Jensen's formula is done!

Nevanlinna/holomorphic_JensenFormula2.lean

@@ -350,6 +350,7 @@ theorem jensen
     simpa
 
   let A := jensen_case_R_eq_one F h₁F h₂F
+
   dsimp [F] at A
   have {x : ℂ} : ℓ x = R * x := by rfl
   repeat
@@ -357,7 +358,6 @@ theorem jensen
   simp at A
   simp
   rw [A]
-
   simp_rw [← const_mul_circleMap_zero]
   simp
 
@@ -394,6 +394,7 @@ theorem jensen
 
   apply finsum_eq_of_bijective e
 
+
   apply Function.bijective_iff_has_inverse.mpr
   use e'
   constructor
@@ -418,6 +419,31 @@ theorem jensen
 
   intro x
   simp
+  by_cases hx : x = (0 : ℂ)
+  rw [hx]
+  simp
 
+  rw [log_mul, log_mul, log_inv, log_inv]
+  have : R = |R| := by exact Eq.symm (abs_of_pos hR)
+  rw [← this]
+  simp
+  left
+  congr 1
 
-  sorry
+  dsimp [AnalyticOn.order]
+  rw [← AnalyticAt.order_comp_CLE ℓ]
+
+  --
+  simpa
+  --
+  have : R = |R| := by exact Eq.symm (abs_of_pos hR)
+  rw [← this]
+  apply inv_ne_zero
+  exact Ne.symm (ne_of_lt hR)
+  --
+  exact Ne.symm (ne_of_lt hR)
+  --
+  simp
+  constructor
+  · assumption
+  · exact Ne.symm (ne_of_lt hR)