uniqueDiffWithinAt_univ — Mathlib

English

If nhdsWithin x s = nhdsWithin x t, then UniqueDiffWithinAt 𝕜 s x ⇔ UniqueDiffWithinAt 𝕜 t x.

Русский

Если nhdsWithin x s = nhdsWithin x t, то UniqueDiffWithinAt 𝕜 s x эквивалентно UniqueDiffWithinAt 𝕜 t x.

LaTeX

$$$ nhdsWithin x s = nhdsWithin x t \\Rightarrow (UniqueDiffWithinAt_{\\mathbb{k}}(s,x) \\iff UniqueDiffWithinAt_{\\mathbb{k}}(t,x) )$$$

Lean4

@[simp]
theorem uniqueDiffWithinAt_univ : UniqueDiffWithinAt 𝕜 univ x :=
  by
  rw [uniqueDiffWithinAt_iff, tangentConeAt_univ]
  simp

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