Theorems · Theorem · general topology
Metric.closedBall_disjoint_ball
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {δ ε : ℝ},
δ + ε ≤ dist x y → Disjoint (Metric.closedBall x δ) (Metric.ball y ε)- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 2 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.
Cites12
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
- LE.le.transproof · cited by 3,151
- Disjointstatement · cited by 2,201
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Metric.ballstatement and proof · cited by 735
- Metric.closedBallstatement and proof · cited by 704
- LE.le.not_gtproof · cited by 189
- Set.disjoint_leftproof · cited by 121
- add_lt_add_of_le_of_ltproof · cited by 31
- dist_triangle_leftproof · cited by 11
Cited by2
Results whose statement or proof uses this declaration.
- Metric.ball_disjoint_ballproof · cited by 3
- Metric.ball_disjoint_closedBallproof · cited by 1