Theorems · Theorem · general topology
Metric.infEDist_anti
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x : α} {s t : Set α}, s ⊆ t → Metric.infEDist x t ≤ Metric.infEDist x sThe edist is antitone with respect to inclusion.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 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.
Cites5
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
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Metric.infEDiststatement · cited by 147
- iInf_le_iInf_of_subsetproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- Metric.infEDist_closureproof · cited by 8
- Metric.thickening_subset_of_subsetproof · cited by 4
- Metric.infEDist_le_infEDist_thickening_addproof · cited by 3
- thickenedIndicatorAux_subsetproof · cited by 1
- Metric.infDist_le_infDist_of_subsetproof · cited by 1
- Metric.cthickening_subset_of_subsetproof · cited by 1
- EMetric.infEdist_antiproof · cited by 0