∀ {p : ℕ} {ε : ℚ} (q' : CauSeq ℚ (padicNorm p))
  (motive : (∃ N, ∀ m ≥ N, ∀ n ≥ N, padicNorm p (↑q' m - ↑q' n) < ε) → Prop)
  (this : ∃ N, ∀ m ≥ N, ∀ n ≥ N, padicNorm p (↑q' m - ↑q' n) < ε),
  (∀ (N : ℕ) (hN : ∀ m ≥ N, ∀ n ≥ N, padicNorm p (↑q' m - ↑q' n) < ε), motive ⋯) → motive this