Theorems · Theorem · general topology
dist_triangle_left
∀ {α : Type u} [inst : PseudoMetricSpace α] (x y z : α), dist x y ≤ dist z x + dist z y- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 11 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 by11
Results whose statement or proof uses this declaration.
- abs_dist_sub_leproof · cited by 8
- Convexity.dist_convexCombPair_leftproof · cited by 4
- TendstoLocallyUniformlyOn.smul₀_of_isBoundedUnderproof · cited by 4
- Metric.dist_le_add_of_nonempty_closedBall_inter_closedBallproof · cited by 3
- LipschitzOnWith.extend_realproof · cited by 3
- Metric.closedBall_disjoint_ballproof · cited by 2
- Metric.dist_lt_add_of_nonempty_closedBall_inter_ballproof · cited by 2
- LocallyLipschitzOn.exists_lipschitzOnWith_of_compactproof · cited by 1
- Metric.closedBall_disjoint_closedBallproof · cited by 1
- ZeroAtInftyContinuousMap.isClosed_range_toBCFproof · cited by 0
- nndist_triangle_leftproof · cited by 0