contDiff — Mathlib

English

The function f: E → ℝ given by a ContDiffBump (c x) has ContDiffWithinAt on any set s, i.e. f is smoothly varying on every part of its domain.

Русский

Функция f: E → ℝ, заданная ContDiffBump (c x), имеет ContDiffWithinAt на любом множестве s.

LaTeX

$$$\\forall {s:Set E}: ContDiffWithinAt Real (WithTop.some n) f.toFun s x$$$

Lean4

protected theorem contDiff : ContDiff ℝ n f :=
  contDiff_const.contDiffBump contDiff_const contDiff_const contDiff_id

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