Theorems · Theorem · general topology
Set.infsep_eq_iInf
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α} [inst_1 : Decidable s.Nontrivial],
s.infsep = if s.Nontrivial then ⨅ d, Function.uncurry dist ↑d else 0- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpaceDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- Set.Elemstatement and proof · cited by 7,166
- Set.imageproof · cited by 5,609
- iInfstatement and proof · cited by 1,690
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- BddBelowproof · cited by 401
- Set.Nontrivialstatement and proof · cited by 145
- dist_nonnegproof · cited by 126
- eq_of_forall_le_iffproof · cited by 65
- Set.infsepstatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- Set.Nontrivial.infsep_eq_iInfproof · cited by 0