Theorems · Theorem · general topology
UniformSpace.Completion.coe_isometry
∀ {α : Type u} [inst : PseudoMetricSpace α], Isometry UniformSpace.Completion.coe'The embedding of a metric space in its completion is an isometry.
- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoMetricSpacestatement and proof · cited by 1,550
- Isometrystatement · cited by 230
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.coe'statement · cited by 144
- Isometry.of_dist_eqproof · cited by 27
- UniformSpace.Completion.dist_eqproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.edist_eqproof · cited by 0
- Isometry.completion_mapproof · cited by 0
- LipschitzWith.completion_mapproof · cited by 0