Theorems · Theorem · general topology
dist_dist_dist_le
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y x' y' : α), dist (dist x y) (dist x' y') ≤ dist x x' + dist y y'- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 116 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- LE.le.transproof · cited by 3,151
- 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
- dist_dist_dist_le_leftproof · cited by 3
- dist_dist_dist_le_rightproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- uniformContinuous_distproof · cited by 4