Theorems · Theorem · global analysis

Diffeomorph.prodCongr_symm

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {E' : Type u_3} [inst_3 : NormedAddCommGroup E'] [inst_4 : NormedSpace 𝕜 E'] {F : Type u_4}
  [inst_5 : NormedAddCommGroup F] [inst_6 : NormedSpace 𝕜 F] {H : Type u_5} [inst_7 : TopologicalSpace H]
  {H' : Type u_6} [inst_8 : TopologicalSpace H'] {G : Type u_7} [inst_9 : TopologicalSpace G] {G' : Type u_8}
  [inst_10 : TopologicalSpace G'] {I : ModelWithCorners 𝕜 E H} {I' : ModelWithCorners 𝕜 E' H'}
  {J : ModelWithCorners 𝕜 F G} {J' : ModelWithCorners 𝕜 F G'} {M : Type u_9} [inst_11 : TopologicalSpace M]
  [inst_12 : ChartedSpace H M] {M' : Type u_10} [inst_13 : TopologicalSpace M'] [inst_14 : ChartedSpace H' M']
  {N : Type u_11} [inst_15 : TopologicalSpace N] [inst_16 : ChartedSpace G N] {N' : Type u_12}
  [inst_17 : TopologicalSpace N'] [inst_18 : ChartedSpace G' N'] {n : WithTop ℕ∞} (h₁ : Diffeomorph I I' M M' n)
  (h₂ : Diffeomorph J J' N N' n), (h₁.prodCongr h₂).symm = h₁.symm.prodCongr h₂.symm

Defined in

Mathlib.Geometry.Manifold.Diffeomorph

Cited by

0 results in Mathlib

Foundations

Depth 206 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace