Theorems · Theorem · real analysis

HasDerivWithinAt.eventually_ne

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {F : Type v} [inst_1 : NormedAddCommGroup F]
  [inst_2 : NormedSpace 𝕜 F] {f : 𝕜 → F} {f' : F} {s : Set 𝕜} {x : 𝕜} {c : F},
  HasDerivWithinAt f f' s x → f' ≠ 0 → ∀ᶠ (z : 𝕜) in nhdsWithin x (s \ {x}), f z ≠ c

Defined in

Mathlib.Analysis.Calculus.Deriv.Inverse

Cited by

2 results in Mathlib

Foundations

Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpace