English
Two simple simplifications: for real-valued cases, log identities yield log relations such as log r = log r and log r^{-1} relations; these are algebraic simplifications used in proximity identities.
Русский
Две простые упрощения: для вещественных случаев логарифмические тождества приводят к соотношениям между log r и log r^{-1}, которые применяются в идентичностях близости.
LaTeX
$$$\log r = \log r$ and $\log r^{-1} = -\log r$ (formally, internal simplifications within proximity identities)$$
Lean4
/-- `f` 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`.
-/
def HasConstantSpeedOnWith :=
∀ ⦃x⦄ (_ : x ∈ s) ⦃y⦄ (_ : y ∈ s), eVariationOn f (s ∩ Icc x y) = ENNReal.ofReal (l * (y - x))
