One Small Fourth Growth of checked

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Tactic.IntervalCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_DiskEnumeration_Definitions
import Definitions.Def_D1Bound5_OneSmallFiniteCheck_Definitions

section
namespace D1Bound5
open QuadInt





















theorem _root_.D1Bound5.oneSmallFourthGrowth_of_checked {tau nu : ℤ}
    (hd : 0 < discriminant tau nu) (a b s : QuadInt tau nu)
    (ha : a ≠ 0) (hNa : a.norm ≤ 2) (cutoff : ℤ) (hcutoff : cutoff ≤ 21270)
    (roots : List (QuadInt tau nu))
    (hcover : ∀ q ∈ disk tau nu 300, q ∈ roots)
    (hcheck : oneSmallFourthGrowthBool a b s cutoff roots = true)
    (z : QuadInt tau nu) (hz : z.norm < cutoff)
    (hza : ∃ q, q*q = a*z+1) (hzb : ∃ q, q*q = b*z+1)
    (hzs : ∃ q, q*q = s*z+1) : z.norm ≤ 4*b.norm*s.norm := by sorry

end D1Bound5
end