instBoundedGENhdsClass — Mathlib

English

Finite Pi-index inherits BoundGENhdsClass given each component has that property.

Русский

Конечный индекс Π наследует BoundGENhdsClass при условии, что каждый компонент обладает этим свойством.

LaTeX

$$$ [Finite ι] [∀ i, Preorder (π i)] [∀ i, TopologicalSpace (π i)] [∀ i, BoundGENhdsClass (π i)] : BoundGENhdsClass (∀ i, π i). $$$

Lean4

instance instBoundedGENhdsClass [Finite ι] [∀ i, Preorder (π i)] [∀ i, TopologicalSpace (π i)]
    [∀ i, BoundedGENhdsClass (π i)] : BoundedGENhdsClass (∀ i, π i) :=
  ⟨(Pi.instBoundedLENhdsClass (π := fun i ↦ (π i)ᵒᵈ)).isBounded_le_nhds⟩

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