# Proof that there is unambigous grammar for every regular language

How can I prove, or where can I find proof that for every regular language there is unambigous grammar?

Something like this might work. First, note that every regular language is accepted by some minimal DFA. Call such a DFA $M$. Next, describe how you could construct a right-regular grammar that accepts the same language as $M$. Take as your set of nonterminal symbols the set $Q$ of states of $M$. Form the set of productions as follows: the smallest set of productions such that if $M$ has a transition from $q_1$ to $q_2$ on $\sigma$, then there is a production $q_1 \rightarrow \sigma q_2$, and also a production $q_1 \rightarrow \sigma$ if $q_2$ is an accepting state. (You'll also need to add the production $q_0 \rightarrow \epsilon$ if the empty string is in the language).
Hint: Use a right-regular grammar. This is a kind of grammar which has rules of the following types: $A \to aB$ and $A \to \epsilon$.