I like the way the files are split, but I'm not sure I like the [Not] in the name. Option 1 did not have that specific element. What do you think @jnyrup? Do you think it adds value?

I can change it of course.

When organizing, I was thinking how logical it is for anybody looking at the code independent of IDE features that both the positive and negative version are in the same file.

I was imagining several ways (that are allowed by the filesystem).
I settled on [Not] as that is also the notation used in the documentation/release notes.

So, the file containing: HaveImplicitConversionOperator, HaveImplicitConversionOperator<T>, NotHaveImplicitConversionOperator and NotHaveImplicitConversionOperator<T> is called...

TypeAssertionSpecs.HaveImplicitConversionOperator.cs 
TypeAssertionSpecs.[Not]HaveImplicitConversionOperator.cs 
TypeAssertionSpecs.Not-HaveImplicitConversionOperator.cs 
TypeAssertionSpecs.Not.HaveImplicitConversionOperator.cs 
TypeAssertionSpecs.Not_HaveImplicitConversionOperator.cs 

Yes, I understand, but I don't quite like it myself.

I would prefer if we just left out the [Not].
Other than that I like the changes here 👍

I'll change it. Downside is that the Be comes before cs