It's based on the assumption that you are going to lose income.
If it's taxed fully, like normal and includes class 4 plus class 2 NI, then you are looking at a total of approx. 30% tax to be deducted.
I don't think you will have to prove anything much, it's based on what the HMRC already know. As far as I know, the HMRC will invite you to apply too, they will contact you.
20k average profit over 3 years
80% of 20k = 16k
16k /12 = £1.333
£1.333 x 3 = £3.999
So, based on an average profit of 20k over the last 3 years, you are eligible for £1,333 per month. I think it will arrive as One payment of £3,999. It is then subject to tax.