A Lucid Dream within a dream

This one's a bit hard to explain, but I'll try my best to make it easy to understand.

This night I dreamt that I was going to sleep. When I fell asleep (inside the dream) I had another dream in which I was doing a reality check. I tried pushing my finger through my palm, which didn't work. But somehow I thought "Why doesn't this work? I'm dreaming, so my finger should go through my palm." (even though I somehow knew I was dreaming I didn't become lucid).

So I tried again, moving my finger around a little while pushing it, and this time it did go through my palm. At this point I realised I was dreaming (so I was having a Lucid Dream within a normal dream). All I thought at that moment was "Oh okey... I'm having a Lucid Dream. Now what?" (I wasn't very enthusiastic about it at all).

Shortly afterwards I woke up from the Lucid Dream, back to the original one, where I wasn't lucid. I thought about how I should do more Reality Checks to get more Lucid Dreams and woke up (for real this time).

Has anyone else ever had something like this before?

Dreams within dreams aren't possible.

You had a dream in which the plot involved lucid dreaming. You didn't realize it was a dream because you were not aware. Awareness and a lucid dream plot are different.

Also you can't have half of a lucid dream.

Thanks for your reply.

I guess that instead of having a lucid dream within a normal one, I just lost lucidity, and somehow teleported back to my bed where I was before dreaming that I fell asleep.

Also, I know you can't have half a lucid dream. You're either lucid or you're not. That "½" in my LD Count is about a dream I had a few months ago, and I didn't know if I should count it as a Lucid Dream or not.
But that's not what this thread is about.

Right the 1/2 thing I just mentioned in passing. If you knew it was a dream it was lucid.

Also a dream where you find yourself waking up in your bed is called a false awakening. It is a good idea to reality check every time you wake up to make sure it isn't a FA.

I'll try to do that from now on.
Thanks for the advice. :)