addition of unit step functions

Question

Recently, I received an answer key for a test and I am trying to understand this line: $$u[n-3]-u[n-4]=δ[n-3]$$

How is this possible? I cant seem to find any resource to this. Here is the original question with solution, for reference: problem

Answer 1

Using the following relationship $$u[n] = \sum_{k=-\infty}^{n} \delta [k],$$ we get $$u[n-3]=\sum_{k=-\infty}^{n-3} \delta [k] = \delta[n-3]+\sum_{k=-\infty}^{n-4} \delta [k] = \delta[n-3]+u[n-4].$$