Theorems · Theorem · general topology
UniformSpace.Completion.dist_comm
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y : UniformSpace.Completion α), dist x y = dist y x- Defined in
- Mathlib.Topology.MetricSpace.Completion
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 154 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- UniformSpace.Completionstatement and proof · cited by 192
- dist_commproof · cited by 188
- UniformSpace.Completion.coe'proof · cited by 144
- continuous_fstproof · cited by 103
- continuous_sndproof · cited by 91
- isClosed_eqproof · cited by 71
- UniformSpace.Completion.dist_eqproof · cited by 10
- UniformSpace.Completion.induction_on₂proof · cited by 5
- UniformSpace.Completion.continuous_distproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- UniformSpace.Completion.mem_uniformity_distproof · cited by 0