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Bennett coeff mul trunc

Proved
D1Bound5.bennett_coeff_mul_trunc

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

diophantine-tuplesnumber-theory

Truncating a multiplier preserves every coefficient below the truncation order, even when the other factor is an infinite series.

Preamble
import Lean.Elab.Tactic.Omega
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polynomial.Degree.Operations
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.PartialFractions
import Mathlib.Algebra.Polynomial.RingDivision
import Mathlib.LinearAlgebra.Matrix.Polynomial
import Mathlib.RingTheory.PowerSeries.Binomial
import Mathlib.RingTheory.PowerSeries.Trunc
import Mathlib.Tactic.Ring

Formal statement
section
open Finset

namespace D1Bound5

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



section Nodes

variable {I : Type*} [Fintype I] [DecidableEq I]




theorem _root_.D1Bound5.bennett_coeff_mul_trunc (P θ : PowerSeries F) (D r : ℕ) (hr : r < D) :
    PowerSeries.coeff r (P * (PowerSeries.trunc D θ : PowerSeries F)) =
      PowerSeries.coeff r (P * θ) := by sorry







end Nodes

end D1Bound5
end
Source
D1Bound5/BennettResidualCancellation.lean, lines 106-117, SHA-256 0e8f4d1dac16aef29c7622ad8fa6e48d05646e38a9ebaf133da673991996797d. Project: https://github.com/tomislav-math/d1-bound5-lean

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