Theorems · Theorem · general topology
Filter.atTop_le_cofinite
∀ {α : Type u_2} [inst : Preorder α] [NoTopOrder α], Filter.atTop ≤ Filter.cofiniteIf α is a preorder with no top element, then atTop ≤ cofinite.
- Defined in
- Mathlib.Order.Filter.Cofinite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoTopOrder
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.
- Filterstatement · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement · cited by 2,405
- Filter.cofinitestatement · cited by 251
- NoTopOrderstatement and proof · cited by 50
- Filter.eventually_ne_atTopproof · cited by 35
- Filter.le_cofinite_iff_eventually_neproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Nat.cofinite_eq_atTopproof · cited by 37
- Polynomial.eventually_atTop_not_isRootproof · cited by 3
- CauchySeq.comp_injectiveproof · cited by 1