Theorems · Theorem · general topology
Filter.ext_iff
∀ {α : Type u_1} {f g : Filter α}, f = g ↔ ∀ (s : Set α), s ∈ f ↔ s ∈ g- Defined in
- Mathlib.Order.Filter.Defs
- Cited by
- 6 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.
- Setstatement and proof · cited by 53,352
- Filterstatement and proof · cited by 8,121
- Filter.extproof · cited by 60
Cited by6
Results whose statement or proof uses this declaration.
- eventually_nhds_nhdsWithinproof · cited by 7
- Filter.pure_injectiveproof · cited by 6
- isUniformInducing_iff_uniformSpaceproof · cited by 3
- discreteUniformity_iff_eq_principal_setRelIdproof · cited by 1
- Bornology.ext_iff'proof · cited by 1
- isBounded_iff_of_bilipschitzproof · cited by 0