Theorems · Theorem · general topology
Filter.atBot_neBot_iff
∀ {α : Type u_6} [inst : Preorder α], Filter.atBot.NeBot ↔ Nonempty α ∧ IsCodirectedOrder α- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
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Cites8
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.NeBotstatement and proof · cited by 853
- Filter.atBotstatement and proof · cited by 512
- Filter.Eventually.existsproof · cited by 168
- Filter.Eventually.andproof · cited by 157
- IsCodirectedOrderstatement and proof · cited by 95
- Filter.eventually_le_atBotproof · cited by 15
- Filter.nonempty_of_neBotproof · cited by 6
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