Theorems · Theorem · general topology
Metric.edist_le_infEDist_add_ediam
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {s : Set α},
y ∈ s → edist x y ≤ Metric.infEDist x s + Metric.ediam s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- ENNRealstatement · cited by 9,879
- iInfproof · cited by 1,690
- le_rflproof · cited by 1,558
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- add_le_addproof · cited by 666
- Metric.ediamstatement · cited by 159
- Metric.infEDiststatement · cited by 147
- le_iInf₂proof · cited by 67
- PseudoEMetricSpace.edist_triangleproof · cited by 24
- Metric.edist_le_ediam_of_memproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Metric.ediam_cthickening_leproof · cited by 2
- Metric.dist_le_infDist_add_diamproof · cited by 1
- EMetric.edist_le_infEdist_add_ediamproof · cited by 0