Theorems · Theorem · real analysis
HasConstantSpeedOnWith.hasLocallyBoundedVariationOn
∀ {E : Type u_2} [inst : PseudoEMetricSpace E] {f : ℝ → E} {s : Set ℝ} {l : NNReal},
HasConstantSpeedOnWith f s l → LocallyBoundedVariationOn f s- Defined in
- Mathlib.Analysis.ConstantSpeed
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PseudoEMetricSpace
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.
- Setstatement and proof · cited by 53,352
- Realstatement and proof · cited by 25,697
- Top.topproof · cited by 9,680
- NNRealstatement and proof · cited by 4,310
- PseudoEMetricSpacestatement and proof · cited by 1,536
- LocallyBoundedVariationOnstatement · cited by 41
- HasConstantSpeedOnWithstatement and proof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- hasConstantSpeedOnWith_iff_variationOnFromTo_eqproof · cited by 1