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Theorems · Theorem · order theory

Set.iInter_union_of_antitone

∀ {ι : Type u_12} {α : Type u_13} [inst : Preorder ι] [IsDirectedOrder ι] {s t : ι → Set α},
  Antitone s → Antitone t → ⋂ i, s i ∪ t i = (⋂ i, s i) ∪ ⋂ i, t i
Defined in
Mathlib.Data.Set.Lattice
Cited by
1 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderIsDirectedOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

cantorSet_eq_union_halves · cited by 1cantorSet_eq_union_halvesSet · cited by 53352SetPreorder · cited by 7952PreorderSet.iInter · cited by 1084Set.iInterAntitone · cited by 563AntitoneIsDirectedOrder · cited by 316IsDirectedOrderiInf_sup_of_antitone · cited by 1iInf_sup_of_antitoneSet.iInter_union_of_antitoneCITED BYCITES

Cites6

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Cited by1

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