Requested feature overview description.
When editing post's tags, I suggest a new button should be present. Clicking on this button would fill in the tags that are added through implications of the tags currently in the editor.

Why would it be useful?
One can never be too sure which tags are added through implications, and which ones not. The only way to check is to close the tag editor and refresh the post page. Having such a button would be useful because it would allow you to check which tags are already added through implications more quickly.

What part(s) of the site page(s) are affected?
Posts -> Post -> Options -> Edit -> Tag Editor area

Not to be that one guy, because the following will be off personal experience, but implications should be easy/easier to pick up as you get more acclimated with tagging.

But I do give this a +1 because of the simple problem where implied tags do not count towards the 4tag minimum. So if this can also be brought to the upload section of the posts part of the site, it can be very useful for new taggers.

I agree with the idea but not the name.
"Implications" is pretty ambiguous, "Apply implications" or "Expand implications" would be a bit better.

or perhaps "Show Implications"

Delian said:
or perhaps "Show Implications"

\+1

+1 this.

I've personally run into many issues where I've gotten the invalid_tag tag, or some variation of it, and had no idea which tag it was until I did ten or twenty minutes of trying to remember and studying which tag/tags weren't there any longer.

It's helped me learn the term tags actually have, but it'd be a helluva lot nicer if I could see what tags implied that one.