TITLE: Proof or citation?
QUESTION [9 upvotes]: I'm writing an article. I suppose that I'll submit it to a more or less decent journal (in English). I have doubts about the following: I have a lemma (with quite a trivial proof). I don't want to include this lemma with complete proof due to its triviality and because it has been already proved before in my Ph.D. thesis.
So I may either prove the lemma in the article (this certainly will not be very good) or simply include a citation of my dissertation instead of proof. But the thesis is in Ukrainian and it's not even available freely via the Internet. Which of the two alternatives would you choose?  
Do there exist other ways to do this well?

REPLY [12 votes]: On my opinion, the main criterion for a reference is that it must be AVAILABLE.
Either on Internet or in most university libraries. An unpublished thesis in Ukrainian
which is not available on Internet does not satisfy this criterion. Such a reference
is meaningless.
So the real options are: a) to leave the proof to the reader or b) to include it.
I do not understand why you call the second option "not very good". What's wrong with including a trivial lemma? A reader for whom it is trivial will just skip the proof.
PS. Why don't you scan your thesis and put in on Internet? Even in Ukrainian.