proposition: Lemma eq_seq_conv_to_same_lim : ∀ (a : ℕ → ℝ) (b : ℕ → ℝ) (l : ℝ), (∀ n : ℕ, a n = b n) ⇒ a ⟶ l ⇒ b ⟶ l.
proof: Proof. Take a, b : (ℕ → ℝ) and l : R. Assume that (for all n : ℕ, a n = b n). By conv_evt_eq_seq it suffices to show that (∃ k : ℕ, ∀ n : ℕ, (n ≥ k)%nat ⇒ a n = b n). Choose k := O. Take n : ℕ; such that (n ≥ k)%nat. We conclude that (a n = b n). Qed.
imports: Coq.Reals.Reals Lra Classical Classical_Pred_Type ClassicalChoice Tactics Automation Libs.Reals Notations