Finite A4Row Form exists 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
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.LinearCombination
import Definitions.Def_D1Bound5_FiniteA4IntegralRows_Definitions

section
open scoped NumberField
open Module

namespace D1Bound5

variable {R S : Type*} [CommRing R] [CommRing S]













theorem _root_.D1Bound5.finiteA4RowForm_exists_ne_zero
    {F : Type*} [Field F] [CharZero F]
    (x y c z sX sY : F) (hx : x ≠ 0) (hy : y ≠ 0) (hc : c ≠ 0) (hxy : x ≠ y) (hz : z ≠ 0) :
    ∃ i : Fin 3, finiteA4RowForm x y c z sX sY i ≠ 0 := by sorry



end D1Bound5
end