I'm working on this : $$\dashv(p \ \land q) \to (( \ r \to p)\ \land \ (r \to q))$$ And a solution is this :
1 assume p & q.
2 assume r.
3 p. &E1 1
4 therefore r => p. =>I 2,3
5 assume r.
6 q. &E2 1
7 therefore r => q. =>I 5,6
8 (r => p) & (r => q). &I 4,7
9 therefore p & q => (r => p) & (r => q). =>I 1,8
Now I'm not able to understand, due to my ignorance, how to convert this into a tree proof? Maybe this question is so idiotic, but I have been trying for 1 hour and nothing. I hope someone helps me.
\begin{align} \cfrac{\cfrac {\cfrac{\cfrac{\cfrac{[p \land q]^2}{[r]^1} }{p \qquad \qquad q } \land \text {-E}} {(r \to p) \quad (r \to q)} \to \text {-I}_1}{(r \to p) \land (r \to q)}\land \text {-I}}{(p \land q) \to ((r \to p) \land (r \to q))}\to \text {-I}_2 \end{align}