Theorems · Theorem · real analysis

contDiffWithinAt_congr

∀ {𝕜 : Type u} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {s : Set E}
  {f f₁ : E → F} {x : E} {n : WithTop ℕ∞},
  (∀ y ∈ s, f₁ y = f y) → f₁ x = f x → (ContDiffWithinAt 𝕜 n f₁ s x ↔ ContDiffWithinAt 𝕜 n f s x)

Defined in

Mathlib.Analysis.Calculus.ContDiff.Defs

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace