Theorems · Theorem · general topology
Filter.eventually_gt_atTop
∀ {α : Type u_3} [inst : Preorder α] [NoTopOrder α] (a : α), ∀ᶠ (x : α) in Filter.atTop, a < x- Defined in
- Mathlib.Order.Filter.AtTopBot.Defs
- Cited by
- 90 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- PreorderNoTopOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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.Eventuallystatement · cited by 3,134
- Filter.atTopstatement · cited by 2,405
- NoTopOrderstatement and proof · cited by 50
- Filter.Ioi_mem_atTopproof · cited by 36
Cited by90
Results whose statement or proof uses this declaration.
- Filter.eventually_ne_atTopproof · cited by 35
- Filter.Tendsto.eventually_gt_atTopproof · cited by 11
- LinearGrowth.linearGrowthSup_botproof · cited by 6
- Polynomial.isEquivalent_atTop_divproof · cited by 5
- Real.isLittleO_const_log_atTopproof · cited by 5
- isLittleO_exp_neg_mul_rpow_atTopproof · cited by 4
- IsLUB.exists_seq_strictMono_tendsto_of_notMemproof · cited by 4
- Filter.HasAntitoneBasis.subbasis_with_relproof · cited by 4
- EisensteinSeries.summable_one_div_norm_rpowproof · cited by 4
- isLittleO_log_rpow_atTopproof · cited by 3
- Real.tendsto_log_comp_add_sub_logproof · cited by 3
- AkraBazziRecurrence.eventually_asympBound_posproof · cited by 3