Theorems · Theorem · general topology
Filter.frequently_congr
∀ {α : Type u} {p q : α → Prop} {f : Filter α},
(∀ᶠ (x : α) in f, p x ↔ q x) → ((∃ᶠ (x : α) in f, p x) ↔ ∃ᶠ (x : α) in f, q x)- Defined in
- Mathlib.Order.Filter.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
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.
- Filterstatement and proof · cited by 8,121
- Filter.Eventuallystatement and proof · cited by 3,134
- Filter.Eventually.monoproof · cited by 646
- Filter.Frequentlystatement and proof · cited by 414
- Filter.Frequently.mpproof · cited by 12
Cited by6
Results whose statement or proof uses this declaration.
- LinearGrowth.linearGrowthInf_le_iffproof · cited by 2
- LinearGrowth.le_linearGrowthSup_iffproof · cited by 2
- ExpGrowth.expGrowthInf_le_iffproof · cited by 2
- ExpGrowth.le_expGrowthSup_iffproof · cited by 2
- asymptoticCone_eq_closure_of_forall_smul_memproof · cited by 1
- clusterPt_principal_subtype_iff_frequentlyproof · cited by 0