I’m currently writing my PhD thesis, in a mathematical field in physics. I have published a handful of papers, and the thesis is going to be mostly based on these results. I assume that, even though they are published, I should be including full proofs in the thesis.

I also assume I will effectively need to rewrite these proofs, if only for copyright reasons, having surrendered some of my rights to the journals in which these papers were published, and also for self-plagiarism reasons.

Is there anything I should look out for, and are my assumptions correct?