Theorems · Theorem · general topology
dist_nndist
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), dist x y = ↑(nndist x y)Express dist in terms of nndist
- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 113 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- NNDist.nndiststatement · cited by 235
Cited by10
Results whose statement or proof uses this declaration.
- edist_nndistproof · cited by 38
- Metric.inseparable_iffproof · cited by 6
- similar_iff_exists_dist_eqproof · cited by 3
- congruent_iff_dist_eqproof · cited by 3
- cauchySeq_of_edist_le_of_summableproof · cited by 2
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- HolderOnWith.dist_le_of_leproof · cited by 2
- antilipschitzWith_lineMapproof · cited by 1
- Complex.nndist_conj_selfproof · cited by 1
- nndist_distproof · cited by 1