Theorems · Theorem · real analysis

HasFDerivAtFilter.of_comp_of_isEmbedding

∀ {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} {g' : E →L[𝕜] F}
  {f' : F →L[𝕜] G} {lE : Filter (E × E)} {lF : Filter (F × F)},
  Filter.Tendsto (Prod.map g g) lE lF →
    HasFDerivAtFilter f f' lF →
      Topology.IsEmbedding ⇑f' →
        HasFDerivAtFilter h (f' ∘SL g') lE → Prod.map (f ∘ g) (f ∘ g) =ᶠ[lE] Prod.map h h → HasFDerivAtFilter g g' lE

Defined in

Mathlib.Analysis.Calculus.FDeriv.OfCompLeft

Cited by

3 results in Mathlib

Foundations

Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace