mfderivWithin_mono_of_mem_nhdsWithin

English

If h.LHS, f1 ≈ f near s and hx, then mfderivWithin values are equal.

Русский

Если значение mfderivWithin совпадает на окрестности, то их значения равны.

LaTeX

$$$mfderivWithin I I' f_1 t x = mfderivWithin I I' f s x$ under mem and insert conditions$$

Lean4

theorem mfderivWithin_mono_of_mem_nhdsWithin (h : MDifferentiableWithinAt I I' f s x) (hxt : UniqueMDiffWithinAt I t x)
    (h₁ : s ∈ 𝓝[t] x) : mfderivWithin I I' f t x = mfderivWithin I I' f s x :=
  (HasMFDerivWithinAt.mono_of_mem_nhdsWithin h.hasMFDerivWithinAt h₁).mfderivWithin hxt

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