Update holomorphic.primitive.lean

Nevanlinna/holomorphic.primitive.lean

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