This is a simplified picture of mathematical practice. Not everything is formal in the sense of an logical derivation, and there are phrases like "trivially..."

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