Proofs are graded in the following way. (This goes for proofs on exams, too.)
Any complete and correct proof gets full credit. It doesn’t matter how many steps you had, whether you used the most clever strategy, etc. If your proof works, you get full credit.
If your proof is incorrect or incomplete, here is what I do to calculate partial credit:
I begin by deleting any unnecessary or incorrect steps you contributed. There are two qualifications on this:
If a step you’ve written is necessary for the proof but its justification is wrong, I leave the step and fix its justification. You then earn at least half credit for that step, depending on how much fixing the justification required.
If I have to fix an otherwise correct step by moving it into or out of a subproof, you get half credit for the step.
I then correct or complete the proof in the fewest possible steps. Points are then awarded based on the proportion of the correct proof that you contributed.