Theorems · Theorem · general topology
Set.Nontrivial.infsep_of_fintype
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α} [inst_1 : Fintype ↑s] (hs : s.Nontrivial),
s.infsep = s.offDiag.toFinset.inf' ⋯ (Function.uncurry dist)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceFintype
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Realstatement and proof · cited by 25,697
- Fintypestatement and proof · cited by 7,736
- Set.Elemstatement and proof · cited by 7,166
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Set.toFinsetstatement and proof · cited by 217
- Set.Nontrivialstatement and proof · cited by 145
- Finset.inf'statement and proof · cited by 117
- Set.infsepstatement · cited by 35
- Set.offDiagstatement and proof · cited by 35
- Set.infsep_of_fintypeproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Finset.coe_infsepproof · cited by 2
- Set.Nontrivial.infsep_exists_of_finiteproof · cited by 1