Theorems · Theorem · general topology
abs_dist
∀ {α : Type u} [inst : PseudoMetricSpace α] {a b : α}, |dist a b| = dist a b- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 112 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- absstatement · cited by 1,814
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- abs_of_nonnegproof · cited by 279
- dist_nonnegproof · cited by 126
Cited by10
Results whose statement or proof uses this declaration.
- EuclideanGeometry.dist_inversion_centerproof · cited by 5
- Metric.uniformity_eq_comap_nhds_zeroproof · cited by 4
- MeasureTheory.tendstoInDistribution_of_tendstoInMeasure_subproof · cited by 2
- Metric.uniformEquicontinuous_of_continuity_modulusproof · cited by 1
- ODE.FunSpace.dist_iterate_next_apply_leproof · cited by 1
- Convexity.dist_convexCombPair_convexCombPairproof · cited by 1
- ContDiffPointwiseHolderAt.of_contDiffOn_holderOnWithproof · cited by 0
- properSpace_iff_isProperMap_distproof · cited by 0
- EuclideanGeometry.Sphere.IsTangentAt.radius_lt_dist_centerproof · cited by 0
- Affine.Simplex.abs_inner_vsub_altitudeFoot_div_lt_oneproof · cited by 0