Actual Inception?

So last night I was in the middle of a non-lucid dream. It had a plot and characters and everything. I went to sleep in that dream, and actually had a lucid dream. When the lucid dream ended about 10 minutes later, I woke up back into the original non-lucid dream which I accepted as reality. I later woke up from that dream and realized what had happened.

I know its not actually inception but like wat.

Does the lucid I had count as a full lucid dream, or was I dreaming about having a lucid dream?

^confusing I know xD

All responses are appreicated!

That's what happened in my first lucid dream. To me it was a lucid dream. I took it that when I woke from my lucid dream that it was a false awakening.

Sometimes you can have dreams where you act just like in waking life, including going to bed.
And since you associate going to bed with dreaming, you may have been extra focused on dreaming and became lucid in the next dream.
Then you probably expected to wake up after a while and created a dream from that expectation as well.

I agree, it's a very interesting experience.
I wouldn't really think of it as "deeper levels" of dreams though, I prefer to think of them as separate dreams happening in succession.

We call it False awakening (FA). It's pretty common oneironautics phenomenon.

So I can cleanse you of your ignorance, the word Inception, based in the film, is the implementing an idea of original thought so deep in somebody's mind that they can't identify the sole origin of said idea.

Second, this is what is known as a False Awakening.

There is no such thing as layered dreaming, or at least there is no evidence of it.