[Merged by Bors] - feat(analysis/inner_product/calculus): [higher] differentiability to/from euclidean_space
#15363
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| {n : with_top ℕ} : | ||
| cont_diff_on 𝕜 n f t ↔ ∀ i, cont_diff_on 𝕜 n (λ x, f x i) t := | ||
| begin | ||
| let φ : euclidean_space 𝕜 ι ≃L[𝕜] ι → 𝕜 := (linear_equiv.refl _ _).to_continuous_linear_equiv, |
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This ought to be called pi_Lp.continuous_linear_equiv or pi_Lp.equivL or something; expecially since you used it in all of these lemmas!
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I added the euclidean_space version because rw was giving me a hard time using a general pi_Lp version
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…from `euclidean_space` (#15363) This duplicates some of the calculus `pi` API to `euclidean_space`. Namely : - we duplicate all the variants of `differentiable_pi` to show that a function to a euclidean space is (higher) differentiable iff all of its components are - we introduce `euclidean_version.proj`, analogous to `continuous_linear_map.proj`. This allows us to avoid duplicating all the `differentiable_apply`-like lemmas, because one can just use the API for smoothness of continuous linear maps Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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…from `euclidean_space` (#15363) This duplicates some of the calculus `pi` API to `euclidean_space`. Namely : - we duplicate all the variants of `differentiable_pi` to show that a function to a euclidean space is (higher) differentiable iff all of its components are - we introduce `euclidean_version.proj`, analogous to `continuous_linear_map.proj`. This allows us to avoid duplicating all the `differentiable_apply`-like lemmas, because one can just use the API for smoothness of continuous linear maps Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>
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This duplicates some of the calculus
piAPI toeuclidean_space. Namely :differentiable_pito show that a function to a euclidean space is (higher) differentiable iff all of its components areeuclidean_version.proj, analogous tocontinuous_linear_map.proj. This allows us to avoid duplicating all thedifferentiable_apply-like lemmas, because one can just use the API for smoothness of continuous linear maps