congr_of_eventuallyEq_insert — Mathlib

English

If f and f1 agree in a neighborhood and are differentiable, their mfderivWithin coincide on the intersection of neighborhoods.

Русский

Если f и f1 совпадают в окрестности и обе дифференцируемы, их mfderivWithin совпадают на пересечении окрестностей.

LaTeX

$$$\text{mfderivWithin } I I' f t x = \text{mfderivWithin } I I' f s x$ under appropriate conditions$$

Lean4

theorem congr_of_eventuallyEq_insert (h : MDifferentiableWithinAt I I' f s x) (h₁ : f₁ =ᶠ[𝓝[insert x s] x] f) :
    MDifferentiableWithinAt I I' f₁ s x :=
  (h.insert.congr_of_eventuallyEq_of_mem h₁ (mem_insert x s)).of_insert

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