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Theorems · Theorem · order theory

Filter.le_limsInf_of_le

∀ {α : Type u_1} [inst : ConditionallyCompleteLattice α] {f : Filter α} {a : α},
  autoParam (Filter.IsCobounded (fun x1 x2 => x1 ≥ x2) f) Filter.le_limsInf_of_le._auto_1 →
    (∀ᶠ (n : α) in f, a ≤ n) → a ≤ f.limsInf
Defined in
Mathlib.Order.LiminfLimsup
Cited by
2 results in Mathlib
Foundations
Depth 11 from the axioms · uses no axioms
Assumes
ConditionallyCompleteLattice
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Around this declaration

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

ENNReal.exists_frequently_lt_of_liminf_ne_top · cited by 1ENNReal.exists_frequently…ENNReal.exists_frequently_lt_of_liminf_ne_top' · cited by 1ENNReal.exists_frequently…Filter · cited by 8121FilterFilter.Eventually · cited by 3134Filter.EventuallyConditionallyCompleteLattice · cited by 364ConditionallyCompleteLatt…le_csSup · cited by 66le_csSupFilter.IsCobounded · cited by 42Filter.IsCoboundedFilter.limsInf · cited by 31Filter.limsInfFilter.le_limsInf_of_leCITED BYCITES

Cites6

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Cited by2

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