Theorems · Theorem · order theory
Set.inter_iUnion
∀ {β : Type u_2} {ι : Sort u_5} (s : Set β) (t : ι → Set β), s ∩ ⋃ i, t i = ⋃ i, s ∩ t i- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 59 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 and proof · cited by 53,352
- Set.iUnionstatement · cited by 2,483
- inf_iSup_eqproof · cited by 4
Cited by59
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_iSupproof · cited by 16
- ProbabilityTheory.Kernel.IndepSets.indepproof · cited by 9
- MeasureTheory.Measure.restrict_iUnion_leproof · cited by 5
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- Set.sdiff_iInterproof · cited by 4
- MeasureTheory.Measure.restrict_iUnion_apply_eq_iSupproof · cited by 3
- MeasureTheory.ae_eq_zero_of_forall_setIntegral_eq_of_sigmaFiniteproof · cited by 3
- MeasureTheory.VectorMeasure.restrict_le_restrict_iUnionproof · cited by 3
- Set.iUnion₂_inter_iUnion₂proof · cited by 3
- Set.inter_iUnion₂proof · cited by 3
- MeasureTheory.Measure.restrict_iUnion_apply_aeproof · cited by 2
- MulAction.isTopologicallyTransitive_iff_dense_iUnion_preimageproof · cited by 2