Complex small anchor descent

import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_DescentAlgebra_Definitions

section
namespace D1Bound5




theorem _root_.D1Bound5.complex_small_anchor_descent
    (a b z r0 r s : ℂ)
    (h0 : r0^2 = a*b+1) (hr : r^2 = a*z+1) (hs : s^2 = b*z+1)
    (hA : ‖a‖ < 3) (hB : ‖b‖ < 3)
    (hp : 1 ≤ ‖a*b‖) (hZ : 33 ≤ ‖z‖)
    (hhyper : 7 ≤ ‖2*a*b+1‖^2) :
    ‖mutate a b z r0 r s‖ < ‖z‖/5+26 ∨
      ‖mutate a b z r0 r (-s)‖ < ‖z‖/5+26 := by sorry

end D1Bound5
end