Update holomorphic.primitive.lean

This commit is contained in:
Stefan Kebekus 2024-06-14 21:00:51 +02:00
parent fcbdd1a2c2
commit 6d36769dab
1 changed files with 10 additions and 10 deletions

View File

@ -153,11 +153,11 @@ theorem primitive_zeroAtBasepoint
theorem primitive_lem1 theorem primitive_lem1
{E : Type u} [NormedAddCommGroup E] [NormedSpace E] [CompleteSpace E] [IsScalarTower E] {E : Type u} [NormedAddCommGroup E] [NormedSpace E] [CompleteSpace E] [IsScalarTower E]
(v : E) : (v : E) :
HasDerivAt (primitive 0 (fun z ↦ v)) v 0 := by HasDerivAt (primitive 0 (fun _ ↦ v)) v 0 := by
unfold primitive unfold primitive
simp simp
have : (fun (z : ) => z.re • v + Complex.I • z.im • v) = (fun (z : ) => z • v) := by have : (fun (z : ) => z.re • v + Complex.I • z.im • v) = (fun (y : ) => ((fun w ↦ w) y) • v) := by
funext z funext z
rw [smul_comm] rw [smul_comm]
rw [← smul_assoc] rw [← smul_assoc]
@ -167,12 +167,10 @@ theorem primitive_lem1
simp simp
rw [this] rw [this]
have hc : HasDerivAt (fun (w : ) ↦ w) 1 0 := by
apply HasDerivAt.smul_const apply hasDerivAt_id'
nth_rewrite 2 [← (one_smul v)]
exact HasDerivAt.smul_const hc v
sorry
@ -182,6 +180,8 @@ theorem primitive_fderivAtBasepoint
HasDerivAt (primitive 0 f) (f 0) 0 := by HasDerivAt (primitive 0 f) (f 0) 0 := by
unfold primitive unfold primitive
simp simp
apply hasDerivAt_iff_isLittleO.2
simp
sorry sorry