First Pair classified rectangular

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_FirstPairData_Definitions
import Definitions.Def_D1Bound5_OneSmallFiniteCheck_Definitions

section
namespace D1Bound5
open QuadInt
set_option maxRecDepth 32768
set_option maxHeartbeats 12000000













































































































































theorem _root_.D1Bound5.firstPair_classified_rectangular {tau nu : ℤ}
    (htau : tau = 0 ∨ tau = 1) (hlo : 1 ≤ nu) (hhi : nu ≤ 8)
    (a b : QuadInt tau nu) (hnorm : FirstPairNorms a b) (hroot : ∃ q, q*q = a*b+1) :
    (a = 1 ∧ b = 3) ∨ (a = -1 ∧ b = -3) ∨ firstPairCoordinates a b ∈ firstPairTable tau nu := by sorry

end D1Bound5
end