Theorems · Theorem · real analysis

DifferentiableOn.inverse

∀ {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 : NormedRing R] [HasSummableGeomSeries R]
  [inst_5 : NormedAlgebra 𝕜 R] {h : E → R} {S : Set E},
  DifferentiableOn 𝕜 h S → (∀ x ∈ S, IsUnit (h x)) → DifferentiableOn 𝕜 (fun x => Ring.inverse (h x)) S

Defined in

Mathlib.Analysis.Calculus.FDeriv.Mul

Cited by

0 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedRingHasSummableGeomSeriesNormedAlgebra