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Theorems · Theorem · order theory

Set.iUnion_union

∀ {β : Type u_2} {ι : Sort u_5} [Nonempty ι] (s : Set β) (t : ι → Set β), (⋃ i, t i) ∪ s = ⋃ i, t i ∪ s
Defined in
Mathlib.Data.Set.Lattice
Cited by
3 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.

MeasurableEmbedding.sigmaFinite_map · cited by 3MeasurableEmbedding.sigma…MeasureTheory.OuterMeasure.map_iInf_comap · cited by 2OuterMeasure.map_iInf_com…Set.insert_iUnion · cited by 0Set.insert_iUnionSet · cited by 53352SetSet.iUnion · cited by 2483Set.iUnioniSup_sup · cited by 3iSup_supSet.iUnion_unionCITED 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
  • iSup_supproof · cited by 3

Cited by3

Results whose statement or proof uses this declaration.