Theorems · Theorem · general topology
Filter.ext
∀ {α : Type u_1} {f g : Filter α}, (∀ (s : Set α), s ∈ f ↔ s ∈ g) → f = g- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
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
- Set.extproof · cited by 2,266
- Filter.filter_eqproof · cited by 6
Cited by60
Results whose statement or proof uses this declaration.
- Filter.comap_principalproof · cited by 47
- nhds_inducedproof · cited by 32
- MeasureTheory.ae_dirac_eqproof · cited by 31
- Filter.principal_singletonproof · cited by 31
- Filter.map_principalproof · cited by 17
- Filter.HasBasis.eq_of_same_basisproof · cited by 13
- MeasureTheory.ae_restrict_eqproof · cited by 11
- Filter.sup_principalproof · cited by 8
- MeasurableEquiv.map_aeproof · cited by 8
- Filter.ext_iffproof · cited by 6
- PseudoMetricSpace.extproof · cited by 6
- Filter.map_fst_prodproof · cited by 5