Theorems · Theorem · general topology
Metric.PiNatEmbed.isometry_embed
∀ {ι : Type u_2} {X : Type u_3} {Y : ι → Type u_4} {f : (i : ι) → X → Y i} [inst : Encodable ι]
[inst_1 : (i : ι) → PseudoEMetricSpace (Y i)], Isometry (Metric.PiNatEmbed.embed X Y f)- Defined in
- Mathlib.Topology.MetricSpace.PiNat
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 161 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EncodablePseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Isometrystatement · cited by 230
- Encodablestatement and proof · cited by 140
- Metric.PiNatEmbedstatement · cited by 20
- Metric.PiNatEmbed.embedstatement and proof · cited by 5
- PseudoEMetricSpace.isometry_inducedproof · cited by 1
- PiCountable.pseudoEMetricSpacestatement · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Metric.PiNatEmbed.isUniformEmbedding_embedproof · cited by 2