Theorems · Theorem · general topology
Filter.iInf_principal_finset
∀ {α : Type u} {ι : Type w} (s : Finset ι) (f : ι → Set α),
⨅ i ∈ s, Filter.principal (f i) = Filter.principal (⋂ i ∈ s, f i)- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 3 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.
Cites18
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
- Finsetstatement and proof · cited by 13,712
- Top.topproof · cited by 9,680
- Filterstatement and proof · cited by 8,121
- iInfstatement and proof · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Filter.principalstatement and proof · cited by 740
- iInf_congr_Propproof · cited by 218
- Set.iInter_congr_Propproof · cited by 170
- Finset.induction_onproof · cited by 167
- Filter.principal_univproof · cited by 46
- Filter.inf_principalproof · cited by 29
Cited by3
Results whose statement or proof uses this declaration.
- Filter.iInf_principal_finiteproof · cited by 2
- Filter.hasBasis_iInf_principal_finiteproof · cited by 1
- Filter.iInf_principalproof · cited by 1