Theorems · Theorem · general topology
PseudoEMetricSpace.ext
∀ {α : Type u_2} {m m' : PseudoEMetricSpace α}, m.toEDist = m'.toEDist → m = m'Two pseudo emetric space structures with the same edistance function coincide.
- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealproof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- UniformSpaceproof · cited by 2,040
- iInfproof · cited by 1,690
- PseudoEMetricSpacestatement and proof · cited by 1,536
- uniformityproof · cited by 765
- Filter.principalproof · cited by 740
- EDist.edistproof · cited by 735
- EDiststatement and proof · cited by 91
- UniformSpace.extproof · cited by 34
- PseudoEMetricSpace.casesOnproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- EMetricSpace.extproof · cited by 2
- PseudoEMetricSpace.replaceEDist_eqproof · cited by 0
- PseudoEMetricSpace.ext_iffproof · cited by 0