Theorems · Definition · global analysis

HasStrictFDerivAt.localInverse

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {F : Type u_3} →
            [inst_3 : NormedAddCommGroup F] →
              [inst_4 : NormedSpace 𝕜 F] →
                (f : E → F) → (f' : E ≃L[𝕜] F) → (a : E) → [CompleteSpace E] → HasStrictFDerivAt f (↑f') a → F → E

Given a function f with an invertible derivative, returns a function that is locally inverse to f.

Defined in

Mathlib.Analysis.Calculus.InverseFunctionTheorem.FDeriv

Cited by

11 results in Mathlib

Foundations

Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceCompleteSpace