Theorems · Theorem · general topology
Set.Finite.infsep_of_nontrivial
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α} (hsf : s.Finite) (hs : s.Nontrivial),
s.infsep = ⋯.toFinset.inf' ⋯ (Function.uncurry dist)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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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
- Set.Finitestatement and proof · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Set.Finite.toFinsetstatement and proof · cited by 351
- Set.Nontrivialstatement and proof · cited by 145
- Finset.inf'statement and proof · cited by 117
- Set.infsepstatement · cited by 35
- Set.offDiagstatement · cited by 35
- Set.Finite.offDiagstatement and proof · cited by 4
- Set.Finite.infsepproof · cited by 1
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