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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.

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    Use pen and paper and draw a proof tree... Start from the top (middle of sheet) with assumption $p \land q$. Then add $r$ as "temporary" assumption. Then unpack $p \land q$ (by $\land$-elim) into $p$ (left) and $q$ (right). – 2017-02-06

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\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}

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    Is that correct? I never seen two assumptions like this: one under the other. Becouse in this way you have just to replace the number of the line with the line. I thounght you have to start with two separate branches and the join them together? Right, I hope you undertand me – 2017-02-07