I am trying to prove the following problem, but honestly I don't know what "proof" is considered a good proof.
I tried to prove it by constructing an NFA that start with w1 and ends with wk, but I feel something is missing.
I also tried to prove it by showing that w1 ∈ L1, w2 ∈ L2, …, wk ∈ Lk and a ∈ La.
thus Language L can be represented by:
L = L1*La*L2*La*…LaLk If L is regular then L1,L2,...,Lk and La are also regular.
Finally drop(L) can be presented as follow: drop(L) = L1*L2*…*Lk, since L1,L2,...Lk are regular is drop(L) (because we know that it is closed under concatenation)
I feel that there are some notation that I am not using correctly, I don't know why I feel something is missing but can't figure it out.