Theorems · Theorem · general topology
Filter.disjoint_principal_right
∀ {α : Type u_1} {f : Filter α} {s : Set α}, Disjoint f (Filter.principal s) ↔ sᶜ ∈ f- Defined in
- Mathlib.Order.Filter.Bases.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Bot.botproof · cited by 4,720
- Compl.complstatement · cited by 2,925
- Disjointstatement and proof · cited by 2,201
- Filter.principalstatement and proof · cited by 740
- compl_complproof · cited by 229
- disjoint_iffproof · cited by 76
- Filter.mem_iff_inf_principal_complproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- MeromorphicOn.analyticAt_mem_codiscreteWithinproof · cited by 7
- Filter.disjoint_principal_leftproof · cited by 4
- MeromorphicOn.codiscrete_setOfPred_meromorphicOrderAt_eq_zero_or_topproof · cited by 2
- Topology.IsInducing.sumElimproof · cited by 2
- IsLindelof.compl_mem_sets_of_nhdsWithinproof · cited by 2
- MeromorphicOn.eventually_codiscreteWithin_analyticAtproof · cited by 1
- disjoint_nhds_atTop_iffproof · cited by 1
- isClosed_sdiff_of_codiscreteWithinproof · cited by 1
- UniformSpace.completelyNormalSpace_of_hasAntitoneBasisproof · cited by 0
- disjoint_nhds_atBot_iffproof · cited by 0