Theorems · Definition · Lie groups

LeftInvariantDerivation.casesOn

{𝕜 : Type u_1} →
  [inst : NontriviallyNormedField 𝕜] →
    {E : Type u_2} →
      [inst_1 : NormedAddCommGroup E] →
        [inst_2 : NormedSpace 𝕜 E] →
          {H : Type u_3} →
            [inst_3 : TopologicalSpace H] →
              {I : ModelWithCorners 𝕜 E H} →
                {G : Type u_4} →
                  [inst_4 : TopologicalSpace G] →
                    [inst_5 : ChartedSpace H G] →
                      [inst_6 : Monoid G] →
                        [inst_7 : ContMDiffMul I (↑⊤) G] →
                          {motive : LeftInvariantDerivation I G → Sort u} →
                            (t : LeftInvariantDerivation I G) →
                              ((toDerivation :
                                    Derivation 𝕜 (ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) G 𝕜 ↑⊤)
                                      (ContMDiffMap I (modelWithCornersSelf 𝕜 𝕜) G 𝕜 ↑⊤)) →
                                  (left_invariant'' :
                                      ∀ (g : G),
                                        (hfdifferential ⋯) ((Derivation.evalAt 1) toDerivation) =
                                          (Derivation.evalAt g) toDerivation) →
                                    motive { toDerivation := toDerivation, left_invariant'' := left_invariant'' }) →
                                motive t

Defined in

Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation

Cited by

1 results in Mathlib

Foundations

Depth 232 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceMonoidContMDiffMul