Theorems · Theorem · general topology
Filter.iInter_mem
∀ {α : Type u} {f : Filter α} {β : Sort v} {s : β → Set α} [Finite β], ⋂ i, s i ∈ f ↔ ∀ (i : β), s i ∈ f- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Filterstatement and proof · cited by 8,121
- Finitestatement and proof · cited by 3,029
- Set.iInterstatement · cited by 1,084
- Set.forall_mem_rangeproof · cited by 135
- Set.finite_rangeproof · cited by 58
- Filter.sInter_memproof · cited by 6
Cited by12
Results whose statement or proof uses this declaration.
- Filter.eventually_allproof · cited by 16
- Filter.mem_iInf_of_iInterproof · cited by 5
- ProperlyDiscontinuousSMul.exists_nhds_image_smul_eq_selfproof · cited by 3
- Filter.HasBasis.iInfproof · cited by 3
- ProperlyDiscontinuousVAdd.exists_nhds_image_vadd_eq_selfproof · cited by 3
- contDiffWithinAt_piproof · cited by 3
- Pairwise.exists_mem_filter_of_disjointproof · cited by 2
- absorbs_iInterproof · cited by 1
- Dynamics.ball_dynEntourage_mem_nhdsproof · cited by 1
- Filter.mem_iInf_of_finiteproof · cited by 1
- Bornology.isCobounded_iInterproof · cited by 0
- Filter.mem_iInf_finsetproof · cited by 0