Theorems · Theorem · general topology
Filter.hasAntitoneBasis_atTop
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] [Nonempty α], Filter.atTop.HasAntitoneBasis Set.Ici- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 63 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.
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement · cited by 2,405
- Set.Icistatement · cited by 1,070
- IsDirectedOrderstatement and proof · cited by 316
- Filter.HasAntitoneBasisstatement · cited by 43
- Set.Ici_subset_Iciproof · cited by 14
- Filter.HasAntitoneBasis.iInf_principalproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Filter.atTop_basisproof · cited by 42
- atTop_hasAntitoneBasis_of_archimedeanproof · cited by 1