Theorems · Theorem · order theory
Filter.liminf_bot
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] (f : β → α), Filter.liminf f ⊥ = ⊤- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Top.topstatement and proof · cited by 9,680
- Filterstatement · cited by 8,121
- Bot.botstatement · cited by 4,720
- CompleteLatticestatement and proof · cited by 1,048
- Filter.liminfstatement · cited by 198
- Filter.limsInfproof · cited by 31
- Filter.map_botproof · cited by 16
- Filter.limsInf_botproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.lintegral_liminf_le'proof · cited by 3
- MeasureTheory.le_measure_compl_liminf_of_limsup_measure_leproof · cited by 1
- ENNReal.limsup_const_subproof · cited by 0
- EReal.le_limsup_mulproof · cited by 0