∀ {V : Type u} {G : SimpleGraph V} {v w : V} {s t : Set V},
  (SimpleGraph.induce s G).Preconnected →
    (SimpleGraph.induce t G).Preconnected → v ∈ s → w ∈ t → G.Adj v w → (SimpleGraph.induce (s ∪ t) G).Connected