Small pair graph excludes three full ring

import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Complex.Norm
import Mathlib.Analysis.Complex.Polynomial.Basic
import Mathlib.Data.Finset.Card
import Mathlib.Data.Finset.Prod
import Mathlib.Data.Int.GCD
import Mathlib.Data.Int.Interval
import Mathlib.Data.Int.Sqrt
import Mathlib.Data.ZMod.Basic
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_Coordinates_Definitions
import Definitions.Def_D1Bound5_DiskEnumeration_Definitions
import Definitions.Def_D1Bound5_FastSquareTest_Definitions
import Definitions.Def_D1Bound5_IsD1Tuple
import Definitions.Def_D1Bound5_PairExtensionCore_Definitions
import Definitions.Def_D1Bound5_SmallPairGraphCheck_Definitions

section
open scoped NumberField
open Module

namespace D1Bound5
open QuadInt








theorem _root_.D1Bound5.small_pair_graph_excludes_three_full_ring
    {K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) (phi : K →+* ℂ)
    {tau nu : ℤ} (hd : 0 < discriminant tau nu)
    (e : QuadInt tau nu ≃+* 𝓞 K) (a b : QuadInt tau nu)
    (ha : a ≠ 0) (hb : b ≠ 0) (hab : a*b+1 ≠ 0)
    (hroot : ∃ r0, r0*r0 = a*b+1) (hNa : a.norm ≤ 8) (hNb : b.norm ≤ 8)
    (bound : ℤ) (roots vertices large : List (QuadInt tau nu))
    (sieve : List (ℕ × ℕ)) (hvalid : CoordinateSquareSieveValid tau nu sieve)
    (hrootdisk : ∀ q ∈ disk tau nu 132, q ∈ roots)
    (hseeds : pairSeedsCoveredBool a b roots vertices = true)
    (hclosed : pairClosureBool a b bound vertices = true)
    (hfilter : largePairVertices a b vertices = large)
    (htriangle : pairGraphTriangleFreeBool sieve large = true)
    (t : Fin 3 → QuadInt tau nu) (ht : IsD1Tuple t)
    (hpair : ∀ i, PairExtension a b (t i))
    (hlarge : ∀ i, 9 ≤ (t i).norm)
    (hbound : ∀ i, (t i).norm ≤ bound)
    (hneA : ∀ i, t i ≠ a) (hneB : ∀ i, t i ≠ b) : False := by sorry

end D1Bound5
end