Theorems · Theorem · global analysis

PartialDiffeomorph.trans_toPartialEquiv

∀ {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∞} (Φ : PartialDiffeomorph I J M N n) (Ψ : PartialDiffeomorph J K N P n),
  (Φ.trans Ψ).toPartialEquiv = (Φ.toOpenPartialHomeomorph.trans Ψ.toOpenPartialHomeomorph).toPartialEquiv

Defined in

Mathlib.Geometry.Manifold.LocalDiffeomorph

Cited by

1 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace