Theorems · Theorem · general topology
Set.Nontrivial.le_infsep_iff
∀ {α : Type u_1} [inst : PseudoMetricSpace α] {s : Set α} {d : ℝ},
s.Nontrivial → (d ≤ s.infsep ↔ ∀ x ∈ s, ∀ y ∈ s, x ≠ y → d ≤ dist x y)- Defined in
- Mathlib.Topology.MetricSpace.Infsep
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 149 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.
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- ENNReal.ofRealproof · cited by 863
- Set.Nontrivialstatement and proof · cited by 145
- dist_nonnegproof · cited by 126
- edist_distproof · cited by 39
- Set.infsepstatement · cited by 35
- ENNReal.ofReal_le_ofReal_iffproof · cited by 20
- ENNReal.ofReal_le_iff_le_toRealproof · cited by 10
- Set.Nontrivial.einfsep_ne_topproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Set.le_edist_of_le_infsepproof · cited by 1
- Set.infsep_eq_iInfproof · cited by 1
- Set.Finite.infsepproof · cited by 1
- Set.infsep_of_fintypeproof · cited by 1
- Set.Nontrivial.infsep_lt_iffproof · cited by 0
- Set.Nontrivial.le_infsepproof · cited by 0