isLittleO_smoothingFn_one — Mathlib

English

The same relation ε = o[atTop] 1 holds in related formulations (reiterated).

Русский

Та же зависимость ε = o[atTop] 1 повторяется в связанных формулировках.

LaTeX

$$Same as above$$

Lean4

theorem isLittleO_smoothingFn_one : ε =o[atTop] (fun _ => (1 : ℝ)) :=
  by
  unfold smoothingFn
  refine isLittleO_of_tendsto (fun _ h => False.elim <| one_ne_zero h) ?_
  simp only [one_div, div_one]
  exact Tendsto.inv_tendsto_atTop Real.tendsto_log_atTop

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