Theorems · Theorem · general topology
Metric.infEDist_le_edist_add_infEDist
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {s : Set α},
Metric.infEDist x s ≤ edist x y + Metric.infEDist y s- Cited by
- 4 results in Mathlib
- Foundations
- Depth 149 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.
Cites7
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 and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- add_commproof · cited by 1,535
- EDist.ediststatement and proof · cited by 735
- Metric.infEDiststatement and proof · cited by 147
- Metric.infEDist_le_infEDist_add_edistproof · cited by 4
Cited by4
Results whose statement or proof uses this declaration.
- Metric.infEDist_le_infEDist_cthickening_addproof · cited by 3
- lipschitzWith_thickenedIndicatorproof · cited by 1
- Metric.thickening_cthickening_subsetproof · cited by 0
- EMetric.infEdist_le_edist_add_infEdistproof · cited by 0