# How to show that Chern number gives the amount of edge states?

When talking about topological insulator and talking about bulk-edge correspondence, it seems to be widely accepted conclusion that the band Chern number (winding number) is equal to, when the boundary becomes open, the amount of edge states. But why? For example, SSH model or Graphene (treat $k_x$ as parameter of a 1D chain and $k_y$ as the wave vector along this 1D chain). When the 1D chain is closed, in the topologically non-trivial phase, Chern number can be calculated to be, say, one. And after cutting the 1D chain open, there is one pair of gapless state living on the two edges. Why is Chern number equal to the amount of gapless edge state pairs? Is there any proof of that?