Theorems · Theorem · order theory
Filter.frequently_lt_of_lt_limsup
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLinearOrder β] {f : Filter α} {u : α → β} {b : β},
autoParam (Filter.IsCoboundedUnder (fun x1 x2 => x1 ≤ x2) f u) Filter.frequently_lt_of_lt_limsup._auto_1 →
b < Filter.limsup u f → ∃ᶠ (x : α) in f, b < u x- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
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.limsupstatement and proof · cited by 226
- Filter.IsCoboundedUnderstatement and proof · cited by 102
- Filter.limsSup_le_of_leproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Filter.le_limsup_iffproof · cited by 10
- Filter.frequently_lt_of_liminf_ltproof · cited by 7
- Filter.le_limsup_iff'proof · cited by 3
- EReal.limsup_const_mul_of_nonneg_of_ne_topproof · cited by 3
- EReal.le_limsup_addproof · cited by 2
- tendsto_of_no_upcrossingsproof · cited by 2
- le_limsup_addproof · cited by 0
- le_limsup_mulproof · cited by 0
- EReal.le_limsup_mulproof · cited by 0
- ENNReal.le_limsup_mulproof · cited by 0