Theorems · Theorem · general topology
Filter.IsBoundedUnder.bddBelow_range_of_cofinite
∀ {α : Type u_1} {β : Type u_2} [inst : Preorder β] [IsCodirectedOrder β] {f : α → β},
Filter.IsBoundedUnder (fun x1 x2 => x2 ≤ x1) Filter.cofinite f → BddBelow (Set.range f)- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsCodirectedOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.ofPredproof · cited by 6,101
- Set.imageproof · cited by 5,609
- Set.rangestatement · cited by 4,705
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- Filter.mapproof · cited by 819
- BddBelowstatement and proof · cited by 401
- Set.image_univproof · cited by 322
- Filter.cofinitestatement and proof · cited by 251
- Filter.IsBoundedUnderstatement and proof · cited by 247
Cited by2
Results whose statement or proof uses this declaration.
- Filter.IsBoundedUnder.bddBelow_rangeproof · cited by 3
- Filter.Tendsto.bddBelow_range_of_cofiniteproof · cited by 0