba bar bar Ḥana when he was unwell.
רַבָּה בַּר בַּר חָנָה חֲלַשׁ, עוּל לְגַבֵּיהּ רַב יְהוּדָה וְרַבָּה, לְשַׁיּוֹלֵי בֵּיהּ. בְּעוֹ מִינֵּיהּ: שְׁנַיִם שֶׁהֵבִיאוּ גֵּט מִמְּדִינַת הַיָּם, צְרִיכִין שֶׁיֹּאמְרוּ "בְּפָנֵינוּ נִכְתַּב וּבְפָנֵינוּ נֶחְתַּם", אוֹ אֵין צְרִיכִין? אָמַר לָהֶם: אֵין צְרִיכִין – מָה אִילּוּ יֹאמְרוּ "בְּפָנֵינוּ גֵּירְשָׁהּ", מִי לָא מְהֵימְנִי?! אַדְּהָכִי, אֲתָא הָהוּא חַבְרָא, שְׁקַלָה לִשְׁרָגָא מִקַּמַּיְיהוּ. אֲמַר: רַחֲמָנָא! אוֹ בְּטוּלָּךְ, אוֹ בְּטוּלָּא דְּבַר עֵשָׂו
The Gemara relates: Rabba bar bar Ḥana was weak, and Rav Yehuda and Rabba entered to visit him and to inquire about his well-being. While they were there, they raised a dilemma before him: With regard to two people who brought a bill of divorce from a country overseas, are they required to say: It was written in our presence and it was signed in our presence, or are they not required to issue this declaration? He said to them: They are not required to say it, for the following reason: What if they said: She was divorced in our presence, wouldn’t they be deemed credible? Therefore, they do not have to state the declaration. In the meantime, while they were sitting there, in came a certain Persian priest [ḥabbara] and took the lamp [sheragga] from before them. It was a Persian holiday on which the Persians prohibited the public from maintaining light outside their temple. Rabba, who was from Eretz Yisrael, said: Merciful One! Let us live either in Your shadow or in the shadow of the descendants of Esau, the Romans.
Ben Yehoyada observes that the rabbinic exchange involved reasoning through a Kal V’chomer, which is a segulah for Refuah. How does a Kal V’chomer assist healing? He says the Benei Yisaschar holds that the 13 derivational principles of the Torah ( https://www.jewishvirtuallibrary.org/hermeneutics ) correspond to the Thirteen Attributes of Mercy (https://en.wikipedia.org/wiki/Thirteen_Attributes_of_Mercy ). (This is also found in Zohar Yisro 90) Thus, the first one, “E-L”, stands for absolute kindness, as we see in Tehilim 52:3. And, Kal V’chomer is the first of the Thirteen Derivational Principles. Thus studying Kal V’chomer leads to an activation of God’s absolute kindness. Indeed, we see that when Moshe prays to Hashem (using the name “E-L”) to forgive Miriam, Hashem himself uses a Kal V’chomer (Bamidbar 12:13-14) :
וַיִּצְעַ֣ק מֹשֶׁ֔ה אֶל ה לֵאמֹ֑ר
אֵ֕-ל נָ֛א רְפָ֥א נָ֖א לָֽהּ
Moshe cried out [in prayer] to Hashem saying: “Please, God, please heal her.”
וַיֹּ֨אמֶר ה אֶל־מֹשֶׁ֗ה וְאָבִ֙יהָ֙ יָרֹ֤ק יָרַק֙ בְּפָנֶ֔יהָ הֲלֹ֥א תִכָּלֵ֖ם שִׁבְעַ֣ת יָמִ֑ים תִּסָּגֵ֞ר שִׁבְעַ֤ת יָמִים֙ מִח֣וּץ לַֽמַּחֲנֶ֔ה וְאַחַ֖ר תֵּאָסֵֽף
Hashem said to Moshe: “If her father were to spit in her face would she not be in shame for seven days? She shall be closed off for seven days, beyond the encampment, and after that, she may join again.”
