Theorems · Theorem · general topology
Set.Finite.compl_mem_cofinite
∀ {α : Type u_2} {s : Set α}, s.Finite → sᶜ ∈ Filter.cofinite- Defined in
- Mathlib.Order.Filter.Cofinite
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 · cited by 8,121
- Compl.complstatement · cited by 2,925
- Set.Finitestatement and proof · cited by 1,814
- Filter.cofinitestatement · cited by 251
- compl_complproof · cited by 229
- Filter.mem_cofiniteproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- Bornology.isBounded_singletonproof · cited by 6
- Set.Finite.isBoundedproof · cited by 4
- Filter.le_cofinite_iff_compl_singleton_memproof · cited by 4
- Polynomial.eventually_atTop_not_isRootproof · cited by 3
- Set.Finite.cofinite_inf_principal_complproof · cited by 2
- Filter.map_piMap_piproof · cited by 2
- LSeriesSummable.congr'proof · cited by 2
- Set.Finite.eventually_cofinite_notMemproof · cited by 2
- Filter.notMem_hyperfilter_of_finiteproof · cited by 1
- Filter.comap_cofinite_leproof · cited by 1
- Polynomial.eventually_cofinite_not_isRootproof · cited by 1
- LSeries.summable_real_of_abscissaOfAbsConv_ltproof · cited by 1