Tail irregular of four le

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.Int.GCD
import Mathlib.Data.Real.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_Regular_Definitions

section
open scoped NumberField
open Module

namespace D1Bound5




theorem _root_.D1Bound5.tail_irregular_of_four_le {K : Type*} [Field K] [NumberField K]
    [NumberField.IsTotallyComplex K] (hK : finrank ℚ K = 2) (phi : K →+* ℂ)
    (a b c d : 𝓞 K) (ha : a ≠ 0)
    (hab : ∃ u : 𝓞 K, u^2 = a*b+1) (hac : ∃ v : 𝓞 K, v^2 = a*c+1)
    (had : ∃ w : 𝓞 K, w^2 = a*d+1) (hbc : ∃ r : 𝓞 K, r^2 = b*c+1)
    (hAB : ‖phi (a : K)‖ ≤ ‖phi (b : K)‖) (hB : 3 ≤ ‖phi (b : K)‖)
    (hC : 4 ≤ ‖phi (c : K)‖) (hCD : ‖phi (c : K)‖ ≤ ‖phi (d : K)‖) :
    regularDefect b c d ≠ 0 := by sorry




end D1Bound5
end