Is writing short proofs inline bad form? I'm TeXing up a paper right now and I would like to ask for a sanity test about proper form.

In the paper, there are some statements which seem too simple to be called a Proposition or Lemma, let alone a Theorem. I use the word Remark for those. However, roughly speaking, there are three kinds of Remarks:


Ones whose proofs are fairly easy or standard, but not completely trivial, so I put a short argument after, using the standard proof environment.
Ones which I think are completely obvious in context, for example they just summarise some exposition directly above, so I simply put a qed sign at the end (I sometimes do the same with Corollaries).
Ones which have very simple proof, which may not be entirely obvious at a glance, but I believe a minimal (say, one short sentence) explanation is enough. In this case, putting the short explanation in the proof environment seems to be a waste of space and makes the whole thing look too important. Instead, I just put the short explanation in a parenthetical comment, which I append to the body of the remark, and follow that with the qed sign.


This system seems to be logical to me, but I would like some confirmation that this is OK, particularly the last kind.

I would also be interested in alternatives, with their pros and cons (I am unlikely to change the style in this paper unless I'm convinced that there is a big problem, but I may try to do something better in the next one).
Maybe this is "opinion based", but here is what I prefer, and I think it is pretty standard.

I would only use the QED box  at the end of a proof environment (which started with Proof) which is preceded by a numbered Theorem / Proposition  / Lemma / Corollary etc.  That way, there is a clear statement of what is being proved, and the statement is clearly distinguished from the proof.  Subconsciously, I think of Proof and  as matched delimiters.

I don't think "too simple" is the main consideration for whether to use Proposition or Remark.  Rather, I think Remark should be used only for statements or discussions which are a digression from the main argument of the paper.  If you have a statement which is important to the paper, even if the proof is very simple, make it a Proposition or Lemma or Corollary (with a number), and follow it with a Proof.  (You might be able to get away with saying something like "we have the following proposition whose proof is obvious", and then omitting the Proof environment, but this can be annoying.)

In a Remark, if discussing a particular claim, you might include a short proof or sketch or outline.  Generally this would be written into the prose of the paragraph and not set off as a separate proof, and I would not use the QED symbol here.


  Remark. The previous result raises the question of whether every snark is a boojum.  In fact, the answer is yes, and this can be seen by noting that cheese is green and the sky is mauve.  However, it is still not known whether every boojum is a snark.


This would be an alternative to:


  Proposition 6.37. Every snark is a boojum.
  
  Proof. Cheese is green and the sky is mauve.