Finite PResidual eq leading tail

Proved

D1Bound5.finitePResidual_eq_leading_tail

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

diophantine-tuplesnumber-theory

Auxiliary result finitePResidual_eq_leading_tail 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.Fin
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.Sym.Basic
import Mathlib.Data.Sym.Card
import Mathlib.LinearAlgebra.Matrix.Determinant.Basic
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.RingTheory.Binomial
import Mathlib.RingTheory.MvPolynomial.Symmetric.Defs
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.FinCases
import Mathlib.Tactic.NormNum
import Mathlib.Tactic.Ring
import Definitions.Def_D1Bound5_FinitePResidualIdentity_Definitions

Formal statement

section
open Finset

namespace D1Bound5

attribute [local simp] Matrix.cons_val_two Matrix.cons_val_three

































theorem _root_.D1Bound5.finitePResidual_eq_leading_tail (a b s c : ℂ)
    (ha : a ≠ 0) (hb : b ≠ 0) (hs : s ≠ 0) (hc : c ≠ 0) (i : Fin 4) :
    finitePResidual a b s c i = finitePLeading a b s i/c^5+finitePTail a b s c i := by sorry

end D1Bound5
end

Source

D1Bound5/FinitePResidualIdentity.lean, lines 154-161, SHA-256 72e3fea4ae1d93b79c83366074679f850f075659fb82a9a62794934f87487052. Project: https://github.com/tomislav-math/d1-bound5-lean

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