Theorems · Theorem · general topology
UniformSpace.Completion.dist_eq
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : α), dist ↑x ↑y = dist x yThe new distance is an extension of the original distance.
- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 153 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- UniformSpace.Completionstatement · cited by 192
- UniformSpace.Completion.coe'statement · cited by 144
- uniformContinuous_distproof · cited by 4
- UniformSpace.Completion.extension₂_coe_coeproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- Isometry.completion_extensionproof · cited by 4
- UniformSpace.Completion.coe_isometryproof · cited by 3
- Complex.affine_of_mapsTo_ball_of_norm_dslope_eq_divproof · cited by 2
- LipschitzWith.completion_extensionproof · cited by 1
- norm_sub_le_integral_of_norm_deriv_le_of_leproof · cited by 1
- UniformSpace.Completion.dist_commproof · cited by 1
- UniformSpace.Completion.dist_selfproof · cited by 1
- UniformSpace.Completion.dist_triangleproof · cited by 0
- Isometry.isometry_mapRingHomproof · cited by 0
- UniformSpace.Completion.mem_uniformity_distproof · cited by 0