I found myself saying the following sentence the other day:
I always fasten my seat belt because my car won't let me not — it starts beeping loudly.
If I were to use allow instead of let, I would say:
I always fasten my seat belt because my car won't allow me not to — it starts beeping loudly.
The latter sentence sounds natural to me because of the additional to that makes it clear what not refers to. Since let takes the bare infinitive, I suppose that using to in the first sentence would be incorrect:
I always fasten my seat belt because my car won't let me not to — it starts beeping loudly.
Wouldn't it?
What would you say about my first sentence? The words "won't let me not" sound strange to my ear. Is it grammatical? Is it clumsy? Is it perfectly natural? What is the general rule of using let + negative verb with the actual verb omitted?