You do both. Prepare a declaration under penalty of perjury itemizing all costs. Next to each item have a reference to an attached exhibit. Each exhibit supports the item of costs that you are claiming. Good luck.
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There is little you can do to stop your landlord from painting your building. However, once the painting is completed, you may be able to file a decrease in services petition with the Oakland Rent Board. You could even check into a hotel while until the painting is completed and add your lodging expenses as part of your Rent Board petition. The Rent Board might reduce your rent because of the problems created by your landlord.
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A tenant could be responsible for "rust" if there was a failure to use a ventilation fan or open a window to let moisture out of the unit. Some use of rental units lead to an excessive amount of moisture which can lead to conditions that are not reasonable wear and tear. But your question says that the unit was a "very small and humid in-law apartment." It could be that the unit was non-permitted and illegal for your landlords to rent. The unit might have been untenantable from the outset....