Alacrity means promptness or cheerful readiness. For example, I might say, “I wrote this entry with alacrity, but without great care or effort.”
The fact that this entry appeared within the deadline that I set for myself is proof that I wrote it with alacrity because I hadn’t even thought about it, let alone written a word shortly before that deadline. At least, it’s proof that I wrote it with promptness.
As to the “cheerful readiness” part, not so much, particularly not the cheerfulness part. But that’s just me. I’m not a particularly cheerful guy.
The fact that the entry is so short, but still probably has a typo or two is proof that I wrote it without great care and with little effort.