diff --git a/Nevanlinna/specialFunctions_CircleIntegral_affine.lean b/Nevanlinna/specialFunctions_CircleIntegral_affine.lean
index 6e628ad..03603be 100644
--- a/Nevanlinna/specialFunctions_CircleIntegral_affine.lean
+++ b/Nevanlinna/specialFunctions_CircleIntegral_affine.lean
@@ -394,7 +394,13 @@ lemma int₄
   have h₁a : a / R ∈ Metric.closedBall 0 1 := by
     simp
     simp at ha
-    sorry
+    rw [div_le_comm₀]
+    simp
+    have : R = |R| := by
+      exact Eq.symm (abs_of_pos hR)
+    rwa [this] at ha
+    rwa [abs_of_pos hR]
+    simp
 
   have t₀ {x : ℝ} : circleMap 0 R x = R * circleMap 0 1 x := by
     unfold circleMap
diff --git a/Nevanlinna/stronglyMeromorphic_JensenFormula.lean b/Nevanlinna/stronglyMeromorphic_JensenFormula.lean
index 3ace982..03dbd04 100644
--- a/Nevanlinna/stronglyMeromorphic_JensenFormula.lean
+++ b/Nevanlinna/stronglyMeromorphic_JensenFormula.lean
@@ -304,16 +304,17 @@ theorem jensen
     simp at hs
     simp [hs.1]
   rw [finsum_eq_sum_of_support_subset _ h₁G'] at decompose_int_G
-  have : ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * ∫ (x_1 : ℝ) in (0)..(2 * π), log ‖circleMap 0 R x_1 - s‖ = 0 := by
-    apply Finset.sum_eq_zero
-    intro x hx
-    rw [int₃ _]
-    simp
-    simp at hx
-    let ZZ := h₁f.meromorphicOn.divisor.supportInU
-    simp at ZZ
-    let UU := ZZ x hx
-    simpa
+  have : ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * ∫ (x_1 : ℝ) in (0)..(2 * π), log ‖circleMap 0 R x_1 - s‖ = ∑ s ∈ h₃f.toFinset, (h₁f.meromorphicOn.divisor s) * (2 * π) * log R := by
+    apply Finset.sum_congr rfl
+    intro s hs
+    have : s ∈ Metric.closedBall 0 R := by
+      let A := h₁f.meromorphicOn.divisor.supportInU
+      have : s ∈ Function.support h₁f.meromorphicOn.divisor := by
+        simp at hs
+        exact hs
+      exact A this
+    rw [int₄ hR this]
+    linarith
   rw [this] at decompose_int_G
 
 
@@ -324,20 +325,42 @@ theorem jensen
   let X := h₄F
   nth_rw 1 [h₄F]
   simp
-  have {l : ℝ} : π⁻¹ * 2⁻¹ * (2 * π * l) = l := by
-    calc π⁻¹ * 2⁻¹ * (2 * π * l)
-    _ = π⁻¹ * (2⁻¹ * 2) * π * l := by ring
-    _ = π⁻¹ * π * l := by ring
-    _ = (π⁻¹ * π) * l := by ring
-    _ = 1 * l := by
+  have : π⁻¹ * 2⁻¹ * (2 * π) = 1 := by
+    calc π⁻¹ * 2⁻¹ * (2 * π)
+    _ = π⁻¹ * (2⁻¹ * 2) * π := by ring
+    _ = π⁻¹ * π := by ring
+    _ = (π⁻¹ * π) := by ring
+    _ = 1 := by
       rw [inv_mul_cancel₀]
       exact pi_ne_zero
-    _ = l := by simp
-  rw [this]
+  --rw [this]
   rw [log_mul]
   rw [log_prod]
   simp
   rw [add_comm]
+  rw [mul_add]
+  rw [← mul_assoc (π⁻¹ * 2⁻¹), this]
+  simp
+  rw [add_comm]
+  nth_rw 2 [add_comm]
+  rw [add_assoc]
+  congr
+  rw [Finset.mul_sum]
+  rw [← sub_eq_add_neg]
+  rw [← Finset.sum_sub_distrib]
+  rw [Finset.sum_congr rfl]
+  intro s hs
+  rw [log_mul, log_inv]
+  rw [← mul_assoc (π⁻¹ * 2⁻¹)]
+  rw [mul_comm _ (2 * π)]
+  rw [← mul_assoc (π⁻¹ * 2⁻¹)]
+  rw [this]
+  simp
+  rw [mul_add]
+  ring
+  --
+
+
   --
   intro x hx
   simp at hx
diff --git a/lake-manifest.json b/lake-manifest.json
index 4bf6777..6d27dba 100644
--- a/lake-manifest.json
+++ b/lake-manifest.json
@@ -5,7 +5,7 @@
    "type": "git",
    "subDir": null,
    "scope": "",
-   "rev": "134c6ee3da5185da90b69d05697c85bfba57e82e",
+   "rev": "a69e6fafa9665613ef0e905036e4d607b75769e0",
    "name": "mathlib",
    "manifestFile": "lake-manifest.json",
    "inputRev": null,
@@ -75,7 +75,7 @@
    "type": "git",
    "subDir": null,
    "scope": "leanprover-community",
-   "rev": "7805acf1864ba1a2e359f86a8f092ccf1438ad83",
+   "rev": "c016aa9938c4cedc9b7066099f99bcae1b1af625",
    "name": "batteries",
    "manifestFile": "lake-manifest.json",
    "inputRev": "main",