Theorems · Theorem · general topology
PseudoEMetricSpace.edist_comm
∀ {α : Type u} [self : PseudoEMetricSpace α] (x y : α), edist x y = edist y x- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 52 results in Mathlib
- Foundations
- Depth 98 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.
- ENNRealstatement · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement · cited by 735
Cited by53
Results whose statement or proof uses this declaration.
- uniformity_basis_edistproof · cited by 17
- continuous_edistproof · cited by 9
- eVariationOn.edist_leproof · cited by 7
- edist_neg_negproof · cited by 6
- EMetric.mem_closure_iffproof · cited by 6
- edist_inv_invproof · cited by 6
- edist_triangle_rightproof · cited by 5
- Metric.hausdorffEDist_singletonproof · cited by 5
- edist_triangle_leftproof · cited by 4
- Metric.AreSeparated.symmproof · cited by 4
- Metric.mem_closedEBall'proof · cited by 4
- Metric.mem_eball'proof · cited by 3