Theorems · Theorem · general topology
isometry_subtype_coe
∀ {α : Type u} [inst : PseudoEMetricSpace α] {s : Set α}, Isometry Subtype.valThe injection from a subtype is an isometry
- Defined in
- Mathlib.Topology.MetricSpace.Isometry
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 148 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.
- Setstatement and proof · cited by 53,352
- PseudoEMetricSpacestatement and proof · cited by 1,536
- Isometrystatement · cited by 230
Cited by7
Results whose statement or proof uses this declaration.
- GromovHausdorff.eq_toGHSpace_iffproof · cited by 3
- GromovHausdorff.ghDist_le_hausdorffDistproof · cited by 3
- GromovHausdorff.eq_toGHSpaceproof · cited by 1
- Real.Convex.dimH_eq_finrank_vectorSpanproof · cited by 1
- GromovHausdorff.ghDist_le_nonemptyCompacts_distproof · cited by 1
- AffineSubspace.euclideanHausdorffMeasure_coe_imageproof · cited by 1
- AffineSubspace.euclideanHausdorffMeasure_eq_lintegralproof · cited by 1