Theorems · Theorem · order theory
Set.sInter_image
∀ {α : Type u_1} {β : Type u_2} (f : α → Set β) (s : Set α), ⋂₀ (f '' s) = ⋂ a ∈ s, f a- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 26 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.
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.imagestatement · cited by 5,609
- Set.iInterstatement · cited by 1,084
- Set.sInterstatement · cited by 225
- sInf_imageproof · cited by 25
Cited by26
Results whose statement or proof uses this declaration.
- Set.sInter_eq_biInterproof · cited by 23
- Set.Finite.isOpen_biInterproof · cited by 10
- Set.compl_sUnionproof · cited by 6
- Topology.IsLower.isTopologicalBasisproof · cited by 3
- IntermediateField.coe_sInfproof · cited by 3
- isMeagre_iff_countable_union_isNowhereDenseproof · cited by 3
- TopologicalSpace.vietoris.isTopologicalBasisproof · cited by 2
- isCompact_generateFromproof · cited by 2
- IsCompact.nonempty_inter_sInterproof · cited by 1
- FirstOrder.Language.Theory.CompleteType.setOfPred_subset_eq_univ_iffproof · cited by 1
- IsSemilinearSet.biInterproof · cited by 1
- IsGδ.biInter_of_isOpenproof · cited by 1