Theorems · Theorem · order theory
Set.iInter_subset
∀ {β : Type u_2} {ι : Sort u_5} (s : ι → Set β) (i : ι), ⋂ i, s i ⊆ s i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 39 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.iInterstatement · cited by 1,084
- iInf_leproof · cited by 104
Cited by39
Results whose statement or proof uses this declaration.
- IsCompact.nonempty_iInter_of_directed_nonempty_isCompact_isClosedproof · cited by 11
- Monotone.measure_iInterproof · cited by 4
- MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trimproof · cited by 4
- uniformity_hasBasis_closedproof · cited by 4
- cantorSet_subset_unitIntervalproof · cited by 3
- MeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trimproof · cited by 3
- contDiffWithinAt_piproof · cited by 3
- Set.mapsTo_iInter_iInterproof · cited by 3
- isStationary_sUnion_iff_of_cof_le_oneproof · cited by 3
- small_iInterproof · cited by 2
- MeasureTheory.Measure.haar.nonempty_iInter_clPrehaarproof · cited by 2
- connectedComponent_eq_iInter_isClopenproof · cited by 2