Theorems · Theorem · general topology
Filter.IsBoundedUnder.bddBelow_range
∀ {β : Type u_2} [inst : Preorder β] [IsCodirectedOrder β] {f : ℕ → β},
Filter.IsBoundedUnder (fun x1 x2 => x2 ≤ x1) Filter.atTop f → BddBelow (Set.range f)- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 81 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Filterproof · cited by 8,121
- Preorderstatement and proof · cited by 7,952
- Set.rangestatement · cited by 4,705
- Filter.atTopstatement and proof · cited by 2,405
- BddBelowstatement · cited by 401
- Filter.IsBoundedUnderstatement and proof · cited by 247
- IsCodirectedOrderstatement and proof · cited by 95
- Nat.cofinite_eq_atTopproof · cited by 37
- Filter.IsBoundedUnder.bddBelow_range_of_cofiniteproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Filter.bddBelow_range_of_tendsto_atTop_atTopproof · cited by 1
- Filter.Tendsto.bddBelow_rangeproof · cited by 1
- Filter.bddBelow_range_of_tendsto_atBot_atTopproof · cited by 0