Theorems · Theorem · order theory
Set.iInter_of_empty
∀ {α : Type u_1} {ι : Sort u_5} [IsEmpty ι] (s : ι → Set α), ⋂ i, s i = Set.univ- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsEmpty
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
- Set.univstatement · cited by 3,945
- Set.iInterstatement · cited by 1,084
- IsEmptystatement and proof · cited by 759
- iInf_of_emptyproof · cited by 12
Cited by23
Results whose statement or proof uses this declaration.
- Filter.biInter_memproof · cited by 22
- ProbabilityTheory.iIndepFun.isProbabilityMeasureproof · cited by 14
- Set.Finite.interior_biInterproof · cited by 5
- ProbabilityTheory.Kernel.iIndepSets.iIndepproof · cited by 4
- Set.image_iInterproof · cited by 4
- Filter.iInf_principal_finsetproof · cited by 3
- ProbabilityTheory.Kernel.iIndepSets.ae_isProbabilityMeasureproof · cited by 3
- Dynamics.dynEntourage_zeroproof · cited by 2
- Convex.helly_theorem_compact'proof · cited by 2
- TopCat.isTopologicalBasis_cofiltered_limitproof · cited by 1
- Finset.indicator_biUnion_eq_sum_powersetproof · cited by 1
- Dynamics.dynEntourage_mem_uniformityproof · cited by 1