Theorems · Theorem · order theory
Set.subset_iUnion
∀ {β : Type u_2} {ι : Sort u_5} (s : ι → Set β) (i : ι), s i ⊆ ⋃ i, s i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 81 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.iUnionstatement · cited by 2,483
- le_iSupproof · cited by 207
Cited by81
Results whose statement or proof uses this declaration.
- Set.InjOn.image_iInter_eqproof · cited by 22
- MeasureTheory.OuterMeasure.ofFunction_leproof · cited by 10
- TopologicalSpace.IsSeparable.iUnionproof · cited by 7
- MeasureTheory.Measure.nullSingletonClass_hausdorffproof · cited by 5
- Directed.measure_iUnionproof · cited by 5
- MeasurableSpace.generateFrom_iUnion_memPartitionproof · cited by 4
- MeasureTheory.ae_restrict_iUnion_eqproof · cited by 4
- Topology.RelCWComplex.Subcomplex.closedCell_subset_of_memproof · cited by 4
- Set.infinite_iUnionproof · cited by 3
- le_ciSup₂proof · cited by 3
- dimH_iUnionproof · cited by 3
- MeasureTheory.generateFrom_squareCylindersproof · cited by 3