Theorems · Theorem · general topology
Filter.mem_atBot_sets
∀ {α : Type u_3} [inst : Preorder α] [IsCodirectedOrder α] [Nonempty α] {s : Set α},
s ∈ Filter.atBot ↔ ∃ a, ∀ b ≤ a, b ∈ s- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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 · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.Iicproof · cited by 1,111
- Filter.atBotstatement · cited by 512
- Filter.HasBasis.mem_iffproof · cited by 193
- IsCodirectedOrderstatement and proof · cited by 95
- Filter.atBot_basisproof · cited by 14
Cited by10
Results whose statement or proof uses this declaration.
- atBot_le_cocompactproof · cited by 4
- Filter.eventually_atBotproof · cited by 4
- MeasureTheory.integrableOn_Iic_iff_integrableAtFilter_atBotproof · cited by 3
- cocompact_le_atBotproof · cited by 3
- MeasureTheory.tendsto_zero_of_hasDerivAt_of_integrableOn_Iicproof · cited by 2
- cocompact_le_atBot_atTopproof · cited by 2
- HasDerivAt.lhopital_zero_atBotproof · cited by 1
- MeasureTheory.integrableAtFilter_atBot_iffproof · cited by 1
- Filter.tendsto_atBot_principalproof · cited by 1
- Filter.tendsto_atBot'proof · cited by 0