Theorem: C03S06.exists_abs_le_of_convergesTo (LeanInRome/S3_Logic/S06_Sequences_and_Convergence.lean)

State before:
s : ℕ → ℝ
a : ℝ
cs : ConvergesTo s a
⊢ ∃ N b, ∀ (n : ℕ), N ≤ n → |s n| < b
Tactic:
rcases cs 1 zero_lt_one with ⟨N, h⟩
State after:
case intro
s : ℕ → ℝ
a : ℝ
cs : ConvergesTo s a
N : ℕ
h : ∀ n ≥ N, |s n - a| < 1
⊢ ∃ N b, ∀ (n : ℕ), N ≤ n → |s n| < b

State before:
case intro
s : ℕ → ℝ
a : ℝ
cs : ConvergesTo s a
N : ℕ
h : ∀ n ≥ N, |s n - a| < 1
⊢ ∃ N b, ∀ (n : ℕ), N ≤ n → |s n| < b
Tactic:
use N, |a| + 1
State after:
case h
s : ℕ → ℝ
a : ℝ
cs : ConvergesTo s a
N : ℕ
h : ∀ n ≥ N, |s n - a| < 1
⊢ ∀ (n : ℕ), N ≤ n → |s n| < |a| + 1

State before:
case h
s : ℕ → ℝ
a : ℝ
cs : ConvergesTo s a
N : ℕ
h : ∀ n ≥ N, |s n - a| < 1
⊢ ∀ (n : ℕ), N ≤ n → |s n| < |a| + 1
Tactic:
sorry
State after:
no goals