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Every edit has the potential to provoke edit war, and nothing inconsiderate has happened. Whether or not it will happen relies on the editors involved. Will you, as the bold editor, decide to engage in discussion or try and edit war your changes in? If you're decided on discussion, then this shouldn't be a problem.
Changes would be better proposed at Talk:Azerbaijan than here. With regards to the Nagorno-Karabakh statement, it's two sentences that seem very relevant to the article, given a bit of Azerbaijan hasn't been controlled by Azerbaijan since independence. There may be more concise ways to write it, but removing all mention of NKR is not an improvement. Something that read as quite puffery was the UN paragraph. It's not remotely unusual for a country to be part of the UN, and it's not particularly special to be elected to the UNSC. The four paragraphs 'rule' is a guide to try and create a concise lead. Again, I recommend you open on the talkpage a discussion along the lines of ""The current text X should be changed to Z because of Y."" Regards,   "