Theorems · Theorem · general topology
dist_edist
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), dist x y = (edist x y).toRealExpress dist in terms of edist
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 112 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- ENNRealproof · cited by 9,879
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- ENNReal.toRealstatement and proof · cited by 859
- EDist.ediststatement · cited by 735
- dist_nonnegproof · cited by 126
- ENNReal.toReal_ofRealproof · cited by 82
- edist_distproof · cited by 39
Cited by21
Results whose statement or proof uses this declaration.
- Metric.infDist_le_dist_of_memproof · cited by 13
- Metric.mem_thickening_iffproof · cited by 6
- Metric.infDist_eq_iInfproof · cited by 4
- dist_pi_constproof · cited by 3
- Metric.diam_unionproof · cited by 2
- Metric.dist_le_diam_of_mem'proof · cited by 2
- Metric.infDist_le_infDist_add_distproof · cited by 2
- variationOnFromTo.abs_sub_le_sub_of_leproof · cited by 2
- variationOnFromTo.tendsto_leftproof · cited by 1
- variationOnFromTo.tendsto_rightproof · cited by 1
- Metric.dist_le_infDist_add_diamproof · cited by 1
- IsCompact.exists_infDist_eq_distproof · cited by 1