The basic structure of a proof is just a series of statements, each one being either:
- An assumption, or
- A conclusion, clearly following from an assumption or previously proved result.
What a proof should be
A well written proof will flow; the reader should be taken directly and inevitably to the desired conclusion, without any irrelevant details.
Each step (statement) should be clear or at least clearly justified.
Testing if a sentence belongs to a proof
Apply this test to every sentence of a proof: Is it clearly
- a. an assumption, or
- b. a justified conclusion?
If the test fails, maybe it doesn’t belong in the proof.