terminology - Is "The trick is to not try to tell yourself not to think about the bad things..." a double-negative used correctly?

An answer to the stackexchange question I've just been bitten by a rattlesnake; how, exactly, do I “keep calm”? includes the following advice:

The trick is to not try to tell yourself not to think about the bad things¹, but instead tell yourself to think about something else. Tell yourself to think about what you need to do now to get proper care and treatment. Tell yourself to think about what you will do to celebrate your recovery. Tell yourself to think about something mundane, like your job or your favorite TV show or that hobby project you've got going.

and has the footnote:

¹Look everyone! A double negative used properly.

Does the term "double negative" have a formal definition? (It seems to have a tag at least.) If so, is this one? If so, is it used properly?

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From what I recall being taught quite a long time ago, a double negative is the negation of two words in a row, or nearly so, with the intent of a single negative. For example

That's not no proper way to negate.

versus

That's not a proper way to negate.

In my original, quoted snake-bite example above, a negation is used twice, and it is used intentionally both times to arrive at the intended meaning. As helpfully pointed out below, The Oxford Dictionary Online says:

1. A negative statement containing two negative elements...

1.1 A positive statement in which two negative elements are used to produce the positive force...

The first does not specify (to me at least) if the desired outcome is positive or still negative, and the second mentions "positive force" but I don't think it means the double negative is intended to result in a positive result. Rather I think "positive force" means a positive emphasis on the negative statement.

At this point I've gone way past my limits of understanding of the English language in the hopes that it demonstrates an honest attempt at doing research into the question. While I'd love to understand if there is more than one kind of double negative, I'm primarily asking about the quoted phrase.

Answer

For those that might be interested in a traditional understanding of "double negative", here it is:

NEVER use a double negative except to created a positive.

As a boy I was not taught anything about "double negatives" but the above "rule".

I would be satisfied were that rule generally observed.
So

You don't owe me nothing

would mean you owe me something.

This "rule" may well be out of fashion, and, I think, the result can be chaos in reading some things.

In English, I will not allow anyone to present me with any writing that employs a "double" negative" that suggests a negative,

The trick is to not try to tell yourself not to think about the bad thing

The statement above has three actions defining "The trick is": to try, to tell yourself and to think about .

But, the two infinitives to tell and to think are tied to to try. To try is negated by not. and to think about is negated by another not.
So:

The trick is to not try to tell yourself (and) not try not to think about the bad thing

there is no double negative as "not try not to think" are two actions. Both are negated by a single negative.