Theorems · Theorem · general topology
PseudoEMetricSpace.edist_triangle
∀ {α : Type u} [self : PseudoEMetricSpace α] (x y z : α), edist x z ≤ edist x y + edist y z- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 112 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 by25
Results whose statement or proof uses this declaration.
- uniformity_basis_edistproof · cited by 17
- Metric.infEDist_closureproof · cited by 8
- edist_triangle_rightproof · cited by 5
- eVariationOn.eVariationOn_on_inter_Iic_eq_Iio_add_edistproof · cited by 4
- Metric.thickening_thickening_subsetproof · cited by 4
- edist_triangle4proof · cited by 4
- edist_triangle_leftproof · cited by 4
- Metric.infEDist_le_infEDist_add_edistproof · cited by 4
- Metric.infEDist_le_infEDist_add_hausdorffEDistproof · cited by 4
- continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWithproof · cited by 3
- Metric.edist_le_infEDist_add_ediamproof · cited by 3
- LipschitzOnWith.ediam_image2_leproof · cited by 3