This is a simplified picture of mathematical practice. Not everything is formal in the sense of an logical derivation, and there are phrases like &quot;trivially...&quot; that show that the proof relies on being read by a competent mathematician.<p>The standards of what makes a good proof are also malleable. Here is a paper that discusses some of these issues in passing:  <a href="https:&#x2F;&#x2F;dl.dropboxusercontent.com&#x2F;u&#x2F;10561191&#x2F;Published&#x2F;ProbProofs.pdf" rel="nofollow">https:&#x2F;&#x2F;dl.dropboxusercontent.com&#x2F;u&#x2F;10561191&#x2F;Published&#x2F;ProbP...</a>