Theorems · Theorem · general topology
dist_self
∀ {α : Type u} [inst : PseudoMetricSpace α] (x : α), dist x x = 0- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 116 results in Mathlib
- Foundations
- Depth 87 from the axioms, rests on 1,591 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
- PseudoMetricSpace.dist_selfproof · cited by 1
Cited by116
Results whose statement or proof uses this declaration.
- norm_zeroproof · cited by 366
- dist_nonnegproof · cited by 126
- Metric.mem_ball_selfproof · cited by 40
- Metric.uniformity_basis_distproof · cited by 25
- dist_eq_zeroproof · cited by 13
- Metric.mem_closedBall_selfproof · cited by 12
- AnalyticAt.derivproof · cited by 10
- norm_one'proof · cited by 10
- EuclideanGeometry.inversion_selfproof · cited by 6
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- Metric.ne_of_mem_sphereproof · cited by 5
- EuclideanGeometry.Sphere.center_mem_iffproof · cited by 5