Triple Extension Filter 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.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions

section
namespace D1Bound5
open QuadInt

































theorem _root_.D1Bound5.tripleExtensionFilter_of_checked {tau nu : ℤ}
    (hd : 0 < discriminant tau nu) (a b c : QuadInt tau nu)
    (vertices allowed : List (QuadInt tau nu))
    (hcheck : tripleExtensionFilterBool a b c vertices allowed = true)
    {z : QuadInt tau nu} (hz : z ∈ vertices)
    (h0 : z ≠ 0) (ha : z ≠ a) (hb : z ≠ b) (hc : z ≠ c)
    (hs : ∃ r, r*r = c*z+1) : z ∈ allowed := by sorry

end D1Bound5
end