I have the following language
$$L = \{w\in\{a,\;b\}^* : a^nv,\; n\geq 1 \wedge |v|_a \geq n\}$$
Formed by characters "$a$" and "$b$" where the word $v$ has more "$a$" characters than $a^n$.
I have to prove that this is a regular language, but I can't see any way to do that, I think this is not a regular language.
Any ideas on how to prove this?
HINT: Every word in $L$ begins with $a$. And $aw\in L$ if and only if $|w|_a\ge 1$.