Theorems · Theorem · Lie groups

ContMDiffAt.div

∀ {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} {n : WithTop ℕ∞}
  {G : Type u_4} [inst_4 : TopologicalSpace G] [inst_5 : ChartedSpace H G] [inst_6 : Group G] {E' : Type u_5}
  [inst_7 : NormedAddCommGroup E'] [inst_8 : NormedSpace 𝕜 E'] {H' : Type u_6} [inst_9 : TopologicalSpace H']
  {I' : ModelWithCorners 𝕜 E' H'} {M : Type u_7} [inst_10 : TopologicalSpace M] [inst_11 : ChartedSpace H' M]
  [LieGroup I n G] {f g : M → G} {x₀ : M},
  ContMDiffAt I' I n f x₀ → ContMDiffAt I' I n g x₀ → ContMDiffAt I' I n (fun x => f x / g x) x₀

Defined in

Mathlib.Geometry.Manifold.Algebra.LieGroup

Cited by

0 results in Mathlib

Foundations

Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceChartedSpaceGroupNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceLieGroup