Theorems · Theorem · general topology
Filter.iInf_principal
∀ {α : Type u} {ι : Sort w} [Finite ι] (f : ι → Set α), ⨅ i, Filter.principal (f i) = Filter.principal (⋂ i, f i)- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 62 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.
Cites16
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
- Fintypeproof · cited by 7,736
- Finset.univproof · cited by 3,473
- Finitestatement and proof · cited by 3,029
- iInfstatement and proof · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Filter.principalstatement and proof · cited by 740
- nonempty_fintypeproof · cited by 261
- iInf_congr_Propproof · cited by 218
- Set.iInter_congr_Propproof · cited by 170
- iInf_posproof · cited by 31
Cited by1
Results whose statement or proof uses this declaration.
- Filter.iInf_principal'proof · cited by 1