isBigO_congr — Mathlib

English

Another form of congruence with constant equality in IsBigOWith.

Русский

Другая форма тавтологического преобразования границы константы в IsBigOWith.

LaTeX

$$$ IsBigOWith c l f g \rightarrow Eq c c' \rightarrow IsBigOWith c' l f g $$$

Lean4

theorem isBigO_congr (hf : f₁ =ᶠ[l] f₂) (hg : g₁ =ᶠ[l] g₂) : f₁ =O[l] g₁ ↔ f₂ =O[l] g₂ :=
  by
  simp only [IsBigO_def]
  exact exists_congr fun c => isBigOWith_congr rfl hf hg

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