Theorems · Theorem · order theory
Set.iInter_coe_set
∀ {α : Type u_12} {β : Type u_13} (s : Set α) (f : ↑s → Set β), ⋂ i, f i = ⋂ i, ⋂ (h : i ∈ s), f ⟨i, h⟩- Defined in
- Mathlib.Data.Set.Lattice
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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.Elemstatement and proof · cited by 7,166
- Set.iInterstatement · cited by 1,084
- Set.iInter_subtypeproof · cited by 9
Cited by17
Results whose statement or proof uses this declaration.
- Filter.HasBasis.liminf_eq_sSup_iUnion_iInterproof · cited by 4
- Dynamics.dynEntourage_eq_inter_Icoproof · cited by 3
- Measurable.liminf'proof · cited by 2
- CantorBendixson.isClosed_iteratedDerivedSetproof · cited by 2
- IsCompact.nonempty_inter_sInterproof · cited by 1
- Dynamics.dynEntourage_mem_uniformityproof · cited by 1
- IsCompact.elim_finite_subfamily_isClosed_subtypeproof · cited by 1
- Matroid.closure_biInter_eq_biInter_closure_of_biUnion_indepproof · cited by 1
- AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompactproof · cited by 1
- Convex.helly_theorem_set_compact'proof · cited by 1
- CantorBendixson.iteratedDerivedSet_limitproof · cited by 1