Theorems · Theorem · general topology
Metric.infEDist_le_edist_of_mem
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {s : Set α}, y ∈ s → Metric.infEDist x s ≤ edist x yThe edist to a set is bounded above by the edist to any of its points
- Cited by
- 13 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.
Cites6
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
- EDist.ediststatement · cited by 735
- Metric.infEDiststatement · cited by 147
- iInf₂_leproof · cited by 45
Cited by13
Results whose statement or proof uses this declaration.
- Metric.infDist_le_dist_of_memproof · cited by 13
- Metric.infEDist_closureproof · cited by 8
- Metric.infEDist_ne_topproof · cited by 8
- Metric.infEDist_zero_of_memproof · cited by 7
- Metric.infEDist_le_infEDist_add_hausdorffEDistproof · cited by 4
- Metric.hausdorffEDist_le_of_mem_edistproof · cited by 3
- IsCompact.exists_infEDist_eq_edistproof · cited by 3
- infEDist_thickeningproof · cited by 3
- Metric.subset_compl_thickening_compl_thickening_selfproof · cited by 2
- Metric.mem_cthickening_of_edist_leproof · cited by 1
- MeasureTheory.OuterMeasure.IsMetric.borel_le_caratheodoryproof · cited by 1
- Metric.disjoint_closedEBall_of_lt_infEDistproof · cited by 1