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HexGraphIso.Nauty.Sparse.DistanceMap

theorem Hex.GraphIso.Nauty.Sparse.distvals_map {n : Nat} (G H : SparseGraph n) (p : Perm n) (hiso : ∀ (u v : Fin n), H.adj (p.get u) (p.get v) = G.adj u v) (root v : Fin n) :
(distvals (Graph.ofGraph H) ↑(p.get root))[↑(p.get v)]! = (distvals (Graph.ofGraph G) ↑root)[↑v]!

Native BFS distances commute with an arbitrary supplied isomorphism, including unreachable vertices and changes to native traversal order.