Theorems · Theorem · general topology
Finset.coe_infsep_of_offDiag_nonempty
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Finset α} (hs : s.offDiag.Nonempty),
(↑s).infsep = s.offDiag.inf' hs (Function.uncurry dist)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement · cited by 8,199
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Finset.Nonemptystatement and proof · cited by 1,001
- Finset.inf'statement and proof · cited by 117
- Finset.offDiagstatement and proof · cited by 44
- Set.infsepstatement · cited by 35
- Finset.coe_infsepproof · cited by 2
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