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Theorems · Theorem · general topology

Filter.IsBounded.isCobounded_ge

∀ {α : Type u_1} {f : Filter α} [inst : Preorder α] [f.NeBot],
  Filter.IsBounded (fun x1 x2 => x1 ≤ x2) f → Filter.IsCobounded (fun x1 x2 => x2 ≤ x1) f
Defined in
Mathlib.Order.Filter.IsBounded
Cited by
3 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.

tendsto_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_geCITED BYCITES

Cites6

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Cited by3

Results whose statement or proof uses this declaration.