Theorems · Theorem · order theory
Filter.limsup_const_bot
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : Filter β}, Filter.limsup (fun x => ⊥) f = ⊥Same as limsup_const applied to ⊥ but without the NeBot f assumption
- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Bot.botstatement and proof · cited by 4,720
- le_rflproof · cited by 1,558
- CompleteLatticestatement and proof · cited by 1,048
- Filter.Eventually.of_forallproof · cited by 526
- Filter.limsupstatement · cited by 226
- eq_bot_iffproof · cited by 159
- sInf_leproof · cited by 110
- Filter.limsup_eqproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- ENNReal.limsup_const_mulproof · cited by 3
- limsup_eq_botproof · cited by 3
- ENNReal.limsup_const_mul_of_ne_topproof · cited by 2
- essSup_const_botproof · cited by 1
- Filter.liminf_const_topproof · cited by 1
- ENNReal.essSup_indicator_eq_essSup_restrictproof · cited by 1