∀ {K : Type u_1} [inst : Field K] (A : ValuationSubring K) (a b : ↥A.unitGroup),
  { val := ⟨↑↑(a * b), ⋯⟩, inv := ⟨↑↑(a * b)⁻¹, ⋯⟩, val_inv := ⋯, inv_val := ⋯ } =
    { val := ⟨↑↑a, ⋯⟩, inv := ⟨↑↑a⁻¹, ⋯⟩, val_inv := ⋯, inv_val := ⋯ } *
      { val := ⟨↑↑b, ⋯⟩, inv := ⟨↑↑b⁻¹, ⋯⟩, val_inv := ⋯, inv_val := ⋯ }