We should ask ourselves how does this actually work? On a simple level, since all of Torah and the world and God are interrelated, referencing a part of the Torah where God heals and states a Kal V’chomer, creates some kind of theurgical resonance, even if we do not know how it works. And since we have another principle of Binyan Av, which essentially allows us to make broad comparisons and inferences from one similar situation in the Torah to another, if one of the 13 Attributes of Mercy corresponds with one of the 13 Derivational Principles, we might assume that they all do. However, later on as we discuss what occurs in the rest of the story on Daf 17, we can see more spiritual mechanisms at work.
Further in the story, we experience our protagonists being harassed by the Persian priest who extinguishes a fire and forbade them to have a light due to their idolatrous observance. Upon experiencing this disruption in their Torah study, they declare, “Merciful One! Let us live either in Your shadow or in the shadow of the descendants of Esau, the Romans.”
Maharam Schiff explains that the nature of exile under the Romans, the descendants of Esau, is different than the nature of exile under the Persians. This is because the prophecy and blessing given by Yaakov states (Bereishis 25:23):
וַיֹּ֨אמֶר ה לָ֗הּ שְׁנֵ֤י (גיים) [גוֹיִם֙] בְּבִטְנֵ֔ךְ וּשְׁנֵ֣י לְאֻמִּ֔ים מִמֵּעַ֖יִךְ יִפָּרֵ֑דוּ וּלְאֹם֙ מִלְאֹ֣ם יֶֽאֱמָ֔ץ וְרַ֖ב יַעֲבֹ֥ד צָעִֽיר׃
And Hashem said to her (Rivka), Two nations are in your womb, Two separate peoples shall issue from your body; One people shall be mightier than the other,
And the older shall serve the younger.”
Our tradition holds that so long as Yaakov is strong in Torah study and observance, he will have dominion over Esav. However, should he slack off, then the seesaw moves in the other direction and Esav becomes dominant. Therefore, the Maharam Schiff says that the Rabbis who are studying Torah naturally preferred to be under Roman dominion, because Torah would have rented them immune. On the other hand, such protections were not available from the Persian exile. This is why the Persian was able to extinguish their lamp (and the light of their Torah).
The Chasam Sofer (see Oros Hasofrim, p. 19) observes that Persian dominion versus that under Esav was different in a key and traumatic manner. The Persian homicidal rage was chaotic and unpredictable. On the other hand, the Romans were methodical, and made their intentions clear. Without being an expert on trauma psychology, the Chasam Sofer correctly intuits that it is more painful to not know when and where your enemy is going to attack, than to live under an consistently oppressive regime, whose intentions and motivations are clear. Psychologically, this is similar to someone having constantly abusive parents versus somebody who has chaotic and disorganized abusive parents. It is easier for the former person to find resilience and recover from trauma than the latter, because in the former case, the very predictability of it makes it manageable and understandable. In the latter case, the trauma is the confusion of sometimes receiving kindness and other times receiving hatred.
This can give us insight as to why a Kal V’chomer represents and activates absolute chessed and kindness. A Kal V’chomer is one of the most logical and orderly inferences of the 13 hermeneutical principles. It simply follows the logic; If such and such is true in regard to a more permissive law, surely it must be true in regard to a stricter law. If you think about it, it is the mechanism of kindness itself. The one who has more power understands intuitively that he therefore has an obligation to be forgiving and more accepting of the one who has less. Our relationship with our “brother” Esav still follows some kind of orderly rules. It might seesaw, where one is on top, and the other is on bottom, but it follows predictable rules based our attachment to God. So, engaging in the Kal V’chomer, not only activated some kind of divine kindness and healing mechanism but it may also have been an effort to protect them from totalitarian oppression of Esav. Unfortunately, because they were under Persian rule, which was random and chaotic without clear motivations and unpredictability, they could not use the force to protect them.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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