Theorems · Definition · global analysis

Diffeomorph.prodCongr

{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∞} →
                                                                        Diffeomorph I I' M M' n →
                                                                          Diffeomorph J J' N N' n →
                                                                            Diffeomorph (I.prod J) (I'.prod J') (M × N)
                                                                              (M' × N') n

Product of two diffeomorphisms.

Defined in

Mathlib.Geometry.Manifold.Diffeomorph

Cited by

2 results in Mathlib

Foundations

Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpace