Theorems · Theorem
Set.mem_iInter
∀ {α : Type u} {ι : Sort v} {x : α} {s : ι → Set α}, x ∈ ⋂ i, s i ↔ ∀ (i : ι), x ∈ s i- Defined in
- Mathlib.Order.SetNotation
- Cited by
- 69 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.ofPredproof · cited by 6,101
- Set.rangeproof · cited by 4,705
- Set.iInterstatement · cited by 1,084
Cited by69
Results whose statement or proof uses this declaration.
- Set.ofPred_forallproof · cited by 48
- Set.InjOn.image_iInter_eqproof · cited by 22
- Submodule.mem_iInfproof · cited by 12
- Set.iInter_ofPredproof · cited by 7
- MeasureTheory.Measure.haar.addCHaar_mem_clAddPrehaarproof · cited by 6
- MeasureTheory.Measure.haar.chaar_mem_clPrehaarproof · cited by 6
- Ordinal.veblenWith_add_oneproof · cited by 3
- ProperlyDiscontinuousSMul.exists_nhds_image_smul_eq_selfproof · cited by 3
- ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_selfproof · cited by 3
- Filter.EventuallyLE.countable_iInterproof · cited by 3
- LowerSet.mem_iInf_iffproof · cited by 3
- CantorScheme.map_memproof · cited by 3