Theorems · Theorem · general topology
LipschitzWith.dist_lt_mul_of_lt
∀ {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 → K ≠ 0 → dist x y < r → dist (f x) (f y) < ↑K * r- Defined in
- Mathlib.Topology.MetricSpace.Lipschitz
- Cited by
- 1 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.
Cites12
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
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement and proof · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- LE.le.trans_ltproof · cited by 795
- zero_leproof · cited by 382
- LipschitzWithstatement and proof · cited by 316
- lt_of_le_of_ne'proof · cited by 149
- mul_lt_mul_of_pos_leftproof · cited by 71
- Mathlib.Meta.Positivity.nnreal_coe_posproof · cited by 31
- LipschitzWith.dist_le_mulproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- LipschitzWith.mapsTo_ballproof · cited by 1