Theorems · Theorem · order theory
Set.compl_iUnion
∀ {β : Type u_2} {ι : Sort u_5} (s : ι → Set β), (⋃ i, s i)ᶜ = ⋂ i, (s i)ᶜ- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Compl.complstatement · cited by 2,925
- Set.iUnionstatement · cited by 2,483
- Set.iInterstatement · cited by 1,084
- compl_iSupproof · cited by 6
Cited by32
Results whose statement or proof uses this declaration.
- Set.Finite.isClosed_biUnionproof · cited by 11
- Set.compl_iUnion₂proof · cited by 9
- isClosed_iUnion_of_finiteproof · cited by 6
- MeasureTheory.TendstoInMeasure.exists_seq_tendsto_aeproof · cited by 5
- Set.Finite.closure_biUnionproof · cited by 4
- Set.sdiff_iUnionproof · cited by 3
- Topology.IsLower.isTopologicalBasisproof · cited by 3
- Bornology.isBounded_biUnionproof · cited by 3
- IsDiscrete.iUnionproof · cited by 3
- isLindelof_of_countable_subfamily_closedproof · cited by 2
- PrimeSpectrum.isOpen_singleton_tfae_of_isNoetherian_of_isJacobsonRingproof · cited by 2
- IsLindelof.elim_countable_subfamily_closedproof · cited by 2