Theorems · Theorem · general topology
Filter.eventually_of_mem
∀ {α : Type u} {f : Filter α} {P : α → Prop} {U : Set α}, U ∈ f → (∀ x ∈ U, P x) → ∀ᶠ (x : α) in f, P x- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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.mem_of_supersetproof · cited by 308
Cited by43
Results whose statement or proof uses this declaration.
- Filter.eventuallyEq_of_memproof · cited by 25
- Real.Gamma_pos_of_posproof · cited by 17
- iteratedFDerivWithin_add_applyproof · cited by 5
- mdifferentiableWithinAt_totalSpaceproof · cited by 5
- Bundle.contMDiffWithinAt_totalSpaceproof · cited by 5
- ContMDiffWithinAt.add_sectionproof · cited by 4
- tendstoLocallyUniformlyOn_iff_filterproof · cited by 4
- mdifferentiableWithinAt_add_sectionproof · cited by 4
- ContDiffWithinAt.fderivWithinproof · cited by 4
- hasDerivAt_of_tendstoLocallyUniformlyOnproof · cited by 3
- MDifferentiableWithinAt.smul_sectionproof · cited by 3
- ProbabilityTheory.Kernel.indep_biSup_limsupproof · cited by 3