Theorems · Theorem · order theory
Filter.blimsup_eq_iInf_biSup_of_nat
∀ {α : Type u_1} [inst : CompleteLattice α] {p : ℕ → Prop} {u : ℕ → α},
Filter.blimsup u Filter.atTop p = ⨅ i, ⨆ j, ⨆ (_ : p j ∧ i ≤ j), u j- Defined in
- Mathlib.Order.LiminfLimsup
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 70 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderproof · cited by 7,952
- iSupstatement and proof · cited by 2,415
- Filter.atTopstatement · cited by 2,405
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- IsDirectedOrderproof · cited by 316
- iSup_congr_Propproof · cited by 247
- iInf_congr_Propproof · cited by 218
- Filter.atTop_basisproof · cited by 42
- Filter.blimsupstatement · cited by 40
- iSup_andproof · cited by 13
- iInf_trueproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- MeasurableSet.measurableSet_blimsupproof · cited by 2
- blimsup_cthickening_ae_le_of_eventually_mul_le_auxproof · cited by 1
- Filter.bliminf_eq_iSup_biInf_of_natproof · cited by 1