I am following a course on complexity theory where languages are a part of the course. There is a proof that no matter how hard I try to understand, it is till so complex that I cannot make it to half of the proof. Namely, the proof of the statement that the intersection of a CFL and a regular language is again CFL.

The proof that is provided to us is 2-3 pages of pure text and notations. The ones online are also heavily dependent on much notations and unfortunately, Sipser does not handle it in his book *Introduction to the theory of computation*. I'm wondering if there's a straight-forward and less-dependent-on-notation proof that someone knows that will contribute to understanding the proof or even reproducing it. Because at this moment, I don't even understand the proof.