Theorems · Theorem · general topology
Finset.coe_infsep
∀ {α : Type u_1} [inst : PseudoMetricSpace α] (s : Finset α),
(↑s).infsep = if hs : s.offDiag.Nonempty then s.offDiag.inf' hs (Function.uncurry dist) else 0- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- Realstatement · cited by 25,697
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Set.Nonemptyproof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Finset.Nonemptystatement and proof · cited by 1,001
- Set.toFinsetproof · cited by 217
- Set.Nontrivialproof · cited by 145
- Finset.inf'statement and proof · cited by 117
- Finset.offDiagstatement and proof · cited by 44
Cited by2
Results whose statement or proof uses this declaration.
- Finset.coe_infsep_of_offDiag_emptyproof · cited by 0
- Finset.coe_infsep_of_offDiag_nonemptyproof · cited by 0