Theorems · Theorem · general topology
coe_nndist
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), ↑(nndist x y) = dist x y- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 4 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 by4
Results whose statement or proof uses this declaration.
- MeasureTheory.hasSum_integral_measureproof · cited by 4
- LocallyLipschitzOn.exists_lipschitzOnWith_of_compactproof · cited by 1
- NNReal.le_add_nndistproof · cited by 1
- Dilation.ratio_unique_of_dist_ne_zeroproof · cited by 1