We present new results in the theory of asynchronous convergence for the Distributed Bellman-Ford (DBF) family of routing protocols which includes distance-vector protocols (e.g. RIP) and path-vector protocols (e.g. BGP). We take the \emph{strictly increasing} conditions of Sobrinho and make three main new contributions.

First, we show that the conditions are sufficient to guarantee that the protocols will converge to a \emph{unique} solution, preventing the possibility of BGP wedgies. Second, we decouple the computation from the asynchronous context in which it occurs, allowing us to reason about a more relaxed model of asynchronous computation in which routing messages can be lost, reordered, and duplicated. Third, our theory and results have been fully formalised in the Agda theorem prover and the resulting library is publicly available for others to use and extend. This is in line with the increasing emphasis on formal verification of software for critical infrastructure.