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Theorems · Theorem · order theory

Set.union_iUnion

∀ {β : Type u_2} {ι : Sort u_5} [Nonempty ι] (s : Set β) (t : ι → Set β), s ∪ ⋃ i, t i = ⋃ i, s ∪ t i
Defined in
Mathlib.Data.Set.Lattice
Cited by
4 results in Mathlib
Foundations
Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
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Around this declaration

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

MeasureTheory.sigmaFinite_restrict_sigmaFiniteSetWRT' · cited by 3MeasureTheory.sigmaFinite…MeasureTheory.FinStronglyMeasurable.exists_set_sigmaFinite · cited by 3FinStronglyMeasurable.exi…FirstOrder.Language.Theory.isSatisfiable_union_distinctConstantsTheory_of_infinite · cited by 1Theory.isSatisfiable_unio…MeasureTheory.OuterMeasure.map_ofFunction · cited by 1OuterMeasure.map_ofFuncti…Set · cited by 53352SetSet.iUnion · cited by 2483Set.iUnionsup_iSup · cited by 2sup_iSupSet.union_iUnionCITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

  • Setstatement and proof · cited by 53,352
  • Set.iUnionstatement · cited by 2,483
  • sup_iSupproof · cited by 2

Cited by4

Results whose statement or proof uses this declaration.