Strict positivity of a quartic on the nonnegative real axis

Proved

WorkbookCorrected.base_54697

by wamlart · Sep 13, 2026 · Mathlib 0df444a (Lean v4.33.1)

corrected-formalizationlean-workbooksource-checked

Let $x$ be a nonnegative real number. Then

663x^4-620x^3-790x^2+284x+503>0.

This establishes strict positivity of the quartic throughout the nonnegative real axis.

Formalization Note: The source record omitted the type of x, causing Lean to default to natural-number arithmetic. This corrected statement explicitly uses real numbers and preserves the source inequality and nonnegative domain.

Source: InternLM Lean-Workbook, record lean_workbook_54697 (Apache-2.0).

Preamble

import Mathlib

Formal statement

theorem WorkbookCorrected.base_54697 (x : ℝ) (hx : 0 ≤ x) : 663*x^4 - 620*x^3 - 790*x^2 + 284*x + 503 > 0 := by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_54697; Apache-2.0

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