Positivity and monotonicity branch safety
ProvedWeightedRootIntegralIdentity.missionBranchSafetybranch-cutcomplex-analysisordered-reals
Positivity keeps every open interval away from the pole at zero, while monotonicity fixes the nonnegative orientation of each ordered interval.
Formal statement
import Mathlib
open scoped Interval
theorem WeightedRootIntegralIdentity.missionBranchSafety
(n : ℕ) (a : ℕ → ℝ) (k : ℕ) (x : ℝ)
(hpos : ∀ i < n, 0 < a i)
(hmono : ∀ i < n - 1, a i ≤ a (i + 1))
(hk : k + 1 < n)
(hx : x ∈ Set.Ioo (a k) (a (k + 1))) :
x ≠ 0 ∧ a k ≤ a (k + 1) := by sorry