Can any expert explain the reasoning behind the constraint in the following formulation of the minimum spanning tree?

To formulate the minimum-cost spanning tree (MST) problem as an LP, we associate a variable $ x_e$ with every edge $ e \in E$ . Each spanning tree $ T$ corresponds to its

incidence vector$ x^T$ , which is defined by $ x^T_e = 1$ if $ T$ contains $ e$ and $ x^T_e = 0$ otherwise. Let $ \Pi$ denote the set of all partitions of the vertex set $ V$ , and suppose that $ \pi \in \Pi$ . Therank$ r(\pi)$ of $ \pi$ is the number of parts of $ \pi$ . Let $ E_\pi$ denote the set of edges whose ends lie in different parts of $ \pi$ . Consider the following LP: $ $ \begin{align*} \min &\sum_{e \in E} c_ex_e \ \text{s.t. } &\sum_{e \in E_\pi} x_e \geq r(\pi) – 1 \quad \forall \pi \in \Pi, \ & x \geq 0. \ \end{align*} $ $