exp_approx_end' — Mathlib

English

ExpBound and its simplifications relate bounds for arbitrary algebraic structures; in particular, the identity expBound_SUB is used to compare real and complex cases.

Русский

Связи между ограничениями экспоненты применяются к сравнению вещественных и комплексных случаев.

LaTeX

$$$\\text{(complex/real bound equivalences)}$$$

Lean4

theorem exp_approx_end' {n} {x a b : ℝ} (m : ℕ) (e₁ : n + 1 = m) (rm : ℝ) (er : ↑m = rm) (h : |x| ≤ 1)
    (e : |1 - a| ≤ b - |x| / rm * ((rm + 1) / rm)) : |exp x - expNear n x a| ≤ |x| ^ n / n.factorial * b :=
  by
  subst er
  exact exp_approx_succ _ e₁ _ _ (by simpa using e) (exp_approx_end _ _ _ e₁ h)

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