Theorems · Theorem · general topology
Filter.Tendsto.eventually_le_atBot
∀ {α : Type u_3} {β : Type u_4} [inst : Preorder β] {f : α → β} {l : Filter α},
Filter.Tendsto f l Filter.atBot → ∀ (c : β), ∀ᶠ (x : α) in l, f x ≤ c- Defined in
- Mathlib.Order.Filter.AtTopBot.Tendsto
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Preorderstatement and proof · cited by 7,952
- Filter.Tendstostatement and proof · cited by 3,814
- Filter.Eventuallystatement · cited by 3,134
- Filter.atBotstatement and proof · cited by 512
- Filter.Tendsto.eventuallyproof · cited by 174
- Filter.eventually_le_atBotproof · cited by 15
Cited by6
Results whose statement or proof uses this declaration.
- Monotone.measure_iInterproof · cited by 4
- MeasureTheory.aecover_Iciproof · cited by 3
- locallyFinite_Icc_of_tendstoproof · cited by 3
- Monotone.lowerBounds_range_comp_tendsto_atBotproof · cited by 1
- IsPreconnected.intermediate_value_Iioproof · cited by 0
- IsPreconnected.intermediate_value_Iiiproof · cited by 0