Theorems · Theorem · order theory

Filter.frequently_lt_of_lt_limsSup

∀ {α : Type u_1} {f : Filter α} [inst : ConditionallyCompleteLinearOrder α] {a : α},
  autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≤ x2) f) Filter.frequently_lt_of_lt_limsSup._auto_1 →
    a < f.limsSup → ∃ᶠ (n : α) in f, a < n

Defined in: Mathlib.Order.LiminfLimsup
Cited by: 3 results in Mathlib
Foundations: Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ConditionallyCompleteLinearOrder

Mathlib docs Source Loogle LeanSearch

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.

Filterstatement and proof · cited by 8,121
Filter.Eventuallyproof · cited by 3,134
ConditionallyCompleteLinearOrderstatement and proof · cited by 542
Filter.Frequentlystatement · cited by 414
Filter.IsCoboundedstatement and proof · cited by 42
Filter.limsSupstatement and proof · cited by 29
Filter.limsSup_le_of_leproof · cited by 4

Cited by3

Results whose statement or proof uses this declaration.

Antitone.map_limsSup_of_continuousAtproof · cited by 6
ClusterPt.limsSupproof · cited by 4
Filter.frequently_lt_of_limsInf_ltproof · cited by 0