Continuity on the branch-safe domain
ProvedWeightedRootIntegralIdentity.missionBranchRegularitybranch-cutcomplex-analysisholomorphicity
A differentiable branch integrand on the slit contour domain is continuous there, hence continuous on each finite contour piece.
Formal statement
import Mathlib
theorem WeightedRootIntegralIdentity.missionBranchRegularity
(F : ℂ → ℂ) (D : Set ℂ)
(hF : DifferentiableOn ℂ F D) :
ContinuousOn F D := by sorry