Theorems · Theorem · general topology
Filter.eventually_ne_atTop
∀ {α : Type u_3} [inst : Preorder α] [NoTopOrder α] (a : α), ∀ᶠ (x : α) in Filter.atTop, x ≠ a- Defined in
- Mathlib.Order.Filter.AtTopBot.Defs
- Cited by
- 35 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, 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.
- Preorderstatement and proof · cited by 7,952
- Filter.Eventuallystatement · cited by 3,134
- Filter.atTopstatement · cited by 2,405
- Filter.Eventually.monoproof · cited by 646
- ne_of_gtproof · cited by 637
- Filter.eventually_gt_atTopproof · cited by 90
- NoTopOrderstatement and proof · cited by 50
Cited by35
Results whose statement or proof uses this declaration.
- Filter.Tendsto.eventually_ne_atTopproof · cited by 9
- AffineSpace.asymptoticNhds_eq_smulproof · cited by 4
- tendsto_natCast_div_add_atTopproof · cited by 3
- Real.tendsto_eulerMascheroniSeq'proof · cited by 3
- Filter.atTop_le_cofiniteproof · cited by 3
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- Complex.tendsto_mul_log_one_add_of_tendstoproof · cited by 3
- summable_jacobiTheta₂'_term_iffproof · cited by 2
- summable_jacobiTheta₂_term_fderiv_iffproof · cited by 2
- tendsto_rpow_atTop_of_base_lt_oneproof · cited by 2
- MonotoneOn.exists_tendsto_deriv_liminf_lintegral_enorm_leproof · cited by 2
- LSeriesSummable_of_sum_norm_bigOproof · cited by 2