Theorems · Theorem · order theory
Filter.liminf_le_of_le
∀ {α : Type u_1} {β : Type u_2} [inst : ConditionallyCompleteLattice α] {f : Filter β} {u : β → α} {a : α},
autoParam (Filter.IsBoundedUnder (fun x1 x2 => x1 ≥ x2) f u) Filter.liminf_le_of_le._auto_1 →
(∀ (b : α), (∀ᶠ (n : β) in f, b ≤ u n) → b ≤ a) → Filter.liminf u f ≤ a- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- ConditionallyCompleteLattice
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 and proof · cited by 3,134
- ConditionallyCompleteLatticestatement and proof · cited by 364
- Filter.IsBoundedUnderstatement and proof · cited by 247
- Filter.liminfstatement · cited by 198
- csSup_leproof · cited by 35
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Lp.eLpNorm_le_of_ae_tendstoproof · cited by 3
- Filter.limsInf_le_limsSupproof · cited by 2
- MeasureTheory.exists_measure_iUnion_gt_of_isCompact_closureproof · cited by 1
- ENNReal.liminf_add_of_right_tendsto_zeroproof · cited by 1
- ENNReal.liminf_toReal_eqproof · cited by 1
- Filter.liminf_le_of_frequently_leproof · cited by 1