Theorems · Theorem · general topology
Filter.mem_iInf_of_iInter
∀ {α : Type u} {ι : Type u_2} {s : ι → Filter α} {U : Set α} {I : Set ι},
I.Finite → ∀ {V : ↑I → Set α}, (∀ (i : ↑I), V i ∈ s ↑i) → ⋂ i, V i ⊆ U → U ∈ ⨅ i, s i- Defined in
- Mathlib.Order.Filter.Finite
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.Elemstatement and proof · cited by 7,166
- Set.Finitestatement and proof · cited by 1,814
- iInfstatement · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- Filter.mem_of_supersetproof · cited by 308
- Set.Finite.fintypeproof · cited by 38
- Filter.mem_iInf_of_memproof · cited by 22
- Filter.iInter_memproof · cited by 12
Cited by5
Results whose statement or proof uses this declaration.
- Filter.eventually_forall_ge_atTopproof · cited by 5
- Filter.pi_mem_piproof · cited by 4
- Filter.atTop_finset_eq_iInfproof · cited by 1
- Filter.mem_iInfproof · cited by 1
- Filter.mem_biInf_principalproof · cited by 0