Finite N3 root coeff decomposition

import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Positivity
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteHomogeneousTwo_Definitions
import Definitions.Def_D1Bound5_FiniteN3Height_Definitions
import Definitions.Def_D1Bound5_FiniteN3Matrix_Definitions

section
namespace D1Bound5













theorem _root_.D1Bound5.finiteN3_root_coeff_decomposition {R : Type*} [CommRing R]
    (x y c : R) (i : Fin 3) (j : Fin 2) :
    ![finiteN3Left x y c i,finiteN3Right x y c i] j =
      finiteHomogeneousTwo 4 (finiteN3Coeff0 i j) x y +
      finiteHomogeneousTwo 5 (finiteN3Coeff1 i j) x y*c +
      finiteHomogeneousTwo 6 (finiteN3Coeff2 i j) x y*c^2 +
      finiteHomogeneousTwo 7 (finiteN3Coeff3 i j) x y*c^3 := by sorry









end D1Bound5
end