Theorems · Theorem · general topology
Filter.eventually_congr
∀ {α : Type u} {f : Filter α} {p q : α → Prop},
(∀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
- 20 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.congrproof · cited by 6
Cited by20
Results whose statement or proof uses this declaration.
- Filter.limsup_congrproof · cited by 20
- Filter.eventuallyEq_setproof · cited by 10
- Filter.map_congrproof · cited by 10
- Filter.eventually_sub_nonnegproof · cited by 4
- Asymptotics.isBigOWith_congrproof · cited by 3
- LinearGrowth.le_linearGrowthInf_iffproof · cited by 3
- LinearGrowth.linearGrowthSup_le_iffproof · cited by 2
- absorbs_iff_eventually_cobounded_mapsToproof · cited by 2
- ExpGrowth.expGrowthSup_le_iffproof · cited by 2
- Filter.blimsup_congr'proof · cited by 2
- ExpGrowth.le_expGrowthInf_iffproof · cited by 2
- OpenPartialHomeomorph.eventually_nhds'proof · cited by 2