Theorems · Theorem · general topology
Filter.IsBoundedUnder.bddAbove_range
∀ {β : Type u_2} [inst : Preorder β] [IsDirectedOrder β] {f : ℕ → β},
Filter.IsBoundedUnder (fun x1 x2 => x1 ≤ x2) Filter.atTop f → BddAbove (Set.range f)- Defined in
- Mathlib.Order.Filter.IsBounded
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderIsDirectedOrder
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
- BddAbovestatement · cited by 620
- IsDirectedOrderstatement and proof · cited by 316
- Filter.IsBoundedUnderstatement and proof · cited by 247
- Nat.cofinite_eq_atTopproof · cited by 37
- Filter.IsBoundedUnder.bddAbove_range_of_cofiniteproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Filter.Tendsto.bddAbove_rangeproof · cited by 2
- Filter.bddAbove_range_of_tendsto_atTop_atBotproof · cited by 1