Theorems · Theorem · real analysis

ContDiff.sub

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type uE} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {F : Type uF} [inst_3 : NormedAddCommGroup F] [inst_4 : NormedSpace 𝕜 F] {n : WithTop ℕ∞}
  {f g : E → F}, ContDiff 𝕜 n f → ContDiff 𝕜 n g → ContDiff 𝕜 n fun x => f x - g x

The difference of two C^n functions is C^n.

Defined in

Mathlib.Analysis.Calculus.ContDiff.Operations

Cited by

11 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceNormedAddCommGroupNormedSpace