Coherent Weights2 eq quotient

Proved

D1Bound5.coherentWeights2_eq_quotient

by tp · Oct 23, 2026 · Mathlib 0df444a (Lean v4.33.1)

diophantine-tuplesnumber-theory

Auxiliary result coherentWeights2_eq_quotient 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 Mathlib.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Analysis.Analytic.Binomial
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Ring.Basic
import Mathlib.Analysis.SpecificLimits.Normed
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Definitions.Def_D1Bound5_CoherentPolynomialWeights_Definitions

Formal statement

section
open Finset

namespace D1Bound5













theorem _root_.D1Bound5.coherentWeights2_eq_quotient
    {F : Type*} [Field F] (a : Fin 2 → F) (hinj : Function.Injective a)
    (i : Fin 2) :
    coherentWeights2 a i = coherentVandermonde2 a * (a i) ^ (2 - 2) /
      (∏ j ∈ Finset.univ.erase i, (a i - a j)) := by sorry

















end D1Bound5
end

Source

D1Bound5/CoherentPolynomialWeights.lean, lines 33-44, SHA-256 f098961571ae9eda9b1aeb7c0bb7cf7d0b039a9b7e5f64da44f922daabe473a5. Project: https://github.com/tomislav-math/d1-bound5-lean

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