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Bennett Repeated Nodes card

Proved
D1Bound5.bennettRepeatedNodes_card

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

diophantine-tuplesnumber-theory

Auxiliary result bennettRepeatedNodes_card 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.Group.Finset.Sigma
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.PartialFractions
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Algebra.Polynomial.RingDivision
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Sym.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_BennettRepeatedHsymm_Definitions

Formal statement
section
open Finset

namespace D1Bound5

section Homogeneous

variable {R ι : Type*} [CommRing R] [DecidableEq ι]









end Homogeneous

section Repeated

variable {F ι : Type*} [Field F] [CharZero F]
variable [Fintype ι] [DecidableEq ι]



theorem _root_.D1Bound5.bennettRepeatedNodes_card (e : ι → ℕ) :
    Fintype.card (BennettRepeatedNodes e) = ∑ i, (e i + 1) := by sorry









end Repeated

end D1Bound5
end
Source
D1Bound5/BennettRepeatedHsymm.lean, lines 84-86, SHA-256 2c35125785b6ff0c9b69a4236b7a718a4b75a5a68706b7a3ada2c46efaddc905. Project: https://github.com/tomislav-math/d1-bound5-lean

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