Theorems · Theorem · global analysis

ContDiff.inner

∀ (𝕜 : Type u_1) {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  [inst_3 : NormedSpace ℝ E] {G : Type u_4} [inst_4 : NormedAddCommGroup G] [inst_5 : NormedSpace ℝ G] {f g : G → E}
  {n : WithTop ℕ∞}, ContDiff ℝ n f → ContDiff ℝ n g → ContDiff ℝ n fun x => inner 𝕜 (f x) (g x)

Defined in

Mathlib.Analysis.InnerProductSpace.Calculus

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceNormedSpaceNormedAddCommGroupNormedSpace