lineDerivWithin_zero_of_not_lineDifferentiableWithinAt

English

If a line-differentiable-within object holds on s and s is contained in nhdsWithin x t, then it holds on t as well.

Русский

Если линейная дифференциация внутри s справедлива и s ⊆ nhdsWithin x t, то она справедлива и на t.

LaTeX

$$$h: LineDifferentiableWithinAt 𝕜 f s x v \land s ∈ 𝓝[t] x \Rightarrow LineDifferentiableWithinAt 𝕜 f t x v.$$$

Lean4

theorem lineDerivWithin_zero_of_not_lineDifferentiableWithinAt (h : ¬LineDifferentiableWithinAt 𝕜 f s x v) :
    lineDerivWithin 𝕜 f s x v = 0 :=
  derivWithin_zero_of_not_differentiableWithinAt h

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