cardinalInterFilter_sup — Mathlib

English

Supremum of two CardinalInterFilters is a CardinalInterFilter with the infimum bound.

Русский

Супремум двух CardinalInterFilter имеет CardinalInterFilter с инфим Bound.

LaTeX

$$$CardinalInterFilter(l_1 \sqcup l_2) (c_1 \sqcap c_2)$$$

Lean4

instance cardinalInterFilter_sup (l₁ l₂ : Filter α) {c₁ c₂ : Cardinal.{u}} [CardinalInterFilter l₁ c₁]
    [CardinalInterFilter l₂ c₂] : CardinalInterFilter (l₁ ⊔ l₂) (c₁ ⊓ c₂) :=
  by
  have : CardinalInterFilter l₁ (c₁ ⊓ c₂) := CardinalInterFilter.of_cardinalInterFilter_of_le l₁ inf_le_left
  have : CardinalInterFilter l₂ (c₁ ⊓ c₂) := CardinalInterFilter.of_cardinalInterFilter_of_le l₂ inf_le_right
  exact cardinalInterFilter_sup_eq _ _

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