Theorems · Theorem · general topology
Filter.mem_iInf_finset
∀ {α : Type u} {β : Type v} {s : Finset α} {f : α → Filter β} {t : Set β},
t ∈ ⨅ a ∈ s, f a ↔ ∃ p, (∀ a ∈ s, p a ∈ f a) ∧ t = ⋂ a ∈ s, p a- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- SetLike.coeproof · cited by 8,199
- Filterstatement and proof · cited by 8,121
- Set.Elemproof · cited by 7,166
- Set.univproof · cited by 3,945
- iInfstatement and proof · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- iInf_subtype'proof · cited by 34
- Filter.mem_iInf_of_memproof · cited by 22
- Set.biInter_eq_iInterproof · cited by 19
- Filter.iInter_memproof · cited by 12
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