Theorems · Theorem · real analysis

DifferentiableOn.inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {R : Type u_5} [inst_3 : NormedDivisionRing R] [inst_4 : NormedAlgebra 𝕜 R] {h : E → R}
  {S : Set E}, DifferentiableOn 𝕜 h S → (∀ x ∈ S, h x ≠ 0) → DifferentiableOn 𝕜 h⁻¹ S

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

3 results in Mathlib

Foundations

Depth 183 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedDivisionRingNormedAlgebra