Bennett delta sum three

Proved

D1Bound5.bennett_delta_sum_three

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

diophantine-tuplesnumber-theory

Auxiliary result bennett_delta_sum_three 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.Algebra.BigOperators.NatAntidiagonal
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.Combinatorics.Enumerative.Catalan.Basic
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.LinearCombination
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring

Formal statement

section
open Finset

namespace D1Bound5

variable {F : Type*} [Field F] [CharZero F]







theorem _root_.D1Bound5.bennett_delta_sum_three (i : Fin 3) :
    (if i = 0 then 1 else 0) + (if i = 1 then 1 else 0) +
      (if i = 2 then 1 else 0) = (1 : ℕ) := by sorry





















end D1Bound5
end

Source

D1Bound5/BennettTwoIntegralEntries.lean, lines 18-22, SHA-256 07d63d84699ae294fc3d395f046972fa36aa179a18de306e5f612beceaaf5f1b. Project: https://github.com/tomislav-math/d1-bound5-lean

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