Theorems · Theorem · order theory
Filter.gt_mem_sets_of_limsInf_gt
∀ {α : Type u_1} [inst : ConditionallyCompleteLinearOrder α] {f : Filter α} {b : α},
Filter.IsBounded (fun x1 x2 => x1 ≥ x2) f → b < f.limsInf → ∀ᶠ (a : α) in f, b < a- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement · cited by 3,134
- ConditionallyCompleteLinearOrderstatement and proof · cited by 542
- Filter.IsBoundedstatement · cited by 45
- Filter.limsInfstatement · cited by 31
- Filter.lt_mem_sets_of_limsSup_ltproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.ProbabilityMeasure.toMeasure_add_pos_gt_mem_nhdsproof · cited by 1
- le_nhds_of_limsSup_eq_limsInfproof · cited by 1