have hi_succi :=
  hi (i + 1) (by simp)
case intro
h : ∀ (ε : ℚ), ε > 0 → ∃ N, ∀ (m : ℕ), m ≥ N → |↑N - ↑m| < ε
i : ℕ
hi : ∀ (m : ℕ), m ≥ i → |↑i - ↑m| < 1
⊢ False
case intro
h : ∀ (ε : ℚ), ε > 0 → ∃ N, ∀ (m : ℕ), m ≥ N → |↑N - ↑m| < ε
i : ℕ
hi : ∀ (m : ℕ), m ≥ i → |↑i - ↑m| < 1
hi_succi : |↑i - ↑(i + 1)| < 1
⊢ False