In addition to you supplying proof, you should put it back on them. Ask *them* to substantiate what they are offering. Ask them to give you a reasonable answer on how they came up with the amount they are offering. They may make some excuses, but be persistent and just tell them you need to see how they came up with this figure.
When I had my accident, the insurance company offered me a good amount, but much lower than I wanted or knew was my car's value. Once I asked how they arrived at that amount, they faxed me the whole deal report. I went through the report, making notations because the condition of my vehicle was not accurate, they left out some options I had, and they did not give me credit for recent repairs done on my vehicle. I faxed back my notations, the repair receipt and some car values I found locally in the newspaper. When all was said and done, they raised their offer over $1,300 and I accepted it.
Make them do the work too
~Diane~