Theorems · Theorem · general topology
dist_triangle_right
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y z : α), dist x y ≤ dist x z + dist y z- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 16 results in Mathlib
- Foundations
- Depth 97 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- dist_commproof · cited by 188
- dist_triangleproof · cited by 44
Cited by16
Results whose statement or proof uses this declaration.
- Metric.isBounded_closedBallproof · cited by 19
- multipliable_one_add_of_summableproof · cited by 4
- IsUnifLocDoublingMeasure.tendsto_closedBall_filterAtproof · cited by 3
- LipschitzWith.dist_rightproof · cited by 3
- cauchySeq_bddproof · cited by 3
- Metric.PiNatEmbed.separationproof · cited by 2
- BoxIntegral.Integrable.dist_integralSum_le_of_memBaseSetproof · cited by 2
- Metric.diam_le_of_subset_closedBallproof · cited by 2
- exists_nat_nat_continuous_surjective_of_completeSpaceproof · cited by 1
- BoxIntegral.hasIntegral_GP_pderivproof · cited by 1
- exists_closed_cover_approximatesLinearOn_of_hasFDerivWithinAtproof · cited by 1
- BoundedContinuousFunction.arzela_ascoli₁proof · cited by 1