Finite A4 root coeff decomposition

Proved

D1Bound5.finiteA4_root_coeff_decomposition

by tp · Oct 24, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result finiteA4_root_coeff_decomposition in the proof of the bound five for Diophantine D(1) sets in imaginary quadratic integer rings. The formal statement specifies its hypotheses and conclusion; a mathematical prose description remains to be supplied.

Preamble

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
import Mathlib.Tactic.GCongr
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FiniteA4Coefficients_Definitions
import Definitions.Def_D1Bound5_FiniteA4Matrix_Definitions

Formal statement

section
namespace D1Bound5













theorem _root_.D1Bound5.finiteA4_root_coeff_decomposition {R : Type*} [CommRing R]
    (x y c : R) (i : Fin 3) (j : Fin 2) :
    ![finiteA4Left x y c i,finiteA4Right x y c i] j =
      ∑ ell : Fin 5, finiteA4RootCoeff x y i j ell*c^(ell : ℕ) := by sorry













end D1Bound5
end

Source

D1Bound5/FiniteA4Coefficients.lean, lines 24-32, SHA-256 81e084e83fa4d83f09a896a30127692abe2447284beb04da6e2eb20845e20c86. Project: https://github.com/tomislav-math/d1-bound5-lean

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