Theorems · Theorem · general topology
Filter.EventuallyEq.mem_iff
∀ {α : Type u} {s t : Set α} {l : Filter α}, s =ᶠ[l] t → ∀ᶠ (x : α) in l, x ∈ s ↔ x ∈ tAlias of the forward direction of Filter.eventuallyEq_set.
- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses propext, 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.EventuallyEqstatement · cited by 1,912
- Filter.eventuallyEq_setproof · cited by 10
Cited by8
Results whose statement or proof uses this declaration.
- StructureGroupoid.LocalInvariantProp.congr_setproof · cited by 5
- StructureGroupoid.LocalInvariantProp.liftPropWithinAt_inter'proof · cited by 3
- indicator_eventuallyEqproof · cited by 2
- mulIndicator_eventuallyEqproof · cited by 2
- MeasureTheory.MeasurePreserving.rnDeriv_comp_aeEqproof · cited by 1
- MeasureTheory.setIntegral_mono_on_ae₀proof · cited by 1
- Filter.EventuallyEq.of_eventually_mem_of_forall_separating_preimageproof · cited by 1
- piecewise_ae_eq_of_ae_eq_setproof · cited by 1