As someone entering graduate school this fall, this is something I would like to know.
For undergraduates, I know that professors generally want students to show very rigorously and clearly their chain of reason when writing proofs. This generally includes showing things that are "obviously" true.
How is proof writing generally done at the graduate level for homework and tests? On one hand, I don't want to be too terse. At best I could come across as arrogant and at worst points could be deducted.
On the other hand, showing too much could be bad. It would waste valuable time on an exam, and the professor's time grading it. It may also come across as pedantic.
So is there a rule of thumb of what can be said to be "clearly" true? Or would it be very specific to both the course and the instructor?