Theorems · Theorem · general topology
Filter.IsBounded.isCobounded_flip
∀ {α : Type u_1} {r : α → α → Prop} {f : Filter α} [IsTrans α r] [f.NeBot],
Filter.IsBounded r f → Filter.IsCobounded (flip r) fA filter which is eventually bounded is in particular frequently bounded (in the opposite direction). At least if the filter is not trivial.
- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IsTransFilter.NeBot
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallyproof · cited by 3,134
- Filter.NeBotstatement and proof · cited by 853
- Filter.Eventually.existsproof · cited by 168
- IsTransstatement and proof · cited by 157
- Filter.Eventually.andproof · cited by 157
- transproof · cited by 111
- Filter.IsBoundedstatement and proof · cited by 45
- Filter.IsCoboundedstatement and proof · cited by 42
Cited by8
Results whose statement or proof uses this declaration.
- Filter.IsBounded.isCobounded_leproof · cited by 4
- Filter.IsBounded.isCobounded_geproof · cited by 3
- limsInf_eq_of_le_nhdsproof · cited by 2
- Filter.IsBoundedUnder.isCoboundedUnder_flipproof · cited by 2
- Filter.Tendsto.isCoboundedUnder_geproof · cited by 0
- Filter.Tendsto.isCoboundedUnder_leproof · cited by 0
- isCobounded_ge_nhdsproof · cited by 0
- isCobounded_le_nhdsproof · cited by 0