Theorems · Theorem · general topology
Metric.eball_disjoint
∀ {α : Type u} [inst : PseudoEMetricSpace α] {x y : α} {ε₁ ε₂ : ENNReal},
ε₁ + ε₂ ≤ edist x y → Disjoint (Metric.eball x ε₁) (Metric.eball y ε₂)- Defined in
- Mathlib.Topology.EMetricSpace.Defs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Disjointstatement · cited by 2,201
- PseudoEMetricSpacestatement and proof · cited by 1,536
- EDist.ediststatement and proof · cited by 735
- LT.lt.trans_leproof · cited by 678
- Metric.eballstatement and proof · cited by 294
- LE.le.not_gtproof · cited by 189
- Set.disjoint_leftproof · cited by 121
- ENNReal.add_lt_addproof · cited by 13
- edist_triangle_leftproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- EMetric.ball_disjointproof · cited by 0