Theorems · Theorem · global analysis

MDifferentiableAt.prodMk_space

∀ {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} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {E' : Type u_5} [inst_6 : NormedAddCommGroup E']
  [inst_7 : NormedSpace 𝕜 E'] {E'' : Type u_8} [inst_8 : NormedAddCommGroup E''] [inst_9 : NormedSpace 𝕜 E''] {x : M}
  {f : M → E'} {g : M → E''}, MDiffAt f x → MDiffAt g x → (MDiffAt fun x => (f x, g x)) x

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

3 results in Mathlib

Foundations

Depth 168 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace