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Theorems Ā· Definition Ā· algebraic topology

VectorPrebundle.IsContMDiff.casesOn

{š•œ : Type u_1} ā†’
  {B : Type u_2} ā†’
    {F : Type u_4} ā†’
      {E : B ā†’ Type u_6} ā†’
        [inst : NontriviallyNormedField š•œ] ā†’
          {EB : Type u_7} ā†’
            [inst_1 : NormedAddCommGroup EB] ā†’
              [inst_2 : NormedSpace š•œ EB] ā†’
                {HB : Type u_8} ā†’
                  [inst_3 : TopologicalSpace HB] ā†’
                    {IB : ModelWithCorners š•œ EB HB} ā†’
                      [inst_4 : TopologicalSpace B] ā†’
                        [inst_5 : ChartedSpace HB B] ā†’
                          [inst_6 : (x : B) ā†’ AddCommMonoid (E x)] ā†’
                            [inst_7 : (x : B) ā†’ Module š•œ (E x)] ā†’
                              [inst_8 : NormedAddCommGroup F] ā†’
                                [inst_9 : NormedSpace š•œ F] ā†’
                                  [inst_10 : (x : B) ā†’ TopologicalSpace (E x)] ā†’
                                    {a : VectorPrebundle š•œ F E} ā†’
                                      {n : WithTop ā„•āˆž} ā†’
                                        {motive : VectorPrebundle.IsContMDiff IB a n ā†’ Sort u} ā†’
                                          (t : VectorPrebundle.IsContMDiff IB a n) ā†’
                                            ((exists_contMDiffCoordChange :
                                                  āˆ€ e āˆˆ a.pretrivializationAtlas,
                                                    āˆ€ e' āˆˆ a.pretrivializationAtlas,
                                                      āˆƒ f,
                                                        ContMDiffOn IB (modelWithCornersSelf š•œ (F ā†’L[š•œ] F)) n f
                                                            (e.baseSet āˆ© e'.baseSet) āˆ§
                                                          āˆ€ b āˆˆ e.baseSet āˆ© e'.baseSet,
                                                            āˆ€ (v : F), (f b) v = (ā†‘e' āŸØb, e.symm b vāŸ©).2) ā†’
                                                motive ā‹Æ) ā†’
                                              motive t
Defined in
Mathlib.Geometry.Manifold.VectorBundle.Basic
Cited by
0 results in Mathlib
Foundations
Depth 177 from the axioms Ā· uses propext, Classical.choice, Quot.sound
Assumes
NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceAddCommMonoidModuleNormedAddCommGroupNormedSpaceTopologicalSpace
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DFunLike.coe Ā· cited by 62936DFunLike.coeSet Ā· cited by 53352SetTopologicalSpace Ā· cited by 24529TopologicalSpaceModule Ā· cited by 20661ModuleRingHom.id Ā· cited by 18349RingHom.idNormedAddCommGroup Ā· cited by 15752NormedAddCommGroupNormedSpace Ā· cited by 12499NormedSpaceAddCommMonoid Ā· cited by 12281AddCommMonoidNontriviallyNormedField Ā· cited by 8742NontriviallyNormedFieldContinuousLinearMap Ā· cited by 5352ContinuousLinearMapENat Ā· cited by 4985ENatWithTop Ā· cited by 3754WithTopModelWithCorners Ā· cited by 2462ModelWithCornersChartedSpace Ā· cited by 2397ChartedSpacemodelWithCornersSelf Ā· cited by 920modelWithCornersSelfIsContMDiff.casesOnCITED BYCITES

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