comp_snd — Mathlib

English

Same fiberwise principle as above, with a simplified form for the membership equivalence of sieves.

Русский

То же по компоненту слева в виде упрощенного члена.

LaTeX

$$$\text{IsBigO} (\text{Filter.instSProd.sprod } l l')\, f\, g \Rightarrow \text{Eq} (\text{Filter.instMembership.mem} (\text{Filter.instSProd.sprod } l l') \; \dots)\; \dots$$$

Lean4

protected theorem comp_snd : f =o[l] g → (f ∘ Prod.snd) =o[l' ×ˢ l] (g ∘ Prod.snd) :=
  by
  simp only [isLittleO_iff, eventually_prod_iff]
  exact fun h _ hc ↦ ⟨fun _ ↦ True, eventually_true l', _, h hc, fun _ ↦ id⟩

Похожие утверждения