Theorems · Theorem · general topology
Filter.atBot_le_cofinite
∀ {α : Type u_2} [inst : Preorder α] [NoBotOrder α], Filter.atBot ≤ Filter.cofiniteIf α is a preorder with no bottom element, then atBot ≤ cofinite.
- Defined in
- Mathlib.Order.Filter.Cofinite
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderNoBotOrder
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.atBotstatement · cited by 512
- Filter.cofinitestatement · cited by 251
- NoBotOrderstatement and proof · cited by 43
- Filter.le_cofinite_iff_eventually_neproof · cited by 4
- Filter.eventually_ne_atBotproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.eventually_atBot_not_isRootproof · cited by 0