Theorems · Theorem · global analysis

IsScalarTower.contMDiffSMul

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {H : Type u_2} [inst_1 : TopologicalSpace H] {E : Type u_3}
  [inst_2 : NormedAddCommGroup E] [inst_3 : NormedSpace 𝕜 E] {I : ModelWithCorners 𝕜 E H} {H' : Type u_4}
  [inst_4 : TopologicalSpace H'] {E' : Type u_5} [inst_5 : NormedAddCommGroup E'] [inst_6 : NormedSpace 𝕜 E']
  {I' : ModelWithCorners 𝕜 E' H'} {H'' : Type u_6} [inst_7 : TopologicalSpace H''] {E'' : Type u_7}
  [inst_8 : NormedAddCommGroup E''] [inst_9 : NormedSpace 𝕜 E''] {I'' : ModelWithCorners 𝕜 E'' H''} {G : Type u_8}
  [inst_10 : TopologicalSpace G] [inst_11 : ChartedSpace H G] {M : Type u_9} [inst_12 : TopologicalSpace M]
  [inst_13 : ChartedSpace H' M] (G' : Type u_11) [inst_14 : TopologicalSpace G'] [inst_15 : ChartedSpace H'' G']
  [inst_16 : Monoid G'] [inst_17 : SMul G G'] [inst_18 : MulAction G' M] [inst_19 : SMul G M] [IsScalarTower G G' M]
  {n : WithTop ℕ∞} [ContMDiffSMul I I'' n G G'] [ContMDiffSMul I'' I' n G' M], ContMDiffSMul I I' n G M

If G acts continuously differentiably on G' and G' acts continuously differentiably on M, then G acts continuously differentiably on M.

Defined in

Mathlib.Geometry.Manifold.Algebra.SMul

Cited by

0 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceTopologicalSpaceChartedSpaceMonoidSMulMulActionSMulIsScalarTowerContMDiffSMulContMDiffSMul