Theorems · Theorem · general topology
AntilipschitzWith.le_mul_dist
∀ {α : Type u_1} {β : Type u_2} [inst : PseudoMetricSpace α] [inst_1 : PseudoMetricSpace β] {K : NNReal} {f : α → β},
AntilipschitzWith K f → ∀ (x y : α), dist x y ≤ ↑K * dist (f x) (f y)Alias of the forward direction of antilipschitzWith_iff_le_mul_dist.
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 151 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.
- Realstatement · cited by 25,697
- NNRealstatement and proof · cited by 4,310
- PseudoMetricSpacestatement and proof · cited by 1,550
- Dist.diststatement · cited by 1,539
- NNReal.toRealstatement · cited by 1,260
- AntilipschitzWithstatement · cited by 132
- antilipschitzWith_iff_le_mul_distproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- HasFDerivWithinAt.tendsto_nhdsWithin_nhdsNEproof · cited by 4
- AntilipschitzWith.le_mul_normproof · cited by 2
- AntilipschitzWith.le_mul_norm'proof · cited by 2
- ApproximatesLinearOn.to_invproof · cited by 1
- MeasureTheory.MemLp.of_comp_antilipschitzWithproof · cited by 1
- AntilipschitzWith.le_mul_norm_subproof · cited by 0
- AntilipschitzWith.le_mul_norm_divproof · cited by 0