Theorems · Definition · Lie groups

LeftInvariantDerivation.mk.noConfusion

{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} →
                          {P : Sort u} →
                            {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} →
                                {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'} →
                                    { toDerivation := toDerivation, left_invariant'' := left_invariant'' } =
                                        { toDerivation := toDerivation', left_invariant'' := left_invariant''' } →
                                      (toDerivation ≍ toDerivation' → P) → P

Defined in

Mathlib.Geometry.Manifold.Algebra.LeftInvariantDerivation

Cited by

1 results in Mathlib

Foundations

Depth 235 from the axioms · uses propext, Classical.choice, Quot.sound