Theorems · Theorem · general topology
PseudoMetricSpace.dist_self
∀ {α : Type u} [self : PseudoMetricSpace α] (x : α), dist x x = 0- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 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.
Cites3
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
Cited by3
Results whose statement or proof uses this declaration.
- dist_selfproof · cited by 116
- PseudoMetricSpace.replaceUniformityproof · cited by 1
- PseudoMetricSpace.replaceBornologyproof · cited by 1