Regular completion cases

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 Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_Regular_Definitions

section
namespace D1Bound5

open QuadInt




theorem _root_.D1Bound5.regular_completion_cases {tau nu : ℤ} (hd : 0 < QuadInt.discriminant tau nu)
    (b c d r : QuadInt tau nu) (hr : r*r = b*c+1) (hreg : regularDefect b c d = 0) :
    d = b+c+2*r ∨ d = b+c-2*r := by sorry










end D1Bound5
end