bind — Mathlib

English

If g is ωScottContinuous, then x ↦ f <$> g x is ωScottContinuous for any f.

Русский

Если g ωScott непрерывна, то x ↦ f <$> g x ωScott непрерывна для любого f.

LaTeX

$$$\omegaScottContinuous g \Rightarrow \omegaScottContinuous (x \mapsto f \leftarrow g x)$$$

Lean4

theorem bind {β γ} {f : α → Part β} {g : α → β → Part γ} (hf : ωScottContinuous f) (hg : ωScottContinuous g) :
    ωScottContinuous fun x ↦ f x >>= g x :=
  ωScottContinuous.of_monotone_map_ωSup
    ⟨hf.monotone.partBind hg.monotone, fun c ↦ by rw [hf.map_ωSup, hg.map_ωSup, ← ωSup_bind]; rfl⟩

Похожие утверждения