In Lean, a sequence \(a₀, a₁, a₂,...\) can be represented by a function \(a : ℕ → ℝ\) so that \(a(n)\) is \(aₙ\).

The statement that \(L\) is the limit of the sequence \(a\) is defined by

def SeqLim (a : ℕ → ℝ) (L : ℝ) : Prop :=
  ∀ ε > 0, ∃ k : ℕ, ∀ n ≥ k, |a n - L| < ε

Prove that if \(aₙ = 1/n\) for all \(n\), then the sequence \(a\) converges to 0.

To do so, complete the following Lean 4 theory:

import Mathlib.Data.Real.Basic
import Mathlib.Tactic

variable (a : ℕ → ℝ)

def SeqLim (a : ℕ → ℝ) (L : ℝ) : Prop :=
  ∀ ε > 0, ∃ k : ℕ, ∀ n ≥ k, |a n - L| < ε

example
  (ha : ∀ n, a n = 1 / n)
  : SeqLim a 0 :=
by sorry

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