Theorems · Definition · global analysis

PartialDiffeomorph.trans

{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∞} →
                                                            PartialDiffeomorph I J M N n →
                                                              PartialDiffeomorph J K N P n →
                                                                PartialDiffeomorph I K M P n

Composition of partial diffeomorphisms.

Defined in

Mathlib.Geometry.Manifold.LocalDiffeomorph

Cited by

2 results in Mathlib

Foundations

Depth 196 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace