Theorems · Theorem · general topology
PseudoEMetricSpace.edist_self
∀ {α : Type u} [self : PseudoEMetricSpace α] (x : α), edist x x = 0- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 50 results in Mathlib
- Foundations
- Depth 105 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
Cited by51
Results whose statement or proof uses this declaration.
- uniformity_basis_edistproof · cited by 17
- AntilipschitzWith.injectiveproof · cited by 8
- Metric.infEDist_zero_of_memproof · cited by 7
- MemHolder.holderWithproof · cited by 7
- LipschitzWith.constproof · cited by 7
- Metric.mem_eball_selfproof · cited by 6
- Metric.ediam_subsingletonproof · cited by 6
- HasFPowerSeriesWithinOnBall.coeff_zeroproof · cited by 5
- edist_eq_zeroproof · cited by 4
- HolderWith.constproof · cited by 3
- Metric.ediam_insertproof · cited by 3
- ContractingWith.eq_or_edist_eq_top_of_fixedPointsproof · cited by 3