Derivation tree

A notation for derivations (cf. Derivation, logical) in a calculus, in which the elements of the derivations from which $P$ is obtained by one application of a derivation rule are written down above each element $P$. For instance, the derivation $P_1,\ldots,P_6$ in which $P_1$, $P_2$ and $P_4$ are axioms, $P_3$ is obtained by one application of some rule from $P_1$ and $P_2$, and $P_5$ is obtained from $P_4$ and $P_3$, while $P_6$ is obtained from $P_3$ and $P_5$, may be written down as follows:
$$\dfrac{P_1,P_2}{P_3}\quad\dfrac{\dfrac{P_4,\dfrac{P_1,P_2}{P_3}}{P_5}}{P_6}$$