How to make a formal proof with A → (B ∨ C) ⊢ (A → B) ∨ (A → C)

Question

Here is what I've got so far

I feel like I need an indirect proof for this and so I need to prove a contradiction with one of line 4 or 5. I'm not sure how to approach it. Any hints that can help me in the right direction please

Answer 1

$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}}$

You have a premise. Make use of it.

Assume $\lnot((A\to B)\vee(A\to C))$.   Assume $A$.   Eliminate the premises' conditional, to derive $B\vee C$.   Eliminate that disjunction to derive $B$.   Discharge the assumption of $A$ to introduce a conditional, and thereafter complete the reduction to absurdity proof.

$$\fitch{A\to B\vee C}{\fitch{\lnot((A\to B)\vee(A\to C))}{\fitch{A}{B\vee C\\{\fitch{B}{~}\\\fitch{C}{\fitch{~}{~}\\~\vdots\\B}}\\B}\\A\to B\\\phantom{(A\to B)\vee (A\to C)}\\\bot}\\\lnot\lnot((A\to B)\vee (A\to C))\\(A\to B)\vee (A\to C)}$$