Theorems · Theorem · general topology
Filter.exists_antitone_seq
∀ {α : Type u_1} (f : Filter α) [f.IsCountablyGenerated], ∃ x, Antitone x ∧ ∀ {s : Set α}, s ∈ f ↔ ∃ i, x i ⊆ s- Defined in
- Mathlib.Order.Filter.CountablyGenerated
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Filter.IsCountablyGenerated
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Antitonestatement and proof · cited by 563
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- Filter.HasBasis.mem_iffproof · cited by 193
- Filter.HasAntitoneBasisproof · cited by 43
- Filter.HasAntitoneBasis.toHasBasisproof · cited by 26
- Filter.HasAntitoneBasis.antitoneproof · cited by 12
- Filter.exists_antitone_basisproof · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- UniformSpace.complete_of_convergent_controlled_sequencesproof · cited by 3
- UniformSpace.complete_of_cauchySeq_tendstoproof · cited by 2