Update partialDeriv.lean

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Stefan Kebekus 2024-05-09 10:39:40 +02:00
parent 6ea989be6b
commit 005cd10a28
1 changed files with 19 additions and 0 deletions

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@ -93,6 +93,25 @@ lemma partialDeriv_fderiv {f : E → F} (hf : ContDiff 𝕜 2 f) (z a b : E) :
· simp
section restrictScalars
variable (𝕜 : Type*) [NontriviallyNormedField 𝕜]
variable {𝕜' : Type*} [NontriviallyNormedField 𝕜'] [NormedAlgebra 𝕜 𝕜']
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace 𝕜 E] [NormedSpace 𝕜' E]
variable [IsScalarTower 𝕜 𝕜' E]
variable {F : Type*} [NormedAddCommGroup F] [NormedSpace 𝕜 F] [NormedSpace 𝕜' F]
variable [IsScalarTower 𝕜 𝕜' F]
--variable {f : E → F}
theorem partialDeriv_restrictScalars {f : E → F} {v : E} :
Differentiable 𝕜' f → partialDeriv 𝕜 v f = partialDeriv 𝕜' v f := by
intro hf
unfold partialDeriv
funext x
rw [(hf x).fderiv_restrictScalars 𝕜]
simp
theorem partialDeriv_comm
{E : Type*} [NormedAddCommGroup E] [NormedSpace E]
{F : Type*} [NormedAddCommGroup F] [NormedSpace F]