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The phrase "a small lesson" is correct and usable in written English.
It can be used when referring to a brief or minor teaching moment or piece of instruction.
Example: "After the main lecture, the teacher gave us a small lesson on the importance of teamwork."
Alternatives: "a brief lesson" or "a minor lesson".
Exact(7)
But perhaps he could do with a small lesson in the way the commercial-services industry works.
It was a small lesson but an illustration of the forensic attention to detail of a true professional.
Eventually we learn that a haircut and a new suit don't make for a better man, which seems like a small lesson after what we've been through.
It was a test, probably, or perhaps a joke; anyway, a deliberate, Grigsonesque manoeuvre to teach close and faithful readers a small lesson about Heisenberg's Principle of Uncertainty.
A small lesson in the way history smooths the sharper edges and corners of the past is being played out at the Cannes Film Festival with the help of that much-loved father figure of the alternative establishment, Sir Mick Jagger.
From blasé it is a short distance to spoiled absolutely rotten, and once you've arrived there, you can depend upon the gods to devise a small lesson in humility.
Similar(53)
Appeaser… Before such abuse of the term gets worse, perhaps we should all take a small history lesson". Kennedy's lesson is magisterial in its specificity and range, but it's indeed as "risky" as its purpose: to commend appeasement to those who hurl the "A" word at American strategists they consider insufficiently aggressive.
All of which is sad, because this case offers the U.S. government the chance to make at least small amends for some of the darkest parts of its official history to demonstrate that it has absorbed at least a few small lessons from that past.
Appeaser… Before such abuse of the term gets worse, perhaps we should all take a small history lesson".
But there's a small historical lesson that may muddy the waters.
So the first step is a small science lesson!
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com