How to prove the following formula using an indirect proof I need to prove that the premise $A \to (B \vee C)$ leads to the conclusion $(A \to B) \vee (A \to C)$. Here's what I have so far.

From here I'm stuck (and I'm not even sure if this is correct). My idea is to use negation intro by assuming the opposite and coming up with a contradiction. I assumed $A$ which led to $B \vee C$ and, as you can see, I'm trying or elim but the only way I can think of doing this is to use conditional intro and then or intro but that seems to only work for a single subproof. In other words, I can't use the assumption of $B$ to say $A \to B$. This is called an indirect proof.

Hint: if you assume $A \to (B \lor C)$, $\lnot(A \to B)$ and $A$, then you can conclude $B \lor C$ and $\lnot B$. Can you take it from there?
