congr — Mathlib

English

If two sets s and t coincide near x, ContDiffWithinAt on s and t are equivalent for a fixed f.

Русский

Если множества s и t совпадают около x, ContDiffWithinAt на s и t равнозначны для заданной f.

LaTeX

$$$ (nhds x).EventuallyEq s t \\Rightarrow ContDiffWithinAt 𝕜 n f s x \\iff ContDiffWithinAt 𝕜 n f t x$$

Lean4

theorem congr (h : ContDiffWithinAt 𝕜 n f s x) (h₁ : ∀ y ∈ s, f₁ y = f y) (hx : f₁ x = f x) :
    ContDiffWithinAt 𝕜 n f₁ s x :=
  h.congr_of_eventuallyEq (Filter.eventuallyEq_of_mem self_mem_nhdsWithin h₁) hx

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