Theorems · Theorem · global analysis

ContMDiffOn.clm_comp

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {F₁ : Type u_8} [inst_6 : NormedAddCommGroup F₁]
  [inst_7 : NormedSpace 𝕜 F₁] {F₂ : Type u_9} [inst_8 : NormedAddCommGroup F₂] [inst_9 : NormedSpace 𝕜 F₂]
  {F₃ : Type u_10} [inst_10 : NormedAddCommGroup F₃] [inst_11 : NormedSpace 𝕜 F₃] {n : WithTop ℕ∞} {g : M → F₁ →L[𝕜] F₃}
  {f : M → F₂ →L[𝕜] F₁} {s : Set M},
  ContMDiffOn I (modelWithCornersSelf 𝕜 (F₁ →L[𝕜] F₃)) n g s →
    ContMDiffOn I (modelWithCornersSelf 𝕜 (F₂ →L[𝕜] F₁)) n f s →
      ContMDiffOn I (modelWithCornersSelf 𝕜 (F₂ →L[𝕜] F₃)) n (fun x => g x ∘SL f x) s

Defined in

Mathlib.Geometry.Manifold.ContMDiff.NormedSpace

Cited by

0 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace