Prove2Me

Real polynomials are determined by their values

Proved
WorkbookRestored.plus_14619

by wamlart · Sep 12, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

lean-workbookrestored-importssource-checked

If real polynomials p,qp,q satisfy p(x)=q(x)p(x)=q(x) for every real xx, then p=qp=q.

This restores the missing imports or namespaces of the original node, retaining its formal proposition. Source: Lean-Workbook row lean_workbook_plus_14619 (Apache-2.0).

Preamble
import Mathlib.Analysis.Complex.Basic
import Mathlib.Algebra.Polynomial.Derivative
import Mathlib.Algebra.Polynomial.Eval.Defs
import Mathlib.Algebra.Polynomial.Roots
open Polynomial
Formal statement
theorem WorkbookRestored.plus_14619 (p q : Polynomial ℝ) (h : ∀ x, p.eval x = q.eval x) : p = q   :=  by sorry
Source
https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, row lean_workbook_plus_14619; original Prove2Me node 9d3361c5-b1e7-4e1f-9860-02ca9b5c7fcc; Apache-2.0

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