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Theorems · Theorem · order theory

Filter.bliminf_eq_iSup_biInf_of_nat

∀ {α : Type u_1} [inst : CompleteLattice α] {p : ℕ → Prop} {u : ℕ → α},
  Filter.bliminf u Filter.atTop p = ⨆ i, ⨅ j, ⨅ (_ : p j ∧ i ≤ j), u j
Defined in
Mathlib.Order.LiminfLimsup
Cited by
1 results in Mathlib
Foundations
Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CompleteLattice
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasurableSet.measurableSet_bliminf · cited by 1MeasurableSet.measurableS…iSup · cited by 2415iSupFilter.atTop · cited by 2405Filter.atTopiInf · cited by 1690iInfCompleteLattice · cited by 1048CompleteLatticeFilter.bliminf · cited by 27Filter.bliminfFilter.blimsup_eq_iInf_biSup_of_nat · cited by 3Filter.blimsup_eq_iInf_bi…Filter.bliminf_eq_iSup_biInf_…CITED BYCITES

Cites6

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Cited by1

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