isLittleO_neg_right — Mathlib

English

Let α be a type, and l a filter. Then IsBigOAbs holds: ((fun x => abs (u x))) =O l (fun x => abs (v x)) iff u =O l v.

Русский

Пусть α — тип; IsBigOAbs: (abs(u)) =O_l abs(v) эквивалентно u =O_l v.

LaTeX

$$$((x \\mapsto |u(x)|)) =O_l (x \\mapsto |v(x)|) \\iff u =O_l v$$

Lean4

@[simp]
theorem isLittleO_neg_right : (f =o[l] fun x => -g' x) ↔ f =o[l] g' :=
  by
  simp only [IsLittleO_def]
  exact forall₂_congr fun _ _ => isBigOWith_neg_right

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