Theorems · Definition · real analysis
HasConstantSpeedOnWith
{E : Type u_2} → [PseudoEMetricSpace E] → (ℝ → E) → Set ℝ → NNReal → Propf has constant speed l on s if the variation of f on s ∩ Icc x y is equal to
l * (y - x) for any x y in s.
- Defined in
- Mathlib.Analysis.ConstantSpeed
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 148 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.
Cites8
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
- Set.Iccproof · cited by 1,702
- PseudoEMetricSpacestatement and proof · cited by 1,536
- NNReal.toRealproof · cited by 1,260
- ENNReal.ofRealproof · cited by 863
- eVariationOnproof · cited by 90
Cited by9
Results whose statement or proof uses this declaration.
- HasUnitSpeedOnproof · cited by 5
- hasConstantSpeedOnWith_iff_orderedstatement and proof · cited by 3
- HasConstantSpeedOnWith.unionstatement and proof · cited by 2
- hasConstantSpeedOnWith_iff_variationOnFromTo_eqstatement and proof · cited by 1
- HasConstantSpeedOnWith.Icc_Iccstatement and proof · cited by 1
- HasConstantSpeedOnWith.hasLocallyBoundedVariationOnstatement and proof · cited by 1
- HasConstantSpeedOnWith.ratiostatement and proof · cited by 1
- hasConstantSpeedOnWith_of_subsingletonstatement · cited by 0
- hasConstantSpeedOnWith_zero_iffstatement · cited by 0