Theorems · Theorem · general topology
Metric.dist_le_add_of_nonempty_closedBall_inter_closedBall
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε₁ ε₂ : ℝ},
(Metric.closedBall x ε₁ ∩ Metric.closedBall y ε₂).Nonempty → dist x y ≤ ε₁ + ε₂- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- Set.Nonemptystatement and proof · cited by 2,627
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Metric.closedBallstatement and proof · cited by 704
- add_le_addproof · cited by 666
- dist_triangle_leftproof · cited by 11
Cited by3
Results whose statement or proof uses this declaration.
- Vitali.exists_disjoint_covering_aeproof · cited by 1
- Besicovitch.TauPackage.color_ltproof · cited by 1
- Vitali.exists_disjoint_subfamily_covering_enlargement_closedBallproof · cited by 0