Theorems · Theorem · general topology
LipschitzWith.dist_le_mul_of_le
∀ {α : Type u} {β : Type v} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β}
{x y : α} {r : ℝ}, LipschitzWith K f → dist x y ≤ r → dist (f x) (f y) ≤ ↑K * r- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- NNRealstatement and proof · cited by 4,310
- LE.le.transproof · cited by 3,151
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- mul_le_mul_of_nonneg_leftproof · cited by 361
- LipschitzWithstatement and proof · cited by 316
- NNReal.coe_nonnegproof · cited by 130
- LipschitzWith.dist_le_mulproof · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- LipschitzWith.cauchySeq_compproof · cited by 3
- LipschitzWith.mapsTo_closedBallproof · cited by 2
- LipschitzWith.diam_image_leproof · cited by 0