Theorems · Theorem · global analysis

ContMDiffWithinAt.mul

∀ {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 : Mul G] [inst_5 : TopologicalSpace G] [inst_6 : ChartedSpace H 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]
  [ContMDiffMul I n G] {f g : M → G} {s : Set M} {x : M},
  ContMDiffWithinAt I' I n f s x → ContMDiffWithinAt I' I n g s x → ContMDiffWithinAt I' I n (f * g) s x

Defined in

Mathlib.Geometry.Manifold.Algebra.Monoid

Cited by

7 results in Mathlib

Foundations

Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldTopologicalSpaceNormedAddCommGroupNormedSpaceMulTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceContMDiffMul