Theorems · Theorem · general topology
LipschitzWith.edist_lt_of_edist_lt_div
∀ {α : Type u} {β : Type v} [inst : PseudoEMetricSpace α] [inst_1 : PseudoEMetricSpace β] {K : NNReal} {f : α → β},
LipschitzWith K f → ∀ {x y : α} {d : ENNReal}, edist x y < d / ↑K → edist (f x) (f y) < d- Defined in
- Mathlib.Topology.EMetricSpace.Lipschitz
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENNRealstatement and proof · cited by 9,879
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- EDist.ediststatement and proof · cited by 735
- LipschitzWithstatement and proof · cited by 316
- ENNReal.mul_lt_of_lt_div'proof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- LipschitzWith.uniformContinuousproof · cited by 33
- LipschitzOnWith.edist_lt_of_edist_lt_divproof · cited by 0