Theorems · Theorem · general topology
HolderOnWith.dist_le_of_le
∀ {X : Type u_1} {Y : Type u_2} [inst : PseudoMetricSpace X] [inst_1 : PseudoMetricSpace Y] {C r : NNReal} {f : X → Y}
{s : Set X} {x y : X}, HolderOnWith C r f s → x ∈ s → y ∈ s → ∀ {d : ℝ}, dist x y ≤ d → dist (f x) (f y) ≤ ↑C * d ^ ↑r- Defined in
- Mathlib.Topology.MetricSpace.Holder
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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 and proof · cited by 1,260
- dist_nonnegproof · cited by 126
- HolderOnWithstatement and proof · cited by 44
- dist_nndistproof · cited by 10
- HolderOnWith.nndist_le_of_leproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- HolderWith.dist_le_of_leproof · cited by 1
- HolderOnWith.dist_leproof · cited by 1