Theorems · Theorem · global analysis

ContMDiffWithinAt.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'] {F' : Type u_11} [inst_8 : NormedAddCommGroup F'] [inst_9 : NormedSpace 𝕜 F'] {s : Set M}
  {x : M} {n : WithTop ℕ∞} {f : M → E'} {g : M → F'},
  ContMDiffWithinAt I (modelWithCornersSelf 𝕜 E') n f s x →
    ContMDiffWithinAt I (modelWithCornersSelf 𝕜 F') n g s x →
      ContMDiffWithinAt I (modelWithCornersSelf 𝕜 (E' × F')) n (fun x => (f x, g x)) s x

Defined in

Mathlib.Geometry.Manifold.ContMDiff.Constructions

Cited by

5 results in Mathlib

Foundations

Depth 188 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace