diff --git a/Nevanlinna/bilinear.lean b/Nevanlinna/bilinear.lean
index 1ed7b86..dacf4c4 100644
--- a/Nevanlinna/bilinear.lean
+++ b/Nevanlinna/bilinear.lean
@@ -32,24 +32,13 @@ orthonormal basis `v` as `∑ i, (v i) ⊗ₜ[ℝ] (v i)`.
 open TensorProduct
 
 
-lemma OrthonormalBasis.sum_repr'
-  {𝕜 : Type*} [RCLike 𝕜]
-  {E : Type*} [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
-  [Fintype ι]
-  (b : OrthonormalBasis ι 𝕜 E)
-  (v : E) :
-  v = ∑ i, ⟪b i, v⟫_𝕜 • (b i) := by
-  nth_rw 1 [← (b.sum_repr v)]
-  simp_rw [b.repr_apply_apply v]
-
-
 noncomputable def InnerProductSpace.canonicalContravariantTensor
   {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
   : E ⊗[ℝ] E →ₗ[ℝ] ℝ := TensorProduct.lift bilinFormOfRealInner
 
 
 noncomputable def InnerProductSpace.canonicalCovariantTensor
-  (E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E] 
+  (E : Type*) [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
   : E ⊗[ℝ] E := ∑ i, ((stdOrthonormalBasis ℝ E) i) ⊗ₜ[ℝ] ((stdOrthonormalBasis ℝ E) i)
 
 
@@ -64,9 +53,9 @@ theorem InnerProductSpace.canonicalCovariantTensorRepresentation
     right
     arg 2
     intro i
-    rw [w.sum_repr' (v i)]
+    rw [← w.sum_repr' (v i)]
   simp_rw [TensorProduct.sum_tmul, TensorProduct.tmul_sum, TensorProduct.smul_tmul_smul]
-  
+
   conv =>
     right
     rw [Finset.sum_comm]
diff --git a/Nevanlinna/cauchyRiemann.lean b/Nevanlinna/cauchyRiemann.lean
index 1884075..9a839b1 100644
--- a/Nevanlinna/cauchyRiemann.lean
+++ b/Nevanlinna/cauchyRiemann.lean
@@ -45,8 +45,8 @@ theorem CauchyRiemann₃ : (DifferentiableAt ℂ f z)
 
 
 theorem CauchyRiemann₄
-  {F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F] 
-  {f : ℂ → F} : 
+  {F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F]
+  {f : ℂ → F} :
   (Differentiable ℂ f) → partialDeriv ℝ Complex.I f = Complex.I • partialDeriv ℝ 1 f := by
   intro h
   unfold partialDeriv
@@ -58,13 +58,13 @@ theorem CauchyRiemann₄
     simp
     rw [← mul_one Complex.I]
     rw [← smul_eq_mul]
-    rw [ContinuousLinearMap.map_smul_of_tower (fderiv ℂ f w) Complex.I 1]
   conv =>
     right
     right
     intro w
     rw [DifferentiableAt.fderiv_restrictScalars ℝ (h w)]
-
+  funext w
+  simp
 
 theorem CauchyRiemann₅ {F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F] {f : ℂ → F} {z : ℂ} : (DifferentiableAt ℂ f z)
   → partialDeriv ℝ Complex.I f z = Complex.I • partialDeriv ℝ 1 f z := by
@@ -77,8 +77,8 @@ theorem CauchyRiemann₅ {F : Type*} [NormedAddCommGroup F] [NormedSpace ℂ F]
     simp
     rw [← mul_one Complex.I]
     rw [← smul_eq_mul]
-    rw [ContinuousLinearMap.map_smul_of_tower (fderiv ℂ f z) Complex.I 1]
   conv =>
     right
     right
     rw [DifferentiableAt.fderiv_restrictScalars ℝ h]
+  simp
diff --git a/Nevanlinna/complexHarmonic.lean b/Nevanlinna/complexHarmonic.lean
index d604f03..a24a32f 100644
--- a/Nevanlinna/complexHarmonic.lean
+++ b/Nevanlinna/complexHarmonic.lean
@@ -33,7 +33,7 @@ theorem HarmonicAt_iff
     · constructor
       · exact Set.mem_inter h₂s₁ h₃s₂
       · constructor
-        · exact h₃s₁.mono (Set.inter_subset_left s₁ s₂)
+        · exact h₃s₁.mono Set.inter_subset_left
         · intro z hz
           exact h₂t₂ (h₁s₂ hz.2)
   · intro hyp
diff --git a/Nevanlinna/holomorphic.lean b/Nevanlinna/holomorphic.lean
index e4eb207..eed131c 100644
--- a/Nevanlinna/holomorphic.lean
+++ b/Nevanlinna/holomorphic.lean
@@ -137,12 +137,11 @@ theorem CauchyRiemann'₅
     simp
     rw [← mul_one Complex.I]
     rw [← smul_eq_mul]
-    rw [ContinuousLinearMap.map_smul_of_tower (fderiv ℂ f z) Complex.I 1]
   conv =>
     right
     right
     rw [DifferentiableAt.fderiv_restrictScalars ℝ h]
-
+  simp
 
 theorem CauchyRiemann'₆
   {f : ℂ → F}
diff --git a/Nevanlinna/laplace2.lean b/Nevanlinna/laplace2.lean
index cf95e5a..c641bae 100644
--- a/Nevanlinna/laplace2.lean
+++ b/Nevanlinna/laplace2.lean
@@ -10,15 +10,6 @@ import Mathlib.LinearAlgebra.Contraction
 open BigOperators
 open Finset
 
-lemma OrthonormalBasis.sum_repr'
-  {𝕜 : Type*} [RCLike 𝕜]
-  {E : Type*} [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
-  [Fintype ι]
-  (b : OrthonormalBasis ι 𝕜 E)
-  (v : E) :
-  v = ∑ i, ⟪b i, v⟫_𝕜 • (b i) := by
-  nth_rw 1 [← (b.sum_repr v)]
-  simp_rw [b.repr_apply_apply v]
 
 variable {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [FiniteDimensional ℝ E]
 
@@ -27,20 +18,20 @@ noncomputable def realInnerAsElementOfDualTensorprod
   : TensorProduct ℝ E E →ₗ[ℝ] ℝ := TensorProduct.lift bilinFormOfRealInner
 
 
-instance 
+instance
   {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [CompleteSpace E]  [FiniteDimensional ℝ E]
-  : NormedAddCommGroup (TensorProduct ℝ E E) where 
-    norm := by 
-      
+  : NormedAddCommGroup (TensorProduct ℝ E E) where
+    norm := by
+
       sorry
-    dist_self := by 
-      
+    dist_self := by
+
       sorry
 
   sorry
 
 /-
-instance 
+instance
   {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E] [CompleteSpace E]  [FiniteDimensional ℝ E]
   : InnerProductSpace ℝ (TensorProduct ℝ E E) where
     smul := _
diff --git a/Nevanlinna/partialDeriv.lean b/Nevanlinna/partialDeriv.lean
index d0395b8..020aca4 100644
--- a/Nevanlinna/partialDeriv.lean
+++ b/Nevanlinna/partialDeriv.lean
@@ -44,6 +44,8 @@ theorem partialDeriv_smul₁ {f : E → F} {a : 𝕜} {v : E} : partialDeriv 
     left
     intro w
     rw [map_smul]
+  funext w
+  simp
 
 
 theorem partialDeriv_add₁ {f : E → F} {v₁ v₂ : E} : partialDeriv 𝕜 (v₁ + v₂) f = (partialDeriv 𝕜 v₁ f) + (partialDeriv 𝕜 v₂ f) := by
@@ -52,6 +54,8 @@ theorem partialDeriv_add₁ {f : E → F} {v₁ v₂ : E} : partialDeriv 𝕜 (v
     left
     intro w
     rw [map_add]
+  funext w
+  simp
 
 
 theorem partialDeriv_smul₂ {f : E → F} {a : 𝕜} {v : E} : partialDeriv 𝕜 v (a • f) = a • partialDeriv 𝕜 v f := by
@@ -90,6 +94,8 @@ theorem partialDeriv_add₂ {f₁ f₂ : E → F} (h₁ : Differentiable 𝕜 f
     intro w
     left
     rw [fderiv_add (h₁ w) (h₂ w)]
+  funext w
+  simp
 
 
 theorem partialDeriv_add₂_differentiableAt
diff --git a/Nevanlinna/smulImprovement.lean b/Nevanlinna/smulImprovement.lean
deleted file mode 100644
index 573f49c..0000000
--- a/Nevanlinna/smulImprovement.lean
+++ /dev/null
@@ -1,40 +0,0 @@
-import Mathlib.Analysis.Complex.CauchyIntegral
---import Mathlib.Analysis.Complex.Module
-
-
-
-example simplificationTest₁
-  {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] [IsScalarTower ℝ ℂ E]
-  {v : E}
-  {z : ℂ} :
-  z • v =  z.re • v + Complex.I • z.im • v := by
-
-  /-
-  An attempt to write  "rw [add_smul]" will fail with "did not find instance of
-  the pattern in the target -- expression (?r + ?s) • ?x".
-  -/
-  sorry
-
-
-theorem add_smul'
-  (𝕜₁ : Type*) [NontriviallyNormedField ℝ]
-  {𝕜₂ : Type*} [NontriviallyNormedField ℂ] [NormedAlgebra ℝ ℂ]
-  {E : Type*} [NormedAddCommGroup E] [NormedSpace ℂ E] [CompleteSpace E] [IsScalarTower ℝ ℂ E]
-  {v : E}
-  {r s : ℂ} :
-  (r + s) • v = r • v + s • v :=
-  Module.add_smul r s v
-
-
-theorem smul_add' (a : M) (b₁ b₂ : A) : a • (b₁ + b₂) = a • b₁ + a • b₂ :=
-  DistribSMul.smul_add _ _ _
-#align smul_add smul_add
-
-
-
-
-example simplificationTest₂
-  {v : E}
-  {z : ℂ} :
-  z • v =  z.re • v + Complex.I • z.im • v := by
-  sorry
diff --git a/Nevanlinna/tensor.lean b/Nevanlinna/tensor.lean
deleted file mode 100644
index f805778..0000000
--- a/Nevanlinna/tensor.lean
+++ /dev/null
@@ -1,47 +0,0 @@
-import Mathlib.Analysis.InnerProductSpace.PiL2
-
-
-open RCLike Real Filter
-open Topology ComplexConjugate
-open LinearMap (BilinForm)
-open TensorProduct
-open InnerProductSpace
-open Inner
-
-
-example
-  {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℝ E]
-  {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℝ F]
-  : 1 = 0 := by
-
-  let e : E →ₗ[ℝ] E →ₗ[ℝ] ℝ := innerₗ E 
-  let f : F →ₗ[ℝ] F →ₗ[ℝ] ℝ := innerₗ F 
-  let e₂ :=  TensorProduct.map₂ e f
-  let l := TensorProduct.lid ℝ ℝ 
-
-  have : ∀ e1 e2 : E, ∀ f1 f2 : F, e₂ (e1 ⊗ f1) (e2 ⊗ f2) = 
-
-  let X : InnerProductSpace.Core ℝ (E ⊗[ℝ] F) := {
-    inner := by
-      intro a b
-      exact TensorProduct.lid ℝ ℝ ((TensorProduct.map₂ (innerₗ E) (innerₗ F)) a b)
-    conj_symm := by
-      simp
-      intro x y
-
-      unfold innerₗ
-      
-      simp
-      sorry
-    nonneg_re := _
-    definite := _
-    add_left := _
-    smul_left := _
-  }
-
-  let inner : E ⊗[𝕜] E → E ⊗[𝕜] E → 𝕜 := 
-    --let x := TensorProduct.lift
-    --E.inner
-    --TensorProduct.map₂
-    sorry
-  sorry
\ No newline at end of file
diff --git a/Nevanlinna/test.lean b/Nevanlinna/test.lean
deleted file mode 100644
index 966fde2..0000000
--- a/Nevanlinna/test.lean
+++ /dev/null
@@ -1,130 +0,0 @@
-import Mathlib.Analysis.Complex.CauchyIntegral
---import Mathlib.Analysis.Complex.Module
--- test
-
-open ComplexConjugate
-
-#check DiffContOnCl.circleIntegral_sub_inv_smul
-
-open Real
-
-theorem CauchyIntegralFormula :
-  ∀
-  {R : ℝ} -- Radius of the ball
-  {w : ℂ} -- Point in the interior of the ball
-  {f : ℂ → ℂ}, -- Holomorphic function
-  DiffContOnCl ℂ f (Metric.ball 0 R)
-  → w ∈ Metric.ball 0 R
-  → (∮ (z : ℂ) in C(0, R), (z - w)⁻¹ • f z) = (2 * π * Complex.I) • f w := by
-
-  exact DiffContOnCl.circleIntegral_sub_inv_smul
-
-#check CauchyIntegralFormula
-#check HasDerivAt.continuousAt
-#check Real.log
-#check ComplexConjugate.conj
-#check Complex.exp
-
-theorem SimpleCauchyFormula :
-  ∀
-  {R : ℝ} -- Radius of the ball
-  {w : ℂ} -- Point in the interior of the ball
-  {f : ℂ → ℂ}, -- Holomorphic function
-  Differentiable ℂ f
-  → w ∈ Metric.ball 0 R
-  → (∮ (z : ℂ) in C(0, R), (z - w)⁻¹ • f z) = (2 * Real.pi * Complex.I) • f w := by
-
-  intro R w f fHyp
-
-  apply DiffContOnCl.circleIntegral_sub_inv_smul
-
-  constructor
-  · exact Differentiable.differentiableOn fHyp
-  · suffices Continuous f from by
-      exact Continuous.continuousOn this
-    rw [continuous_iff_continuousAt]
-    intro x
-    exact DifferentiableAt.continuousAt (fHyp x)
-
-
-theorem JensenFormula₂ :
-  ∀
-  {R : ℝ} -- Radius of the ball
-  {f : ℂ → ℂ}, -- Holomorphic function
-  Differentiable ℂ f
-  → (∀ z ∈ Metric.ball 0 R, f z ≠ 0)
-  → (∫ (θ : ℝ) in Set.Icc 0 (2 * π), Complex.log ‖f (circleMap 0 R θ)‖ ) = 2 * π * Complex.log ‖f 0‖ := by
-
-  intro r f fHyp₁ fHyp₂
-
-  /- We treat the trivial case r = 0 separately. -/
-  by_cases rHyp : r = 0
-  rw [rHyp]
-  simp
-  left
-  unfold ENNReal.ofReal
-  simp
-  rw [max_eq_left (mul_nonneg zero_le_two pi_nonneg)]
-  simp
-  /- From hereon, we assume that r ≠ 0. -/
-
-  /- Replace the integral over 0 … 2π by a circle integral -/
-  suffices (∮ (z : ℂ) in C(0, r), -(Complex.I * z⁻¹ * Complex.log ↑(Complex.abs (f z)))) = 2 * ↑π * Complex.log ↑‖f 0‖ from by
-    have : ∫ (θ : ℝ) in Set.Icc 0 (2 * π), Complex.log ↑‖f (circleMap 0 r θ)‖ = (∮ (z : ℂ) in C(0, r), -(Complex.I * z⁻¹ * Complex.log ↑(Complex.abs (f z)))) := by
-      have : (fun θ ↦ Complex.log ‖f (circleMap 0 r θ)‖) = (fun θ ↦ ((deriv (circleMap 0 r) θ)) • ((deriv (circleMap 0 r) θ)⁻¹ • Complex.log ↑‖f (circleMap 0 r θ)‖)) := by
-        funext θ
-        rw [← smul_assoc, smul_eq_mul, smul_eq_mul, mul_inv_cancel, one_mul]
-        simp
-        exact rHyp
-      rw [this]
-      simp
-      let tmp := circleIntegral_def_Icc (fun z ↦ -(Complex.I * z⁻¹ * (Complex.log ↑‖f z‖))) 0 r
-      simp at tmp
-      rw [← tmp]
-    rw [this]
-
-
-
-  have : ∀ z : ℂ, log (Complex.abs z) = 1/2 * Complex.log z + 1/2 * Complex.log (conj z) := by
-    intro z
-
-    by_cases argHyp : Complex.arg z = π
-
-    · rw [Complex.log, argHyp, Complex.log]
-      let ZZ := Complex.arg_conj z
-      rw [argHyp] at ZZ
-
-      simp at ZZ
-
-      have : conj z = z := by
-        apply?
-        sorry
-
-    let ZZ := Complex.log_conj z
-
-    nth_rewrite 1 [Complex.log]
-
-    simp
-
-    let φ := Complex.arg z
-    let r := Complex.abs z
-    have : z = r * Complex.exp (φ * Complex.I) := by
-      exact (Complex.abs_mul_exp_arg_mul_I z).symm
-
-    have : Complex.log z = Complex.log r + r*Complex.I := by
-      apply?
-      sorry
-    simp at XX
-
-
-    sorry
-
-
-
-
-
-
-
-
-
-  sorry
diff --git a/lake-manifest.json b/lake-manifest.json
index bbb73cc..7830064 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -1,10 +1,11 @@
-{"version": "1.0.0",
+{"version": "1.1.0",
  "packagesDir": ".lake/packages",
  "packages":
  [{"url": "https://github.com/leanprover-community/batteries",
    "type": "git",
    "subDir": null,
-   "rev": "555ec79bc6effe7009036184a5f73f7d8d4850ed",
+   "scope": "leanprover-community",
+   "rev": "d2b1546c5fc05a06426e3f6ee1cb020e71be5592",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -13,7 +14,8 @@
   {"url": "https://github.com/leanprover-community/quote4",
    "type": "git",
    "subDir": null,
-   "rev": "a7bfa63f5dddbcab2d4e0569c4cac74b2585e2c6",
+   "scope": "leanprover-community",
+   "rev": "01ad33937acd996ee99eb74eefb39845e4e4b9f5",
    "name": "Qq",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -22,7 +24,8 @@
   {"url": "https://github.com/leanprover-community/aesop",
    "type": "git",
    "subDir": null,
-   "rev": "30619d94ce4a3d69cdb87bb1771562ca2e687cfa",
+   "scope": "leanprover-community",
+   "rev": "622d52c803db99ff4ea4fb442c1db9e91aed944c",
    "name": "aesop",
    "manifestFile": "lake-manifest.json",
    "inputRev": "master",
@@ -31,25 +34,28 @@
   {"url": "https://github.com/leanprover-community/ProofWidgets4",
    "type": "git",
    "subDir": null,
-   "rev": "87c1e7a427d8e21b6eaf8401f12897f52e2c3be9",
+   "scope": "leanprover-community",
+   "rev": "d1b33202c3a29a079f292de65ea438648123b635",
    "name": "proofwidgets",
    "manifestFile": "lake-manifest.json",
-   "inputRev": "v0.0.38",
+   "inputRev": "v0.0.39",
    "inherited": true,
    "configFile": "lakefile.lean"},
   {"url": "https://github.com/leanprover/lean4-cli",
    "type": "git",
    "subDir": null,
+   "scope": "",
    "rev": "a11566029bd9ec4f68a65394e8c3ff1af74c1a29",
    "name": "Cli",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
    "inherited": true,
    "configFile": "lakefile.lean"},
-  {"url": "https://github.com/leanprover-community/import-graph.git",
+  {"url": "https://github.com/leanprover-community/import-graph",
    "type": "git",
    "subDir": null,
-   "rev": "1588be870b9c76fe62286e8f42f0b4dafa154c96",
+   "scope": "leanprover-community",
+   "rev": "68b518c9b352fbee16e6d632adcb7a6d0760e2b7",
    "name": "importGraph",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",
@@ -58,7 +64,8 @@
   {"url": "https://github.com/leanprover-community/mathlib4.git",
    "type": "git",
    "subDir": null,
-   "rev": "dcc73cfb2ce3763f830c52042fb8617e762dbf60",
+   "scope": "",
+   "rev": "cc495260156b40dcbd55b947c047061e15344000",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
    "inputRev": null,
diff --git a/lean-toolchain b/lean-toolchain
index e5ea660..6a4259f 100644
--- a/lean-toolchain
+++ b/lean-toolchain
@@ -1 +1 @@
-leanprover/lean4:v4.9.0-rc3
+leanprover/lean4:v4.10.0-rc2