A distributed proof (also known as local certification, or
proof-labeling scheme) is a mechanism to certify that the
solution to a graph problem is correct.
It takes the form of an assignment of labels to the nodes, that
can be checked locally.
There exists such a proof for the minimum spanning tree problem, using
$O(\log n \log W)$ bit labels (where $n$ is the number of nodes in the
graph, and $W$ is the largest weight of an edge).
This is due to Korman and Kutten who describe it in concise and
formal manner in [Korman Kuttten 07].
In this note, we propose a more intuitive description of the
result, as well as a gentle introduction to the problem.