∀ {α : Type u_1} {G : SimpleGraph α} (c : G.ConnectedComponent) (w : α) (hv : w ∈ c.supp) {a b : ↥c},
  (Nonempty.some ⋯).length % 2 = (Nonempty.some ⋯).length % 2 →
    ((Classical.choice ⋯).length + (Classical.choice ⋯).length) % 2 = 0