This new question is related to this What to do when a section of a published paper has a section which contains similar results as mine?.
In my previous question(linked above), I had asked that inspite of a paper of mine posted in arXiv, how can a paper be published which has a Section containing exactly same results as mine with wordings changed. The answer from most of the members were that there is no harm in doing so as two researchers can develop similar ideas and hence can publish same results. In fact it is wrong to accuse other person whose results were published later than mine of plagiarism. Also there is no need for the other person to be aware of my result because it is posted in arXiv.
My humble question is : How do you prove then that a paper has been plagiarized? I found that there are several punishments for plagiarism, one loses ones grant, ones job, ones reputation and so on. Now if someone proves a theorem of a published paper by changing the wordings of the proof and when accused of stealing simply says "Oh! This got proved already, sorry I was not aware of this", should the author of the original paper let him/her go away with this excuse?
My questions are : How to prove plagiarism? and How to spot accidental/ deliberate plagiarism?
If someone can please help me, I will be grateful.