As the following link shows, I thought "publishing" a mathematical idea in a form of Q&A is being encouraged in this site.
Since Stack Overflow launched, we've been trying to explain that it's not just a Q&A platform: it's also a place where you can publish things that you've learned: recipes, FAQs, HOWTOs, walkthroughs, and even bits of product documentation, as long you format it as a question and answer."
However, some say this site is different from other SE sites. And the above is not necessarily true. If so, answering own question is not a good thing here?
What I was doing is as follows.
(1) I asked a question. I had no pre-answer when I posted this.
(2) After a while(almost a month), I got an idea which could solve (1). So I posted a series of questions. I answered each of the questions. Sometimes other people's answers helped greatly.
(3) I answered (1)
(4) I generalized the question (1).
(5) I repeated a similar process.
Edit Another reason why I'm writing proofs is that they can be reference. When I answer to other's questions, I thought I'd be able to use them.