diff --git a/nevanlinna/test.lean b/nevanlinna/test.lean index 0849845..f92eb4f 100644 --- a/nevanlinna/test.lean +++ b/nevanlinna/test.lean @@ -1,3 +1,17 @@ -import Mathlib.Topology.Basic +import Mathlib.Analysis.Complex.CauchyIntegral -#check TopologicalSpace +#check DiffContOnCl.circleIntegral_sub_inv_smul + + +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 * Real.pi * Complex.I) • f w := by + + exact DiffContOnCl.circleIntegral_sub_inv_smul + +#check CauchyIntegralFormula