Theorems · Theorem · real analysis

HasStrictFDerivAt.of_comp_of_leftInverse

∀ {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {G : Type u_4} [inst : NontriviallyNormedField 𝕜]
  [inst_1 : NormedAddCommGroup E] [inst_2 : NormedSpace 𝕜 E] [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F]
  [inst_5 : NormedAddCommGroup G] [inst_6 : NormedSpace 𝕜 G] {g : E → F} {f : F → G} {h : E → G} {f' : F →L[𝕜] G}
  {h' : E →L[𝕜] G} {f'symm : G →L[𝕜] F} {a : E},
  ContinuousAt g a →
    HasStrictFDerivAt f f' (g a) →
      HasStrictFDerivAt h h' a →
        f ∘ g =ᶠ[nhds a] h → Function.LeftInverse ⇑f'symm ⇑f' → HasStrictFDerivAt g (f'symm ∘SL h') a

Defined in

Mathlib.Analysis.Calculus.FDeriv.OfCompLeft

Cited by

1 results in Mathlib

Foundations

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

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace