Theorems · Theorem · general topology
edist_triangle_left
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x y z : α), edist x y ≤ edist z x + edist z yTriangle inequality for the extended distance
- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 113 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- PseudoEMetricSpace.edist_commproof · cited by 52
- PseudoEMetricSpace.edist_triangleproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- LocallyLipschitzOn.exists_lipschitzOnWith_of_compactproof · cited by 1
- Metric.eball_disjointproof · cited by 1
- Disjoint.exists_thickeningsproof · cited by 1
- edist_ne_top_of_mem_ballproof · cited by 0