Theorems · Theorem · general topology
Filter.HasAntitoneBasis.toHasBasis
∀ {α : Type u_1} {ι'' : Type u_6} [inst : Preorder ι''] {l : Filter α} {s : ι'' → Set α},
l.HasAntitoneBasis s → l.HasBasis (fun x => True) s- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Preorderstatement and proof · cited by 7,952
- Filter.HasBasisstatement · cited by 604
- Filter.HasAntitoneBasisstatement and proof · cited by 43
Cited by26
Results whose statement or proof uses this declaration.
- Filter.atTop_basisproof · cited by 42
- Filter.HasBasis.exists_antitone_subbasisproof · cited by 8
- Filter.HasAntitoneBasis.memproof · cited by 6
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- Filter.HasAntitoneBasis.mem_iffproof · cited by 3
- Filter.HasAntitoneBasis.comp_monoproof · cited by 2
- Filter.HasAntitoneBasis.eventually_subsetproof · cited by 2
- UniformOnFun.hasAntitoneBasis_uniformityproof · cited by 2
- measurableSet_tendstoproof · cited by 2
- IsGδ.setOfPred_continuousAtproof · cited by 2
- Filter.exists_antitone_seqproof · cited by 2
- Filter.HasAntitoneBasis.comapproof · cited by 1