Theorems · Theorem · general topology
dist_triangle
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y z : α), dist x z ≤ dist x y + dist y z- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 44 results in Mathlib
- Foundations
- Depth 96 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.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- PseudoMetricSpace.dist_triangleproof · cited by 1
Cited by44
Results whose statement or proof uses this declaration.
- dist_nonnegproof · cited by 126
- norm_add_leproof · cited by 68
- Metric.uniformity_basis_distproof · cited by 25
- dist_triangle_rightproof · cited by 16
- norm_mul_le'proof · cited by 15
- dist_triangle_leftproof · cited by 11
- abs_dist_sub_leproof · cited by 8
- Metric.closedBall_subset_closedBall'proof · cited by 7
- Metric.ball_subset_ball'proof · cited by 7
- dist_triangle4proof · cited by 5
- dist_add_add_leproof · cited by 4
- LipschitzOnWith.extend_realproof · cited by 3