Rashi on Amud Aleph (“Eyno Din”) discusses the rule of dayo in relation to a kal v’chomer. This is a lomdishe piece, that also involves exegesis,, and then more mystical discussion as well.
Let’s start with a basic kal v’chomer. A kal v’chomer is the first of the thirteen hermeneutical principles that tradition says we use to understand and derive Torah laws. A kal v’chomer works by making an assumption that if this rule applies to one one situation, surely in a more stringent situation it must also apply. Thus, the Torah says one may not eat maaser as an Onan. Maaser has less holiness requirements than Teruma. So if an Onan cannot eat maaser surely, kal v’chomer, he cannot eat Terumah.
Then we have the principle of Dayo. Dayo says that even though we are deriving an application to a more stringent case, it is enough to limit it to the rules of the less stringent case and not go beyond. The classic case is in Mishna Bava Kama (2:5). There is a rule that a goring ox pays half damages for actions in a public space. But if someone’s animal did damage by eating in a public space, there is no liability, (presumably people should know to be careful in public area and guard their possession from a goat who Might try to make mischief, unlike an ox who might suddenly gore out of the blue.) There also is a rule that on private property, if someone’s animal ate the field owner’s produce, the owner of the animal must make full payment. Now you might argue, if goring is liable for half Damage in a public Area, where eating is not even liable for any damages, surely on private property where eating is liable for full damages, goring should be liable for full damages. Yet, because of the principle of Dayo, we will limit the liability for goring, even in a private area, because it can’t be more than its original source. Since original source was gorijg in a public area which is only liable for half damage, so too on private property it will be only liable for half damage.
The most famous case of Dayo comes from the Chumash. When Miriam is given her punishment of Tzoraas for speaking ill of Moshe and his relationship with God, God offers the following rationale for her seven day exile from the camp (Numbers 12:14):
If her father spat in her face, would she not bear her shame for seven days? Let her be shut out of camp for seven days, and then let her be readmitted.
Disrespect to God is obviously more severe than to a parent. So really Miriam should have suffered a longer exile than seven days. But the Gemara (Bava Kama 25a) tells us that due to the principle of Dayo, Miriam still was only punished for seven days.
We finished the lomdus and the exegesis part. Now we will go into the mystical. Given that God has Thirteen attributes of Mercy and also there are thirteen hermeneutical principles for Torah, the coincidence begs interpretation. The Kedushas Levi (Ki Tissah) says that each of the hermeneutical principles correspond with one God’s attributes. Thus, א-ל corresponds with Kal V’chomer. The kal v’chomer and Dayo was used in Miriam’s punishment and redemption as actually an enactment of the middah of א-ל which is extreme chessed as we shall soon see.
Now how does kal v’chomer and Dayo represent א-ל and chessed? When it comes to the universe, God is obviously the Chomer and everything else is the Kal. Thus, if God were to enact the cosmic Kol V’chomer in the fullest way without using any restraint, His presence would overwhelm and blot everything else out of existence.Thus God employs the Cosmic Dayo, to be metzamtzem, to limit His presence to allow for anything else to exist. This is the ultimate Chessed, to make room for the existence of another and is why the Kal V’chomer corresponds to א-ל which is extreme chessed.
Another example of this comes from Agra Dekallah (Bereishis 155) where he quotes a Gemara (Chulin 60a) that discusses primordial reasoning of the Earth’s vegetation at the time of creation:
Rabbi Ḥanina bar Pappa taught: “May the glory of the Lord endure forever; let the Lord rejoice in His works” (Psalms 104:31). This verse was stated by the minister of the world, i.e., the angel charged with overseeing the world. When the Holy One, Blessed be He, said: “Let the earth put forth grass, herb yielding seed, and fruit tree bearing fruit after its kind” (Genesis 1:11), the grasses drew an a fortiori inference with regard to themselves.
They reasoned: If the Holy One, Blessed be He, wishes the mixing of species, why did he say: After its kind, with regard to the trees? And furthermore, let us draw an a fortiori inference: If with regard to trees, which do not naturally grow mixed, as they are large and distinct from one another, the Holy One, Blessed be He, said: “After its kind,” all the more so with regard to us, since grass naturally grows mixed.
This story begs the question, what difference does it make that the vegetation made a Kal V’chomer? And, why did God leave it to them to make this Kal V’chomer?
Using our new understanding that the Kal V’chomer represents chessed, Agra Dekallah says that this was to activate chessed when it comes to sustenance. I would like to add, for those who are interested in developing ways that a slower evolutionary process can be read into the creation narrative, here is another Midrashic hint. The vegetation went through a process of development that was inspired by God’s intellectual force but came from their own ontological truths.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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