Theorems · Theorem · general topology
edist_triangle4
∀ {α : Type u} [inst : PseudoEMetricSpace α] (x y z t : α), edist x t ≤ edist x y + edist y z + edist z t- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 121 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement · cited by 9,879
- le_reflproof · cited by 2,061
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
- PseudoEMetricSpace.edist_triangleproof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- continuous_edistproof · cited by 9
- continuousOn_prod_of_subset_closure_continuousOn_lipschitzOnWithproof · cited by 3
- Metric.ediam_union_le_add_edistproof · cited by 3
- ContractingWith.edist_inequalityproof · cited by 1