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Homogeneous Multiset Sum singleton

Proved
D1Bound5.homogeneousMultisetSum_singleton

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

diophantine-tuplesnumber-theory

A single variable has exactly one monomial in each degree.

Preamble
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Sym.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Definitions.Def_D1Bound5_HomogeneousSymmetric_Definitions

Formal statement
section
open Polynomial Finset

namespace D1Bound5






theorem _root_.D1Bound5.homogeneousMultisetSum_singleton
    {ι R : Type*} [DecidableEq ι] [CommSemiring R]
    (a : ι → R) (t : ι) (n : ℕ) :
    homogeneousMultisetSum (fun i : ({t} : Finset ι) => a i) n = (a t)^n := by sorry





end D1Bound5
end
Source
D1Bound5/LagrangeHomogeneous.lean, lines 36-49, SHA-256 b4a9130e2e09325e0a7c90a60c13433e1e3d45746589329d45719e084b45b442. Project: https://github.com/tomislav-math/d1-bound5-lean

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