Theorems · Theorem · general topology
Filter.eventually_inf_principal
∀ {α : Type u} {f : Filter α} {p : α → Prop} {s : Set α},
(∀ᶠ (x : α) in f ⊓ Filter.principal s, p x) ↔ ∀ᶠ (x : α) in f, x ∈ s → p x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement · cited by 3,134
- Filter.principalstatement · cited by 740
- Filter.mem_inf_principalproof · cited by 9
Cited by18
Results whose statement or proof uses this declaration.
- eventually_nhdsWithin_iffproof · cited by 34
- HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNEproof · cited by 4
- Filter.blimsup_congrproof · cited by 4
- AbsolutelyContinuousOnInterval.smulproof · cited by 2
- Filter.set_eventuallyLE_iff_mem_inf_principalproof · cited by 2
- indicator_eventuallyEqproof · cited by 2
- MeasureTheory.Measure.FiniteAtFilter.integrableAtFilterproof · cited by 2
- mulIndicator_eventuallyEqproof · cited by 2
- MeasureTheory.le_ae_restrictproof · cited by 1
- BoxIntegral.IntegrationParams.eventually_isPartitionproof · cited by 1
- ContinuousMap.AlgHom.closure_ker_interproof · cited by 1
- mem_nhdsWithin_iff_eventuallyproof · cited by 1