The second one isstatement obviousfollows if the first one holds. For the first onestatement, suppose n’ chose the edge e and sent a test message to n via edge e. Then, node n will delay the response (according to case 3 of "How to find minimum weight incident outgoing edge?"). Then, it is impossible for the case that n’ has already sent its convergecast message. By 1 and 2, we can conclude it is safe forto absorbingabsorb F tointo F' since e’ is still the minimum outgoing edge to report after F is absorbed.
