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The paper announces an incremental mechanically-verified design of the algorithm of Gallager, Humblet, and Spira for the distributed determination of the minimum-weight spanning tree in a graph of processes. The processes communicate by means of asynchronous messages with their neighbours in the graph. Messages over one link may pass each other. The proof of the algorithm is based on ghost variables, invariants, and a decreasing variant function. The verification is mechanized by means of thedoi:10.1007/s001650050035 fatcat:xmyo7avv6bhd5pldthcgaid7zu