Theorems · Theorem · general topology
Metric.ball_subset
∀ {α : Type u} [inst : PseudoMetricSpace α] {x y : α} {ε₁ ε₂ : ℝ},
dist x y ≤ ε₂ - ε₁ → Metric.ball x ε₁ ⊆ Metric.ball y ε₂- Defined in
- Mathlib.Topology.MetricSpace.Pseudo.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 106 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.
Cites9
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- Metric.ballstatement and proof · cited by 735
- lt_of_le_of_ltproof · cited by 432
- add_sub_cancelproof · cited by 195
- dist_triangleproof · cited by 44
- add_lt_add_of_lt_of_leproof · cited by 37
Cited by3
Results whose statement or proof uses this declaration.
- Metric.exists_ball_subset_ballproof · cited by 2
- FDerivMeasurableAux.isOpen_Aproof · cited by 0
- Metric.ball_half_subsetproof · cited by 0