Confusion with は when using なくて

I’m going through the grammar lessons and came across the example usage of は with なくて.

Here is the explanation along with the example:

As discussed in our initial lesson about ない, there are two forms of this particular word. One form is an auxiliary verb, and is used with verbs. The other form of ない is an い-Adjective (形容詞), and is used with nouns, な-Adjectives, and い-Adjectives.

The difference between these two, is that the い-Adjective form may have は in between it and the word it is connected to (では in the case of nouns and な-Adjectives). With verbs, due to ない being an auxiliary verb, this is not possible.

The examples provided don’t make a lot of sense to me.

この風呂は汚れはなくて、いつもいい匂いがする。
This bath is not dirty, so it always smells good. (Unnatural Japanese, as は will never come between a verb and ない)

How is 汚れ a verb? I know 汚れる is an 一段 verb, but 汚れ is not; it is a noun (at least according to my dictionary). The は in 汚れは makes me think of the noun since the particle terminates any other conjugation.

In the second example:

この風呂は汚れなくて、いつもいい匂いがする。
This bath doesn’t get dirty, and it always smells good. (Natural Japanese)

Seems to be making use of the verb. I’m confused which is which. Are both examples using the verb or the noun? I think the first example uses the noun, while the second example is conjugating the verb into 汚れなくて. The explanation under the first example contradicts this though, so I’m not sure if that’s correct.

Unnatural Japanese, as は will never come between a verb and ない

Can someone tell me what’s going on here? Could some other examples be provided as well? I don’t entirely understand when you should and shouldn’t use は with なくて.

Thanks in advance.

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Maybe what is confusing here is that the negation of an ichidan verb is formed by combining the nominal form (汚れ) with ない: 汚れ+ない = 汚れない.

You can use the nominal form with は + ない, but I think the meaning is subtly different than if you were negating the verb:

  • このお風呂に汚れは何一つもない: There isn’t a speck of dirt in this bathtub (right now)

  • このお風呂は汚れない: This bathtub doesn’t get dirty.

What I think they are stressing is that you can’t say

  • このお風呂は汚れはない

And have it mean that this bathtub doesn’t get dirty, ie where 汚れ functions as a verb carrying its aspect over to ない.

So in both of the original examples above I think they are treating 汚れる in its various guises as a verb, and attempting to show for one of them that it doesn’t work well.

I think this may refer to these kind of structures:

  • お風呂は汚くはない: The bathtub isn’t dirty
  • お風呂はきれいではない: The bathtub is not clean

Because 汚い is an い-adjective, it is negated as 汚くない, and we can stick は between the parts (汚く+は+ない).