Theorems · Theorem · general topology
EReal.limsup_neg
∀ {α : Type u_3} {f : Filter α} {v : α → EReal}, Filter.limsup (-v) f = -Filter.liminf v f- Defined in
- Mathlib.Topology.Instances.EReal.Lemmas
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Filterstatement and proof · cited by 8,121
- ERealstatement and proof · cited by 793
- Filter.limsupstatement · cited by 226
- Filter.liminfstatement · cited by 198
- Filter.isBounded_ge_of_botproof · cited by 55
- Filter.isCobounded_ge_of_topproof · cited by 38
- OrderIso.liminf_applyproof · cited by 6
- EReal.negOrderIsoproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- EReal.liminf_const_mul_of_nonneg_of_ne_topproof · cited by 0
- EReal.liminf_const_mul_of_nonpos_of_ne_botproof · cited by 0
- LinearGrowth.linearGrowthSup_invproof · cited by 0
- EReal.limsup_const_mul_of_nonpos_of_ne_botproof · cited by 0
- ExpGrowth.expGrowthSup_invproof · cited by 0