Let G be a digraph and $\phi$ be a circulation, $\phi(e) \ge 0$ an integer, i.e.,
$\displaystyle\sum\limits_{e\in\delta^{-}(v)} \phi(e) = \displaystyle\sum\limits_{e\in\delta^{+}(v)} \phi(e), \; \; \forall \; v \in V(G)$
Prove that there exists a set of directed cycles $C_{1}, C_{2},....,C_{n}$ (not necessarily unique) such that $\forall \; e \in E(G)$:
$\phi(e) = |\{i: 1 \le i \le n, \; e \in E(C_{i})\}|$
I'm not quite sure what is supposed to be meant by the last line. Does it mean that $\phi(e)$ is equal to the number of times $e$ appears in the given cycle?