Full ring finite PDivided Matrix det ne zero

import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Algebra.QuadraticAlgebra.Basic
import Mathlib.Algebra.Ring.Basic
import Mathlib.Algebra.Ring.Equiv
import Mathlib.Analysis.Complex.Norm
import Mathlib.Data.Finset.Card
import Mathlib.Data.Int.GCD
import Mathlib.LinearAlgebra.Dimension.Free
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.NumberTheory.NumberField.InfinitePlace.TotallyRealComplex
import Mathlib.NumberTheory.NumberField.Norm
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FinitePMatrix_Definitions

section
open scoped NumberField
open Module

namespace D1Bound5















theorem _root_.D1Bound5.full_ring_finitePDividedMatrix_det_ne_zero
    {K : Type*} [Field K] [NumberField K] [NumberField.IsTotallyComplex K]
    (hK : finrank ℚ K = 2) (phi : K →+* ℂ) (a b s c : 𝓞 K)
    (ha : a ≠ 0) (hb : b ≠ 0) (hs : s ≠ 0)
    (hab : a ≠ b) (has : a ≠ s) (hbs : b ≠ s)
    (hAB : ‖phi (a : K)‖ ≤ ‖phi (b : K)‖)
    (hBS : ‖phi (b : K)‖ ≤ ‖phi (s : K)‖)
    (hC : 200*‖phi (s : K)‖ ≤ ‖phi (c : K)‖) :
    (finitePDividedMatrix (phi (a : K)) (phi (b : K)) (phi (s : K)) (phi (c : K))).det ≠ 0 := by sorry







end D1Bound5
end