Theorems · Theorem · general topology
dist_triangle4
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y z w : α), dist x w ≤ dist x y + dist y z + dist z w- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 103 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
- le_reflproof · cited by 2,061
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- add_le_addproof · cited by 666
- dist_triangleproof · cited by 44
Cited by5
Results whose statement or proof uses this declaration.
- dist_triangle4_rightproof · cited by 3
- MeasureTheory.IntegrableOn.hasBoxIntegralproof · cited by 2
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- dist_triangle8proof · cited by 1
- dist_triangle4_leftproof · cited by 0