refine continuous_id.continuousOn.log ?_
N : ℕ
Npos : 0 < N
s : ℂ
s_re_gt : 0 < s.re
⊢ ContinuousOn
    (fun x =>
      Decidable.rec (fun h => (fun hx => Real.expOrderIso.symm ⟨|x|, ⋯⟩) h) (fun h => (fun hx => 0) h)
        (x.decidableEq 0))
    (Ioi ↑N)
N : ℕ
Npos : 0 < N
s : ℂ
s_re_gt : 0 < s.re
⊢ ∀ x ∈ Ioi ↑N, id x ≠ 0