Theorems · Theorem · global analysis

IsLocalDiffeomorphAt.comp

∀ {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' : Type u_4}
  [inst_5 : NormedAddCommGroup F'] [inst_6 : NormedSpace 𝕜 F'] {H₁ : Type u_5} [inst_7 : TopologicalSpace H₁]
  {H₂ : Type u_6} [inst_8 : TopologicalSpace H₂] {H₃ : Type u_7} [inst_9 : TopologicalSpace H₃]
  {I : ModelWithCorners 𝕜 E H₁} {J : ModelWithCorners 𝕜 F H₂} (K : ModelWithCorners 𝕜 F' H₃) {M : Type u_8}
  [inst_10 : TopologicalSpace M] [inst_11 : ChartedSpace H₁ M] {N : Type u_9} [inst_12 : TopologicalSpace N]
  [inst_13 : ChartedSpace H₂ N] (P : Type u_10) [inst_14 : TopologicalSpace P] [inst_15 : ChartedSpace H₃ P]
  {n : WithTop ℕ∞} {f : M → N} {x : M},
  IsLocalDiffeomorphAt I J n f x →
    ∀ {g : N → P}, IsLocalDiffeomorphAt J K n g (f x) → IsLocalDiffeomorphAt I K n (g ∘ f) x

Defined in

Mathlib.Geometry.Manifold.LocalDiffeomorph

Cited by

0 results in Mathlib

Foundations

Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace