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Theorems · Theorem · general topology

Filter.IsBounded.isCobounded_le

∀ {α : Type u_1} {f : Filter α} [inst : Preorder α] [f.NeBot],
  Filter.IsBounded (fun x1 x2 => x2 ≤ x1) f → Filter.IsCobounded (fun x1 x2 => x1 ≤ x2) f
Defined in
Mathlib.Order.Filter.IsBounded
Cited by
4 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
PreorderFilter.NeBot
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ClusterPt.le_limsSup · cited by 3ClusterPt.le_limsSuptendsto_of_no_upcrossings · cited by 2tendsto_of_no_upcrossingsBoundedContinuousFunction.tendsto_integral_of_forall_integral_le_liminf_integral · cited by 1BoundedContinuousFunction…BoundedContinuousFunction.tendsto_integral_of_forall_limsup_integral_le_integral · cited by 1BoundedContinuousFunction…Filter · cited by 8121FilterPreorder · cited by 7952PreorderFilter.NeBot · cited by 853Filter.NeBotFilter.IsBounded · cited by 45Filter.IsBoundedFilter.IsCobounded · cited by 42Filter.IsCoboundedFilter.IsBounded.isCobounded_flip · cited by 8IsBounded.isCobounded_flipIsBounded.isCobounded_leCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.