Not sure how valid "x is a subset of y" is supposed to be. Sure, in common language, a hand mirror is a type of mirror, but danbooru tags don't often reflect common language.
A better question to ask is "do users searching for mirror want to find all the results for hand_mirror?". I'm not sure I'd want to find images with the mirror pointing away from the viewer.
Understandable, but at the same time, not all mirrors shown are reflecting the subject of the picture either. Mirrors by themselves are mere objects; if one wanted to find specifically use of a mirror such that the camera can see the image in it, the reflection tag in conjunction works just fine, and has to be done already to omit the aforementioned non-reflecting mirrors.Pun not intended.
