isBigOTVS_map — Mathlib

English

Post-composing both f and g with a fixed map k preserves the big-OTVS relation: f =O[𝕜; map k l] g if and only if f ∘ k =O[𝕜; l] g ∘ k.

Русский

Пост-композиция сохраняет отношение big-OTVS: f =O[map k l] g эквивалентно f ∘ k =O[ l ] g ∘ k.

LaTeX

$$$f =O[𝕜; map\\ k\\ l]\\ g \\iff (f \\circ k) =O[𝕜; l] (g \\circ k).$$$

Lean4

@[simp]
theorem isBigOTVS_map {k : β → α} {l : Filter β} : f =O[𝕜; map k l] g ↔ (f ∘ k) =O[𝕜; l] (g ∘ k) := by
  simp [isBigOTVS_iff, EventuallyLE]

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