Theorems · Theorem · general topology
Filter.Tendsto.exists_within_forall_le
∀ {α : Type u_4} {β : Type u_5} [inst : LinearOrder β] {s : Set α},
s.Nonempty → ∀ {f : α → β}, Filter.Tendsto f Filter.cofinite Filter.atTop → ∃ a₀ ∈ s, ∀ a ∈ s, f a₀ ≤ f a- Defined in
- Mathlib.Order.Filter.Cofinite
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.ofPredproof · cited by 6,101
- Filter.Tendstostatement and proof · cited by 3,814
- Set.Nonemptystatement and proof · cited by 2,627
- Filter.atTopstatement and proof · cited by 2,405
- LT.lt.leproof · cited by 2,189
- Set.Finiteproof · cited by 1,814
- le_transproof · cited by 985
- Filter.cofinitestatement and proof · cited by 251
- lt_or_geproof · cited by 182
- Set.Finite.inter_of_leftproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Filter.Tendsto.exists_forall_leproof · cited by 2
- ModularGroup.exists_max_improof · cited by 1
- Filter.Tendsto.exists_within_forall_geproof · cited by 0